Maths Outcomes Grade 1 (6 - 7 Years)

Hanoi International School Elementary School Curriculum

Maths 2014-2015

Adapted from: IBO PYP Maths 2 The IB learner profile

Inquirers We nurture our curiosity, developing skills for inquiry and research. We know how to learn independently and with others. We learn with enthusiasm and sustain our love of learning throughout life.

Knowledgeable We develop and use conceptual understanding, exploring knowledge across a range of disciplines. We engage with issues and ideas that have local and global significance.

Thinkers We use critical and creative thinking skills to analyse and take responsible action on complex problems. We exercise initiative in making reasoned, ethical decisions.

Communicators We express ourselves confidently and creatively in more than one language and in many ways. We collaborate effectively, listening carefully to the perspectives of other individuals and groups.

Principled We act with integrity and honesty, with a strong sense of fairness and justice, and with respect for the dignity and rights of people everywhere. We take responsibility for our actions and their consequences.

Open-minded We critically appreciate our own cultures and personal histories, as well as the values and traditions of others. We seek and evaluate a range of points of view, and we are willing to grow from the experience.

Caring We show empathy, compassion and respect. We have a commitment to service, and we act to make a positive difference in the lives of others and in the world around us.

Risk-takers We approach uncertainty with forethought and determination; we work independently and cooperatively to explore new ideas and innovative strategies. We are resourceful and resilient in the face of challenges and change.

Balanced We understand the importance of balancing different aspects of our lives—intellectual, physical and emotional—to achieve well-being for ourselves and others. We recognize our interdependence with other people and with the world in which we live.

Reflective We thoughtfully consider the world and our own ideas and experience. We work to understand our strengths and weaknesses in order to support our learning and personal development. Elementary School Curriculum Maths Curriculum

It is the mission of our school to provide a stimulating, balanced and challenging education for our students, as well as encouraging them to be independent, life long learners, critical thinkers and responsible citizens. We therefore structure all our teaching in the Primary School to achieve these aims, so that our students not only learn skills and knowledge, but also the bigger ideas and concepts which will allow them to transfer their skills and knowledge to solve real life problems. Our students will learn in an integrated environment where subject matter, attitudes, skills and behaviour are all valued equally so that they develop their complete potential as enthusiastic, well balanced, creative and reflective thinkers, ready to accept the challenges of their secondary education and of their future lives. Mathematics is not a fixed body of knowledge to be transmitted, but is a way of thinking and a language for understanding meaning. To study mathematics is to inquire into this language and to learn to think in this way. Teachers can use the eight key concepts and related questions to guide theirs and the students’ inquiry. By engaging in inquiry themselves, teachers will not only achieve a deeper understanding of the mathematical issues involved, but will also provide a model for their students of the teacher as a learner. What teachers understand themselves will shape how well they select from activities and texts available, and how effectively they teach. Cognitive psychologists have described the stages through which children learn mathematics and the stages are as follows.

Constructing meaning

Teachers plan activities, through which students construct meaning from direct experience, by using manipulatives and conversation.

Transferring meaning into signs and symbols

Teachers connect the notation system with the concrete objects and associated mathematical processes. The teacher provides the symbols for the students. Students begin to describe their understanding using signs and symbols.

Understanding and applying

Teachers plan authentic activities in which students independently select and use appropriate symbolic notation to process and record their thinking.

The methodology which will be used to teach Mathematics will therefore reflect these developmental stages. The following points need to be considered.

Each grade curriculum is an indicator of expected attainment levels at that grade, so there will be children in each grade working above or below the work outlined by this curriculum dependent upon their individual ability. The learning outcomes for each grade assume that teachers and students will revisit, review and revise work which has been covered in the previous grade level, so there might not be mention of a particular introductory activity for different units. Mathematics will be taught by a hands-on, practical approach wherever possible to gain and consolidate understanding. Where appropriate, concrete experiences will precede conceptual and computational work.

What do we want students to learn?  develop problem-solving skills, decision making and critical thinking.  develop mathematical reasoning rather than memorising rules and procedures.  integrate mathematics with other subject areas and with their everyday experiences.  use manipulatives to link concrete experience to pictorial representations and finally to abstract symbols.  develop accurate computation skills.  develop skills in the use of computers and calculators.  develop cooperative and group learning.  use mathematical materials appropriate to their developmental level.  develop a positive attitude and enthusiasm for the subject.

The mathematics curriculum is arranged in seven interwoven strands of knowledge:

In number, pattern and function, students inquire into our number system, and its operations, patterns and functions. This is where students become fluent users of the language of arithmetic, as they learn to understand its meanings, symbols and conventions. These three strands are best taught as stand-alone mathematical topics, although aspects can be successfully included in the units of inquiry.

In number students will read, write, estimate, count, compare and order numbers. They will read, write, model and understand the four operations of addition, subtraction, multiplication and division using mathematical vocabulary and symbols both mentally and using pen and paper. They will explore fractions and decimals and the relationships between them. They will select and explain appropriate methods for solving a problem and be aware of the reasonableness of answers.

In pattern and function students will use real-life problems to investigate, model and explain number patterns and will understand and use the relationships between the four operations.

The next three strands, measurement, shape and space and data handling, are the areas of mathematics that other disciplines use to research, describe, represent and understand aspects of their subject areas. The topics in these three strands are best studied in authentic contexts so will generally be studied in the transdisciplinary Units of Inquiry. In data handling students will collect data in a variety of ways, but especially in authentic situations around school or their homes. They will then display and interpret the data in a variety of ways through charts, tables and graphs. In measurement students will estimate, measure, compare and record the measurements of length, perimeter, area, volume, weight, capacity, time and temperature in authentic situations. The scope and depth to which they go in each of these areas will depend on their age and development, but the experiences must be realistic where the students use real measuring instruments. They should start by using non-standard measures like hand widths or squares and move on to standard imperial (eg miles) or metric measures (eg km). 5 Useful Maths Websites http://www.spartacus.schoolnet.co.uk/REVmaths.htm, www.primaryresources.co.uk, www.ixl.com, http://cte.jhu.edu/techacademy/web/2000/heal/mathsites.htm www.gamequarium.com, www.primarygames.com, www.toonuniversity.com, www.funbrain.com, www.bbc-schools.co.uk, http://www.edina.k12.mn.us/creekvalley/staffdev/Internet Sites/studentsites.htm, www.aaamath.com, www.aplusmath.com, www.multiplication.com, www.math.com, www.allmath.com , www.edu4kids.com www.ed.gov/pubs.parents/math.index.html

www.illuminations.ntcm.org www.primarygames.com, www.gamequarium.com www.math.rice.edu/~lanius/fractions/ www.mathcats.com www.brainpop.com www.firstinmath.com www.starfall.com www.firstmath.com www.brainchild.com www.funbrain.com http://nces.ed.gov/nceskids/createagraph/default.aspx http://www.homeschoolmath.net/online/ www.funbrain.com, www.mangahigh.com www.aplusmath.com www.funschool.com www.kidsdomain.com/reviews/kdr/zoombinisdeluxe.html http://www.amazon.com/Learning-Company-Logical-Journey-Zoombinis/dp/B000287MLK 6 Maths Outcomes Reception (5 - 6 years) Number Learners will understand that numbers are used for many different purposes in the real world. They will develop an understanding of one-to-one correspondence and conservation of number, and be able tocount and use number words and numerals to represent quantities. KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students know understand be able to do Resources

ATTITUDES: What attitudes will be developed?

Reads, write, compares and orders Find the next and preceding numbers for each Skills: mental arithmetic, keep Various manipulatives, numbers number. records. Base ten

Find different ways to make up numbers to 10 Teacher notes, peer assessment. coloured beads, cubes, and record them. counters, buttons,

Selects the appropriate method for Compute with objects up to 10 using numbers Skills: mental arithmetic, keep cards with pictures of 1-10 solving a problem and signs, +, -, =. records. wall pictures for the Use pictures to make up and solve problems Assessment: teacher notes, peer sequence 0-10, floor using signs : +, -, =. assessment. number

What + or - + what? Thinking skills strip, large outline of the numerals 0-10, paired dot Create number sentences and leave out the pattern, cards for 1-10, operation for others to solve classroom day/date chart Connects number names and numerals Matching games Making connections large geared clock, to the quantities that they represent Containers, Cubes blocks

Recognizes groups of zero to five Show me a group of 5 objects Observational skills String, Sticks objects without counting (subitizing) Dice games and recognition of dots Cuisenaire rods

7 Uses number words and numerals to Matching games Making connections 1-100 chart represent quantities in real-life situations

Uses simple fraction names in real-life Slicing real items in half Observational skills situations e.g. ½ Building halves up to create wholes

Models numbers to tens or beyond Exploring base 10 Observational skills using the base 10 place value system Keep count of days at school

Uses the language of mathematics to Collection of maths vocabulary Thinking skills compare quantities

Models addition and subtraction of Modeling on whiteboards/notebooks whole numbers

Describes and uses mental and written Show me how you solved that/draw strategies for adding and subtracting to 10

Estimates quantities How many do you think?

Estimates sums and differences Playing games using a large number line

Dice games, Pair games Measurement Learners will develop an understanding of how measurement involves the comparison of objects and the ordering and sequencing of events. They will be able to identify, compare and describe attributes of real objects as well as describe and sequence familiar events in their daily routine. KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students know understand be able to do Resources

8 Identifies, describes and sequences Sequencing daily events Skills: identify a process, think Sticks events in their daily routine logically, measure. Daily schedule/home/school/ASA activities Ropes

Identifies, compares and describes What is the same? What is different? Why? Sand attributes of real objects Various rulers for Compares the length, mass and Measuring activities measurement capacity of objects using non-standard units of measure weighing scales.

Estimates, measures and compares Select a measurement, for example, a length, a Containers objects using standard units of width or a height, and estimate the size of the measurement object using 2-3 different measurements. attribute materials

Compare the length of real objects. structured sorting Measure length using standard units of materials, attribute measurement materials

Understands that time is measured Learning and revising units of measurement beads, bricks, boxes, using universal units of measure – trays, years, months, days & hours tubs, books, Uses non-standard units of Use non standard units of measurement to measurement to solve problems in real- weigh/measure different objects and distances construction life situations materials, grid paper, dice, Uses standard units of measurement to Measure the volume/length of granular materials solve problems in real-life situations dominoes, and liquids using non standard units of measurement. Sand timers

Reads and writes the time to the hour How can I measure a minute? Presenting skits in a limited amount and half hour of time Use timers in class to measure length of activities

9 Shape and Space Learners will understand that shapes have characteristics that can be described and compared. They will understand and use common language to describe paths, regions and boundaries of their immediate environment. KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students know understand be able to do Resources

Describes position and direction Orientation games Paired work mathematical games

mosaic

Sorts, describes and labels 2D shapes Identify, classify and name 2D and 3D shapes, Observational skills tangrams by sorting objects with similar forms, for example, boxes or jugs, and discuss what is similar and magnetic numbers different in these forms and describe their sets of 2D shapes properties. gummed paper Sorts, describes and labels 3D shapes Sorting games paint

Creates and describes symmetrical and What patterns can you see? Play-doh tessellating patterns Create/invent your own patterns Hoops

Identifies lines of reflective symmetry Using pictures and real objects find symmetry in Sticks the environment Ropes Make mirror prints Sand

Geometry Kit, Shape puzzles, shape games, shape sorting abacus, threading shapes, Mosaic Magnetic blocks, pattern

10 Interprets, creates and uses simple Maze games blocks. Wooden color and directions to describe paths, regions, shape board positions and boundaries of the Leading activities immediate environment Blindfolded games Pattern and Function Learners will understand that shapes have characteristics that can be described and compared. They will understand and use common language to describe paths, regions and boundaries of their immediate environment. KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students know understand be able to do Resources

Describes patterns in various ways Pattern games Observational skills Geoboards

Extends and creates patterns Pattern games Elastic bands

Uses number patterns to represent and Can you see a pattern….? Presentation skills Whiteboards and markers understand real-life situations

Understands the inverse relationship Teacher led Responding to questions between addition and subtraction

Understands the associative and Examples Observations commutative properties of addition

Uses the properties and relationships of Whiteboard activities addition and subtraction to solve problems Data Handling Learners will develop an understanding of how the collection and organization of information helps to make sense of the world. They will sort, describe and label objects by attributes and represent information in graphs including pictographs and tally marks. The learners will discuss chance in daily events.

11 KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students know understand be able to do Resources

Teacher observations Structured sorting materials shapes, large Representing and interpreting Discuss different types of graphs and what they hoops, large bar graphs information from bar graphs show

Matching chance word with a picture

Discusses chance in daily events Weather activities

Sorting different attributes

Describes, sorts and labels objects by Sorting activities attributes

Teacher observation

Represents the relationship between Using a venn diagram to show differences and objects using a Venn diagram similarities between oneself and a friend

Interprets data from different types of What does this graph show….? simple graphs

Represent information through Growth of plants Peer assessment pictographs, tally marks, bar graphs and living bar graphs Classroom observations

12 Creates living graphs using real objects Sharing personal information about oneself and people Making graphs for different criteria, birthdays, languages spoken, favourite things to do

Uses objects to sort into graphs to show different criteria

Maths Outcomes Grade 1 (6 - 7 years) Number Learners will understand that numbers are used for many different purposes in the real world. They will develop an understanding of one-to-one correspondence and conservation of number, and be able to count and use number words and numerals to represent quantities. Learners will develop their understanding of the base 10 place value system and will model, read, write, estimate, compare and order numbers to hundreds or beyond. They will have automatic recall of addition and subtraction facts and be able to model addition and subtraction of whole numbers using the appropriate mathematical language to describe their mental and written strategies. Learners will have an understanding of fractions as representations of whole-part relationships and will be able to model fractions and use fraction names in real-life situations.

KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students Resources understand be able to do ATTITUDES: What attitudes will be developed? Students will know: Students will understand Students will be able to do Read and write numbers up to That the value of a number is The base 10 place value system is used 100 determined by the place value to organize and represent number and number relationships Model a number up to 100 That estimation is used to guide the using a place value chart or Units and tens place value checking of an answers’ other place value tools. reasonableness. How to make a reasonable Discuss why and how we use estimation of quantities up to 20. estimation.

That estimation is used in real Identify and use an estimation life situations. strategy to develop and check How to model addition and the quantity of objects up to 20. 13 subtraction using different tools and recording methods.

That addition involves the joining Operations of addition and subtraction Model and solve addition and of groups to make a bigger are related to each other and are used subtraction problems with both number. That subtraction to process and solve problems. objects and in print. involves the removing a smaller group from a larger group to Number operations ( + and - )can be Model and record the make a smaller number. modeled in a variety of ways. associative and commutative Guided by the concepts of FORM, properties of addition and How to do and record 1D+1D FUNCTION, CONNECTION subtraction. and 1D =2D with no trading. Model the inverse relationships Know how to model 1D+1D, of addition and subtraction. 1D=2D with trading. Identify the best strategy for The + sign means addition and solving a problem using the has different names (Addition, key mathematical words they have seen or heard.

The - sign means subtraction Will discuss and explore the and has different names language and symbols of (Subtraction, take away, minus) addition and subtraction.

How to choose the appropriate action for solving a problem.

Students will know what Understands that fractions are made up of Students will be able to What a whole is equal portions. Draw a whole shape and cut it That a whole can be separated Understands the part whole relationship in into equal sections. into smaller equal sections fractions That the equal sections of a Join equal sections together to whole have specific names that create a whole describe their quantity. Use the vocabulary of whole, half and quarter.

14 Pattern and Function Grade 1 (6 - 7 years) Learners will understand that numbers are used for many different purposes in the real world. They will develop an understanding of one-to-one correspondence and conservation of number, and be able to count and use number words and numerals to represent quantities. Learners will develop their understanding of the base 10 place value system and will model, read, write, estimate, compare and order numbers to hundreds or beyond. They will have automatic recall of addition and subtraction facts and be able to model addition and subtraction of whole numbers using the appropriate mathematical language to describe their mental and written strategies. Learners will have an understanding of fractions as representations of whole-part relationships and will be able to model fractions and use fraction names in real-life situations. KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students Resources know understand be able to do ATTITUDES: What attitudes will be developed? Students will know: Students will understand: Students will be able to do: This is a good unit to Patterns can be found in numbers, Patterns have attributes or numbers Identify and develop and extend teach alongside the for example, odd and even numbers, organized in repeating groups. simple number patterns using skip STP inquiry of ‘Animals skip counting counting and simple rules. and people interact’ Number patterns can be used as a strategy using the habitat project. That patterns can be represented in a to solve problems Identify that numbers can be used variety of ways for example, using to represent and describe a Uno’s garden words, drawings, symbols, materials, Patterns and number groupings are pattern made of different actions, numbers connected to repeated addition or attributes. multiplication. Know that attributes can be used Model and record skip counting describe a the parts of a patterns Guided by the concepts of function, form patterns connected to the unit. and connection. groupings of 2, 5, 10.

Know that number patterns for odd Examine and with support and even numbers, skip counting. complete repeated addition sums related to a skip counting pattern. Know that rules can be written for a pattern Model and record a completed Know that skip counting is connected pattern following a rule. to repeated addition and a way of grouping numbers. Use a pattern to solve a problem/describe what comes Know that patterns can be used to next. solve problems and predict what comes next. Learner profile: will match the TD 15 UOI of the time. That pattern can occur in many Pre-assessment should focus on situations as grouping strategies in the students’ current the real world. mathematical vocabulary, and ability to model, extend and describe a pattern. Early Formative assessment should identify how students can use rules to extend a pattern or predict what comes next. Summative Assessment will be determined by the data gathered during pre assessment. Students will know: Students will understand: Students will be able to do: That there is inverse relationship Whole numbers exhibit patterns and Describe and model the inverse between addition and subtraction relationships that can be observed and relationship of addition and identified. subtraction. The associative and commutative properties of addition. Pattern and addition and subtraction are Read and solve number and word problem solving strategies. That the process problems using the properties of The properties and relationships of of grouping and regrouping numbers is a addition and subtraction. addition can be used to solve and way of modeling addition and subtraction. represent real life problems. Identify the ways patterns, addition and subtraction can be used to solve problems. Identify and practice in role play the different ways we can use addition and subtraction in real life. Examine and describe the formats that can be used to record addition and subtraction sums. Identify the role that grouping has in both addition and subtraction. Learner profile: will match the TD UOI of the time. 16 Pre-assessment should focus on the students’ current mathematical vocabulary used to describe the process of addition and subtraction, and ability to model and record the process and answer of an addition or subtraction sum Early Formative assessment should identify students knowledge, understanding and skill around the recording format of addition and subtraction and the role they have in problem solving; Students should also be assessed on their ability to describe, model and use their knowledge of grouping in relation to the commutative /associative properties of addition. Summative Assessment will be determined by the data gathered during pre assessment. Measurement Learners will develop an understanding of how measurement involves the comparison of objects and the ordering and sequencing of events. They will be able to identify, compare and describe attributes of real objects as well as describe and sequence familiar events in their daily routine. Learners will understand that standard units allow us to have a common language to measure and describe objects and events, and that while estimation is a strategy that can be applied for approximate measurements, particular tools allow us to measure and describe attributes of objects and events with more accuracy. Learners will develop these understandings in relation to measurement involving length, mass, capacity, money, temperature and time. KNOW: What will the students know UNDERSTAND: What will the students SKILLS: What will the Resources understand students be able to do ATTITUDES: What attitudes will be developed?

17 Students will know: Students will understand: Students will be able to Real objects can be compared and Objects have attributes that can be do: described, for example, longer, shorter, measured using non-standard and standard heavier, empty, full, hotter, colder. units. Use comparative and the language of attribute when How to use different tools for different There are tools that we use to measure making comparisons. objects. objects and events. Compare and order That we measure using a unit and materials according to working out how many of the unit it Guided by the concept of form, function, attributes. takes to match the thing. change and connection. Choose the same unit to How to use non-standard units of compare two things. measurement to solve problems in real- life situations involving time, Use a wide variety of length, mass, capacity and money. materials informally to represent units- rods, paper Why gaps or overlaps are a problem clips, pop sticks etc. when measuring. Use informal materials to investigate.

Measure beginning with the zero mark. How to use everyday language of Events can be ordered and sequenced. Sequencing dates and attributes and comparison when There are special words and phrases that events on a calendar. communicating. help us to describe and compare quantity. Identify, describe and Estimate and compare lengths of time- sequence events in daily hour, day and week. routine, Calendars can be used to determine the Use standard units to date, and to identify and sequence days measure their surroundings. of the week and months of the year.

18 Shape and Space Grade 1 (6-7) Learners will understand that numbers are used for many different purposes in the real world. They will develop an understanding of one-to-one correspondence and conservation of number, and be able to count and use number words and numerals to represent quantities. Learners will develop their understanding of the base 10 place value system and will model, read, write, estimate, compare and order numbers to hundreds or beyond. They will have automatic recall of addition and subtraction facts and be able to model addition and subtraction of whole numbers using the appropriate mathematical language to describe their mental and written strategies.

KNOWLEDGE: What will the students CONCEPTUAL UNDERSTANDINGS: What SKILLS: What will the students Resources know will the students understand be able to do ATTITUDES: What attitudes will be developed? Students will know: Students will understand: Students will be able to do: Knows and understands properties of Objects can be classified and named Identify and develop familiar 2D and 3D objects. according to their properties. understandings of the mathematical vocabulary need The vocabulary to describe the That there are relationships between 2D to describe the properties of characteristics of 2D shapes. and 3D shapes. shapes. (face, corner/vertices, angle, sides, equal, opposite The vocabulary to describe the That everyday objects are constructed of Name, compare and sort 2D characteristics of 3D shapes. 2D and 3D shapes. against 3D objects using correct property vocabulary. That 3D can be created by putting Guided by the concept of form, reflection Identify and describe the together/taking apart 2D shapes. or change and connection. relationships and connections Examine the between a 2D and Create tessellating and symmetrical 3D shape. patterns using 2D shapes. Examine the 2D shapes in the net of a 3D shape. Use nets to create 3D shapes. Can locate and identify 2D and 3D shapes in real life environment. Create, and extend 2D symmetrical and tessellating patterns. Learner profile: will match the TD UOI of the time. Pre-assessment should focus on the students’ current 19 mathematical vocabulary and ability to group and name 2D and 3D shapes. Early Formative assessment should identify what knowledge and understandings students have about the connections between 2D and 3D shapes. Summ. Assessment will be determined by the data gathered during pre assessment. Students will know: Students will understand: Students will be able to do: Know the appropriate vocabulary to Identify and develop describe space, shape and location Positional language can be used to understandings of the describe a location according to a point of mathematical vocabulary need Know that directions can be described reference. to describe the direction, pathways, boundaries and regions of a locations and boundaries. specific environment. Specific vocabulary can be used to Read and create simple maps describe an objects position in space. of an immediate environment. That map’s can be drawn or created to Create, track and record a path show a path. Guided by the concepts of function, from A to B that a peer can change and perspective. follow.

20 Identify the function of maps and ICT mapping tools. Describe an immediate environment using mathematically correct vocabulary. Learner profile: will match the TD UOI of the time. Pre-assessment should focus on the students’ current mathematical vocabulary, and ability to describe a known environment using specific language. Early Formative assessment should identify what knowledge of vocabulary and function of directions. Summative Assessment will be determined by the data gathered during pre assessment. Data handling Learners will develop an understanding of how measurement involves the comparison of objects and the ordering and sequencing of events. They will be able to identify, compare and describe attributes of real objects as well as describe and sequence familiar events in their daily routine. Learners will understand that standard units allow us to have a common language to measure and describe objects and events, and that while estimation is a strategy that can be applied for approximate measurements, particular tools allow us to measure and describe attributes of objects and events with more accuracy. Learners will develop these understandings in relation to measurement involving length, mass, capacity, money, temperature and time. KNOW: What will the students know UNDERSTAND: What will the students SKILLS: What will the Resources understand students be able to do ATTITUDES: What attitudes will be developed?

21 Know: Understand: Able to Do: Recognize that there is a Clipboards, Paper, graph How to design a survey, collect, That data handling and probability are degree of uncertainty about paper, maths books represent and interpret data. useful to know in everyday life. the outcome of some events but others are certain or How to discuss chance in daily life. impossible.

Apply the concepts of Form, Function and Understand how to collect, Connection. interpret and present data using different types of simple graphs, charts and diagrams. E.g. pictographs, tally marks, bar graphs and living graphs.

Describe, sort and label objects by attributes.

Represent the relationship between objects using a Venn diagram Maths Outcomes: Grade 2 (7 - 8 years) Number Learners will understand that standard units allow us to have a common language to measure and describe objects and events, and that while estimation is a strategy that can be applied for approximate measurements, particular tools allow us to measure and describe attributes of objects and events with more accuracy. Learners will develop these understandings in relation to measurement involving length, mass, capacity, money, temperature and time. KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students Resources know understand be able to do ATTITUDES: What attitudes will be developed? Students will know: Students will understand Students will be able to do Maths manipulatives in class That the value of a number is The base 10 place value system is used to Read, write and model numbers up determined by the place value organize and represent number and number to 500. position. relationships Model and record a numerals place 22 Units and tens and hundreds place That estimation is strategy for checking of value within a 3D number using a value an answers’ reasonableness and solving place value chart or other place problems value tools. How to make a reasonable estimation of quantities up to 50. Guided by the concepts of FORM, Explore and record the biggest and FUNCTION, CONNECTION smallest possible numbers that can That estimation is used in real life be made with the same 3 numerals situations. Discuss why and how we use estimation in real life.

Investigate the role of estimation in measurement.

Identify and use an estimation strategy to develop and check the quantity of objects up to 50.

That addition involves the joining of Operations of addition and subtraction are Model and solve addition and groups to make a bigger number. related to each other and are used to subtraction problems with both process and solve problems. objects and in print. That subtraction involves the removing a smaller group from a Operations of multiplication are connected Model and connect repeated larger group to make a smaller to repeated addition. addition and multiplication number. operations. Number operations ( +, -, x )can be How to model and record 1D+2D modeled in a variety of ways. Model and record the associative and 2D +2D with trading from units and commutative properties of to tens column only addition and subtraction.

The + sign means addition and has Model the inverse relationships of different names (Addition, plus, add) addition and subtraction.

The - sign means subtraction and Identify the best strategy for solving has different names (Subtraction, a problem using the key take away, minus) mathematical words they have 23 seen or heard. Know what key words enable us to decide on the best strategy for Will discuss and explore the solving a problem. language and symbols of addition, subtraction and grouping in How to model addition and multiplication. subtraction using different tools and recording methods.

Know how to record addition and subtraction using vertical and horizontal formats.

Knows what a denominator and Understands, models and can record the Can explain the form and function numerator are. part whole relationship of fractions. of a numerator and denominator. Knows how to model and record half, Models and uses fractions in real quarter and thirds. life situations Knows the relationship a denominator and numerator in the part whole relationship. Maths Outcomes Grade 2 (7 - 8 years) Pattern and Function Learners will understand that whole numbers exhibit patterns and relationships that can be observed and described, and that the patterns can be represented using numbers and other symbols. As a result, learners will understand the inverse relationship between addition and subtraction, and the associative and commutative properties of addition. They will be able to use their understanding of pattern to represent and make sense of real-life situations and, where appropriate, to solve problems involving addition and subtraction.

24 Students will know: Students will understand: Students will be able to do: This is a good unit to Patterns can be found in numbers, Patterns have attributes or numbers Identify and develop and extend teach alongside the square numbers, triangular numbers, organized in repeating groups. number patterns using skip STP inquiry of skip counting connected to counting and simple rules such as ‘Animals and people multiplication Number patterns can be used as a strategy doubling or the triangular numbers.. interact’ using the to solve problems habitat project. That pattern can be represented in a Identify, use and record numbers variety of ways and interpreted to Patterns and number groupings are that can be used to represent and Uno’s garden predict what comes next or to solve connected to repeated addition or describe a patterns. problems. multiplication. Model and record skip counting Know that attributes can be used Guided by the concepts of function, form patterns connected to a variety of describe the parts of a patterns unit. and connection. multiplication tables.

Know that rules can be written for a Know how to model and record pattern and that rules can be used to number patterns using both a create patterns. sequence of numbers and a repeated addition or multiplication Know that skip counting is connected sum. to repeated addition and grouping for multiplication. Examine and complete repeated addition sums/ multiplication Know that patterns can be used to grouping related to a skip counting solve problems and predict what pattern. comes next. Create, model and record a That pattern can occur in many completed pattern following a rule. situations as grouping strategies in the real world. Use a pattern to solve a problem and develop a rule. Know that calculators can be used to complete and extend patterns. Use calculators to extend a pattern.

Learner profile: will match the TD UOI of the time.

Pre-assessment should focus on 25 the students’ current mathematical vocabulary, and ability to model, extend and describe a pattern.

Early Formative assessment should identify how students can use rules to extend a pattern or predict what comes next. Summative Assessment will be determined by the data gathered during pre assessment.

Students will know: Students will understand: Students will be able to do: That there is inverse relationship Whole numbers exhibit patterns and Describe and model the inverse between addition and subtraction. relationships that can be observed and relationship of addition and subtraction identified. (using 2D and 1D numbers) The associative and commutative properties of addition. Pattern and addition and subtraction are Read and solve number and word problem solving strategies. problems using the properties of The properties and relationships of addition and subtraction. addition can be used to solve and Understand that multiplication is related to Identify the ways patterns, addition represent real life problems. repeated addition. and subtraction can be used to solve problems. Know how to describe the relationship That the process of grouping and regrouping between addition and subtraction. numbers is a way of modeling addition, Identify and practice in role play the subtraction and multiplication. different ways we can use addition and Know that repeated addition and subtraction in real life. multiplication are related. Examine and describe the formats that can be used to record addition and 26 Know how to model the groupings for a subtraction sums. given sum (+.- or x) Identify the role that grouping has in both addition and subtraction.

Learner profile: will match the TD UOI of the time. Pre-assessment should focus on the students’ current mathematical vocabulary used to describe the process of addition and subtraction, and ability to model and record the process and answer of an addition or subtraction sum

Early Formative assessment should identify students knowledge, understanding and skill around the recording format of addition and subtraction and the role they have in problem solving; Students should also be assessed on their ability to describe, model and use their knowledge of grouping in relation to the commutative /associative properties of addition.

Summative Assessment will be determined by the data gathered during pre assessment

27 Measurement Learners will understand that standard units allow us to have a common language to measure and describe objects and events, and that while estimation is a strategy that can be applied for approximate measurements, particular tools allow us to measure and describe attributes of objects and events with more accuracy. Learners will develop these understandings in relation to measurement involving length, mass, capacity, money, temperature and time. KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students Resources know understand be able to do ATTITUDES: What attitudes will be developed?

Students will know: Students will understand: Students will be able to do: How to use different tools for There are tools that we use to measure Identify and decide on an different objects. objects and events. appropriate tool for measuring given objects attributes. How to use everyday language of There are special words and phrases that attributes and comparison when help us to describe and compare quantity Use appropriate mathematical communicating. and measurement vocabulary to describe and record measurement information. Estimate and compare lengths of Guided by the concept of form, function, time: second, minute, hour, day, change and connection. Sequencing dates and events on week and month. a calendar. Objects have attributes that can be How to read and write the time to the measured using standard units. Identify, describe and sequence hour, half hour and quarter hour. events in daily routine,

Calendars can be used to determine Events can be ordered and sequenced. Compare and order materials the date, and to identify and according to attributes. sequence days of the week and months of the year. Choose the same unit to compare two things. That we measure using a unit and working out how many of the unit it Measure beginning with the zero takes to match the thing. mark.

How to use standard units of Use standard units to measure measurement to solve problems in objects in their surroundings. real-life situations involving time, length, mass, capacity, money and Use cm, dm and m to measure 28 temperature. particular objects.

Why gaps or overlaps are a problem Estimates capacity of containers when measuring. using non-standard units of Different currencies exist around measurement. them. Read, write, estimate and record time using days, hours and minutes.

Use timeline to represent information.

Measure temperature to one degree. Shape and Space Learners will continue to work with 2D and 3D shapes, developing the understanding that shapes are classified and named according to their properties. They will understand that examples of symmetry and transformations can be found in their immediate environment. Learners will interpret, create and use simple directions and specific vocabulary to describe paths, regions, positions and boundaries of their immediate environment.

KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students Resources know understand be able to do ATTITUDES: What attitudes will be developed?

Students will know: Students will understand: Students will be able to do: Knows and understands properties of Objects can be classified and named Identify and develop familiar 2D and 3D objects. according to their properties. understandings of the mathematical vocabulary need to The vocabulary to describe the That there are relationships between 2D describe the properties of characteristics of 2D shapes. and 3D shapes. shapes. (face, corner/vertices, angle, sides, equal, opposite The vocabulary to describe the That everyday objects are constructed of characteristics of 3D shapes. 2D and 3D shapes. Name, compare and sort 2D against 3D objects using correct That 3D can be created by putting Symmetry and transformation property vocabulary. 29 together/taking apart 2D shapes. Guided by the concept of form, reflection or change and connection. Identify and describe the Create tessellating and symmetrical Students will understand: relationships and connections patterns using 2D shapes. Positional language can be used to describe a location according to a point of Examine the between a 2D and Know that real world ideas can be reference. 3D shape. represented using geometric vocabulary and symbols. Specific vocabulary can be used to Examine the 2D shapes in the describe an objects position in space. net of a 3D shape. Know how to identify the line of symmetry and qualities of a Guided by the concepts of function, change Use nets to create 3D shapes. tessellating pattern. and perspective. Students will know: Can locate and identify 2D and Know the appropriate vocabulary to 3D shapes in real life describe space, shape and location environment.

Know that directions can be Create, extend and describe the described pathways, boundaries and properties of 2D symmetrical and regions of a specific environment. tessellating patterns.

That map’s can be drawn or created Recognize and explain to show a path. symmetrical designs in the environment. Apply the knowledge of symmetry to problem solving situations. Learner profile: will match the TD UOI of the time. Pre-assessment should focus on the students’ current mathematical vocabulary and ability to group and name 2D and 3D shapes.

Early Formative assessment should identify what knowledge

30 and understandings students have about the connections between 2D and 3D shapes. Summative Assessment will be determined by the data gathered during pre assessment. Students will be able to do: Identify and develop understandings of the mathematical vocabulary need to describe the direction, locations and boundaries.

Read and create simple maps of an immediate environment.

Create, track and record a path from A to B that a peer can follow.

Identify the function of maps and ICT mapping tools.

Describe an immediate environment using mathematically correct vocabulary. Learner profile: will match the TD UOI of the time. Pre-assessment should focus on the students’ current mathematical vocabulary, and ability to describe a known environment using specific language. Early Formative assessment should identify what knowledge 31 of vocabulary and function of directions. Summative Assessment will be determined by the data gathered during pre assessment.

Maths Outcomes: Grade 3 (8- 9 years) Number Learners will be able to model, read, write, compare and order fractions, and use them in real-life situations. Learners will have automatic recall of addition, subtraction, multiplication and division facts. They will select, use and describe a range of strategies to solve problems involving addition, subtraction, multiplication and division, using estimation strategies to check the reasonableness of their answers. KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students know understand be able to do Resources

Models numbers up to and beyond Use different numbers of tiles to total 100 and Skills: number work. First Steps Maths 1000 using the base 10 value system. make up squares, for example, 37+63. Assessment: teacher, self Investigation into maths Solve expressions. assessment –student reflection – how did I do? 0-100 number strip,

Reads, writes and compares numbers Show me…..point to….How can I read this Assessment: teacher, self hundred square, up to 1000 number? assessment cubes, 0-1000 number line Understands situations that involve Multiply whole numbers by 10 or 100, for Multiplication test marked in multiples multiplication and division, addition and example, 6 х 10, 8 х 10, 10 х 10, 12 х 10 etc. and subtraction ask, ‘What pattern do we see? and find what will of 100, happen if we multiply by 100 100-200 number line Real-life problem solving

32 Identify the concept of place values of units, Skills: place value test marked in multiples tens, hundreds, thousands and tens of thousands, of whole numbers and make up and of 10, solve expressions, for example, identify the place large & small, value of the number 7 in 2374 and 72695? How are they different? envelopes

Complete and learn the multiplication tables Skills: computation Number fact cards

up to 10 times and play practice games to Quiz Base 10 blocks and reinforce them. base ten cards Practice multiplying 2-digit numbers by 1-digit Skills: computation numbers mentally and on paper. Cuisenaire rods Self assessment.

Divide two-digit numbers by one digit numbers Skills: computation both mentally and on paper. Teacher observations

Add and subtract two digit numbers mentally, Show me...... and three digit numbers on paper and complete the tables given in books

Practice multiplying 2-digit numbers by 1-digit Show me.... numbers mentally and on paper

Divide two-digit numbers by one digit numbers Skills: computation both mentally and on paper.

Describes and uses mental and written Give students real life problems to solve. Identify Give student a real-life problem to strategies for multiplication and division strategies needed to solve problem solve (First Step maths) and show using real-life strategies the teacher how to solve it

Reads, writes compares and orders Creating timelines, smallest to biggest Where on the timelines would we put fractions and decimals 75%? Student teacher conference

Understands numbers can be modeled Guess the number game How many ways can Show me..... in a variety of ways you show me the number….?

33 Selects an efficient method for solving a Timed maths activities – how long does it take to Which method is more efficient? problem solve this problem compared to this problem… Why? Student conference

Uses strategies to evaluate the Teacher taught strategies from First Step Maths List strategies used reasonableness of answers Pattern and Function Learners will understand the inverse relationship between multiplication and division, and the associative and commutative properties of multiplication. They will be able to use their understanding of pattern and function to represent and make sense of real-life situations and, where appropriate, to solve problems involving the four operations. KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students know understand be able to do Resources

Understands the inverse relationship Solve addition expressions using the associative Skills: identify a process, mental and- Tangrams between addition and subtraction law, for example, (3 + 7) + 4 = 3 + (7 + 4) and written arithmetic make up equation of operations and find the answers.

Understands the associative and Solve multiplication expressions without commutative properties of addition computation using the associative and commutative laws, for example, find the missing number in, 4 х 7 = ? х 4; (2 х ?) х 5 = 2 х (6 х 5)

Understands that multiplication is Brainstorm what is multiplication? Show how it Skills: identify a process, mental and- repeated addition and that division is connects to repeated addition written arithmetic repeated subtraction

Represents and describes rules for Identify multiples from 2 - 10 in number patterns, Skills: identify a process, mental patterns for example understand that the pattern 9, 18, and-written arithmetic 27, 36, are multiples of 9 and of 3 and the 34 numbers 6, 12, 18, 24, are connected with a Teacher created test multiple 3

Investigates the multiplication patterns, Creating rules for numbers

odd х odd = odd 7 х 3 = 21

even х even = even 6 х 4 = 24

even х odd = even 6 х 3 = 18

odd х even = even 3 х 6 = 18

Uses number patterns to make Use a calculator to learn that 3 х 89 = 89 + 89 + Skills: identify a process, calculator predictions and solve problems 89 and compute (3 х 89) – 3 work and mental arithmetic

Uses the properties and relationships of Solve practical problems, for example, ‘How Skills: identify a process, calculator the four operations to solve problems many skipping ropes for an increasing number of work and mental arithmetic children?’ Measurement Learners will continue to use standard units to measure objects, in particular developing their understanding of measuring perimeter, area and volume. They will select and use appropriate tools and units of measurement, and will be able to describe measures that fall between two numbers on a scale. KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students know understand be able to do Resources

Measuring activities Skills: measure, think logically. Clocks

Estimates, measures and compares How would I measure…? Practical Stop watches objects using standard units of solving activities measurement Calendars Develops and describes formulas for Measure the sides of a book and record in mm Skills: measure, problem solving. Scales and weights finding perimeter and volume. and cm. Calculate how far a snail can move in 5 minutes Tapes

35 Understands area using standard units Calculate and measure area, using cm², for Skills: measure, problem solving. Rules example, put shapes on cm squared paper and calculate their area in cm², and is there any Self assessment Trundle Wheel quicker way? Take 3 triangles with the same Thermometers perimeter. Are their areas equal?

Measure spaces in school How could we find out the biggest space in school?

Estimate and weigh objects, using more than one Skills: weigh and record standard unit of measurement, grammes, kilogrammes and hectogrammes, for example, Teacher observation record the weight, of students in the class, using different units

Understands how to read and record Connecting to Science unit measuring Students show measuring skills temperature temperatures of different liquids

Understands the digital and analogue Revises telling the time by analog and digital Using clocks show me…… clock methods and introduce 24 hour time

Reads and writes the time to the hour, Investigate 24 hour time by looking at a timetable Skills: measure time, think logically, half hour and quarter hour and comparing, using standard and 24 hour time. record

Time activities What times is this…?

Uses standard units of measurement to Record time, using minutes and seconds, for Skills: measure time, record. solve problems in real-life situations example, measure how long t takes to do tasks in the classroom.

How can I measure.....?

Measure the passage of time, how many months, Skills: calculate time, think logically. days in a year and a leap year? Assessment: teacher marking.

Use different measurement tools Skills: measure, think logically.

Self assessment

36 Selects and uses an appropriate Understand when to use an estimated answer or Skills: measuring and comparing. standard measuring tool and unit of an accurate computation in certain situations. measurement for different situations Understands the relationship between Measure area and perimeter of everyday objects Skills: measure, keep records area and perimeter Shape and Space Learners will sort, describe and model regular and irregular polygons, developing an understanding of their properties. They will be able to describe and model congruency and similarity in 2D shapes. Learners will continue to develop their understanding of symmetry. They will understand how geometric shapes and associated vocabulary are useful for representing and describing objects and events in real-world situations. KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students know understand be able to do Resources

Sorts, describes, compares, labels and modelsSorting activities How can we sort theses shapes? A variety of 2D and regular and irregular polygons 3D shapes Analyses and describes 2D/3D shapes Sorting vocabulary Vocabulary list – what does this word using geometrical vocabulary mean? Protractors, Ccompasses, various sized paper to Recognises and explains symmetrical Investigate which capital letters have symmetry Skills: show me symmetry draw different shapes, patterns paper, pattern blocks Investigate rotational symmetry in 2D shapes. Teacher notes

Investigate plane symmetry in 3D shapes

Pattern making, comparing with others

Recognizes right, acute and obtuse Measures and draw angles less then 180º using Skills: measure, think logically angles a protractor. Use watch hands to measure an angle, for example, when the time is 3 o’clock Skills: draw, think logically

Creates and describes tessellating Makes and check predictions about the Skills: measure, keep records patterns relationships between shapes, using materials Teacher marking

37 Identifies, describes and models congruency Learn and properties of regular shapes. Skills: line symmetry similarities in 2D shapes

Finds regular shapes which tessellate Data Handling Learners will continue to collect, organize, display and analyse data, developing an understanding of how different graphs highlight different aspects of data more efficiently. They will understand that scale can represent different quantities in graphs and that mode can be used to summarize a set of data. The learners will make the connection that probability is based on experimental events and can be expressed numerically. KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students know understand be able to do Resources

Understands how to collect data, Conduct a data collection survey of litter around Skills: collecting and recording data Excel present it and interpret it the school and graph the results as a bar graph Assessment: checklist Dice Identifies the mode and range of a set Collect examples of data Spinners

Designs a survey and systematically Students organize their own data Coins collects, organises and displays data in an appropriate simple graph

Expresses and uses probability to Use a scale of probability from ‘impossible’ Skills: discussion, logical thinking explain possible outcomes through ‘possible’ to ‘certain’ to recognise, discuss and categorise the possibility of everyday events occurring

38 Maths Outcomes: Grade 4 (9 - 10 years) Number Learners will develop the understanding that fractions and decimals are ways of representing whole-part relationships and will demonstrate this understanding by modelling equivalent fractions and decimal fractions to hundredths or beyond. They will be able to model, read, write, compare and order fractions, and use them in real-life situations. Learners will have automatic recall of addition, subtraction, multiplication and division facts. They will select, use and describe a range of strategies to solve problems involving addition, subtraction, multiplication and division, using estimation strategies to check the reasonableness of their answers.

KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students know understand be able to do Resources

Models numbers to thousand or beyond Different activities using manipulatives Skills: mental and written arithmetic, Interactive using the base 10 place value system identify a process, explain, make notes whiteboards sites Models, reads and writes numbers up Show me…. to 1,000(thousands) and beyond) 100 number track/

Estimates and makes approximations Understands and explains rounding numbers strip, for different operations number cards Identifies when an accurate answer is Understand when to give an exact or approximate Skills: mental and written arithmetic, needed and when approximate answer when solving problems. identify a process, explain showing

Describes and uses mental and written Mental maths games three-digit numbers, strategies for multiplication and division How many different ways can you show me? number line

39 Understands fractions and their Introduce the concept of fractions and percentage, Skills: mental and written arithmetic, marked in multiples relationship to percentages for example, understand that when all students are identify a process, explain in the classroom, it is 100%. of 100/1000,

Compute percentages of whole numbers, for structured example, 25% of 200; materials ½, ¼ ¾ - what are these has percentages and representing fractions thousands, hundreds, tens, Make up and solve problems for others to solve and units, place Converts between fractions, decimals How are the three interconnected? and percentages value notation

Adds and subtracts fractions and Add and subtract numbers up to thousands using Skills: addition, subtraction, boards, number ‘flip’ decimals including money decomposition and check by reversing the estimating operation and by estimating. cards

Understands computation involving Use four operations to compute and solve money Skills: computation Fraction kit money problems. Fraction games

Number lines

Coins, notes Pattern and function Learners will analyse patterns and identify rules for patterns, developing the understanding that functions describe the relationship or rules that uniquely associate members of one set with members of another set. They will understand the inverse relationship between multiplication and division, and the associative and commutative properties of multiplication. They will be able to use their understanding of pattern and function to represent and make sense of real-life situations and, where appropriate, to solve problems involving the four operations. KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students know understand be able to do Resources

40 Understands the inverse relationship Complete examples Computation Calculators between addition and subtraction

Understands that multiplication is Show different ways of showing 7 x 3 and a range Teacher observations repeated addition of examples

Selects appropriate methods to analyse Collect examples of patterns and learn how to Teacher observations patterns and identify rules analyse them (weather patterns, number pattern, patterns in buildings)

Uses number patterns to make Solve examples Teacher observations predictions and solve problems

Understands relationships and patterns Identify that patterns follow a rule and investigate Skills: patterns, mental computation in fractions patterns in fractions, for example, in the fractions 2/4, 3/6, 4/8, what happens to the numerator must also happen to the denominator

Investigates the relationship between Investigate when there are two interrelated Skills:-identify a process, think two variables quantities, then the value of the 1st quantity logically, explain. determines the value of the 2nd quantity; for Peer assessment. example, investigate the number of large shapes which can be made from different numbers of small triangles. Measurement Learners will continue to use standard units to measure objects, in particular developing their understanding of measuring perimeter, area and volume. They will select and use appropriate tools and units of measurement, and will be able to describe measures that fall between two numbers on a scale. The learners will be given the opportunity to construct meaning about the concept of an angle as a measure of rotation. KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students know understand be able to do Resources

41 Measuring activities Self assessment Geared analogue clock, digital clock, minute timer Estimates, measures and compares (sandtimer, watch, objects using standard units of stopwatch), supply of measurement cubes

Rulers, thermometers, Uses decimal and fraction notation in measurement Trundle wheel, scales, Develops and describes formulas for Measure the sides of a book and record in mm and Skills: measure, problem solving. geoboards finding perimeter and volume cm. Teacher marking Weight kit

Students make measuring Understands area using standard Calculate and measure area, using cm², for Skills: measure, problem solving. instruments units. example, put shapes on cm squared paper and calculate their area in cm², and is there any quicker Self assessment Scales way? Stop watch Take 3 triangles with the same perimeter. Are their areas equal? Calendars

Measure spaces in school Skills: measure, problem solving. Schedules/timetables of

Self assessment different events

Understands, estimates weight in real- Estimate and weigh objects, using more than one Skills: weigh and record life situations standard unit of measurement, grammes, kilogrammes and hectogrammes, for example, Teacher observation record the weight, of students in the class, using different units.

Solve calorie problems. Skills: weigh and record.

Weigh and compare weight of foods. Assessment: teacher observation

42 Understands litres and millilitres Use the standard units of litres and milliliters to Skills: measure capacity, think estimate and measure different sized containers. logically, record

Teacher observation

Understand the digital and analogue Revise telling the time by analog and digital Skills: measure time, think logically, clock methods and introduce 24 hour time. record

Investigate 24 hour time by looking at a timetable Teacher observation and comparing, using standard and 24 hour time.

Reads and writes the time to the hour, Time activities Peer checking half hour and quarter hour Understand tools used to record time Record time, using minutes and seconds, for Skills: measure time, record example, measure how long it takes to do tasks in the classroom.

Understands days, months and years. Measure the passage of time, how many months, Skills: calculate time, think logically days in a year and a leap year? Assessment: teacher marking

Select and use an appropriate Use different measurement tools, for example, Skills: measure, think logically standard measuring tool and unit of which units of measurements are used to measure: measurement for different situations the quantity of precipitation, the weight of your bag, the distance to the sun.

Uses timetables and schedules in real- Analysing timetables Analysis skills life situations Develops and describes formulas for Measuring classroom school objects finding perimeter, area and volume. Shape and Space Learners will sort, describe and model regular and irregular polygons, developing an understanding of their properties. They will be able to describe and model congruency and similarity in 2D shapes. Learners will continue to develop their understanding of symmetry, in particular reflective and rotational symmetry. They will understand how geometric shapes and associated vocabulary are useful for representing and describing objects and events in real-world situations.

43 KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students know understand be able to do Resources

Sorts, describes, compares, labels Investigate the meaning of parallel, perpendicular, Skills: learn vocabulary, think Protractor, compasses, and models regular and irregular vertical and horizontal, etc. in 2D shapes. logically, paper polygons Solve problems, for example, are all shapes with 3 Assessment: teacher notes Sets with 3D shapes with sides triangles? Are all shapes with 4 sides cubes, cuboids, cones, rectangles? Can a triangle have 4 angles? cylinders, spheres, hemispheres, square, Analyses and describes 2D/3D Sorting vocabulary rectangles, pentagons, shapes using geometrical vocabulary hexagons, interlocking Identifies, describes and models Activities with 2D shapes construction materials, congruency and similarities in 2D interlocking cubes, straws shapes & ‘joiners’ (pipecleaners, plastic. . .), nets of cubes Recognises and explains symmetrical Investigate which capital letters have symmetry Skills: show me symmetry & cuboids patterns Investigate rotational/plane symmetry in 3/2D Assessment: teacher notes Tangrams shapes. Class room objects Creates and describes tessellating Pattern making, comparing with others patterns Maps

Recognizes right, acute and obtuse Measure and draw angles less then 180º using a Skills: measure, think logically Clocks angles protractor. Compass Use watch hands to measure an angle, for example, when the time is 3 o’clock.

Identifies parts of a circle and draws a Identify and learn, radius, diameter and Skills: draw, think logically circle circumference and draw circles with, for example, 6 сm radius, and then draw a circle with 6 сm diameter

44 Identifies and uses scale (ratios) to Art work enlarging/reducing shapes Teacher observation enlarge and reduce shapes

Locates features on a grid using Battleships, plotting coordinates onto a familiar map coordinates

Describes lines and angles using Using vocab to describe lines in the environment geometrical vocabulary Data handling Learners will continue to collect, organize, display and analyse data, developing an understanding of how different graphs highlight different aspects of data more efficiently. They will understand that scale can represent different quantities in graphs and that mode can be used to summarize a set of data. The learners will make the connection that probability is based on experimental events and can be expressed numerically. KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students know understand be able to do Resources

Collects, displays and interprets data Reads and interprets a variety of graphs and tables Skills: researching, thinking, Half/one/two centimetre using a variety of graphs and ask and answer questions about the cooperation, state logically & two millimetre squared information contained in them. paper of graphs, calculator, a simple Identify different ways of collecting data. for Skills: researching, thinking, computer graphing example, by questioning, by observing, etc. and cooperation, state logically. programme/ database understand the concept that a sample is big spreadsheet. . . enough. Peer, self, teacher assessment. flashcards of the Collect data, for example, the favorite sport of all language of probability students, draw a line graph, ask questions, for such as likely, no chance example, ‘Will everybody choose the same sport?’ Decimals and explain the results.

Expresses and uses probability to Discuss which events are possible or impossible Skills: researching, thinking, explain possible outcomes and understand that some explanations can be cooperation, state logically wrong.

45 Identifies, describes and explains the Collect data to find, mean, median and mode Presenting graphs and showing range, mode, median and mean in a mean, median and mode set of data

Understand all possible consequences Investigate that the repetition of an event can lead Skills: researching, thinking, of events. to different consequences, for example, throw a cooperation, state logically. dice a few times, record the results and check which number occurs most often and why and check their hypothesis against their results.

Make their own algorithm of events, for example, getting up in the morning, washing, having breakfast, etc or number algorithms, for example, 2,4,6,8 etc.

Designs a survey and systematically Collection of data collects, organizes and displays data in an appropriate simple graph

Maths Outcomes: Grade 5 (10 – 11 years) Number Learners will understand that the base 10 place value system extends infinitely in two directions and will be able to model, compare, read, write and order numbers to millions or beyond, as well as model integers. They will develop an understanding of ratios. They will understand that fractions, decimals and percentages are ways of representing whole-part relationships and will work towards modelling, comparing, reading, writing, ordering and converting fractions, decimals and percentages. They will use mental and written strategies to solve problems involving whole numbers, fractions and decimals in real-life situations, using a range of strategies to evaluate reasonableness of answers. KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students be know understand able to do Resources

46 Models numbers to millions of beyond Show me the number...... Show me the number...... a pizza model using the 10 place value system Read, write and order numbers up to billions Skills: mental, written arithmetic, give Fraction tiles and investigate the relationships between the reasonable answers, solve problems. place values of numbers, for example, write and Timelines draw 0.2, 0.23 and 2.3 on squared paper and Teacher designed quiz analyze which is bigger and why Calculators

Reads, writes, compare, models and Timelines 100-squares, interlocking orders whole numbers up to millions cubes in different colour, and beyond number cards showing Understands properties of numbers Investigate properties of numbers, for example, Skills: mental, written arithmetic, give fractions, decimals and factors, multiples, prime numbers, prime factors, reasonable answers, solve problems. percentage etc, Assessment: teacher test, quiz. 17 0.17 Understands when to give an accurate Discuss when an accurate or a rough answer is Skills: mental, written arithmetic, give or an estimate needed, for example, how much should you pay reasonable answers, solve problems. 100 as a tax for a bicycle or a car? 17%

Make up their own variations, analyze and solve Reads, writes, compares and orders Show me..... Show me….. fractions, decimals and percentages

Simplifies fractions How can I simplify? Why do I simplify? Show me….

Converts improper fractions to mixed Conversion activities Skills: mental, written arithmetic, give numbers and vice versa reasonable answers, solve problems.

Assessment: teacher test, quiz.

Understands equivalent fractions Introduce equivalent fractions with different Skills: mental, written arithmetic. denominators, by drawing and shading fraction strips, for example, 2/3 = 4/6 = 3/9, etc. Teacher marking.

47 Convert between fractions, decimals Rewrite fractions as decimals, for example, ½ = Skills: mental, written arithmetic, solve and percentages 0.5, ¼ = 0.25. problems, give reasonable answers.

Write recurring decimals and round the answer, for example, 2/3 = 0.66666 ≈ 0.7.

Find mistakes or extra values in teacher given examples.

Understands the connection between Work examples of linking fractions to decimals Skills: mental, written arithmetic fractions, decimals and percentages. and percentages, for example, 2/5 = 4/10 = 0.4 = 40%. Assessment: teacher marking

Estimates and makes approximations Show me.... for adding subtracting, multiplying and dividing fractions and decimals Practice exercises

Selects an efficient method for solving Experiment with strategies and reason the best Student teacher conference…why a problem strategy for a given situation would you choose that method? selects and uses an appropriate sequence of operations to solve word problems

Uses strategies to evaluate the Math’s investigations and games Self mark and teacher mark reasonableness of answers Pattern and Function Learners will understand the properties of regular and irregular polyhedra. They will understand the properties of 2D shapes and understand that 2D representations of 3D objects can be used to visualize and solve problems in the real world, for example, through the use of drawing and modelling. Learners will develop their understanding of the use of scale (ratio) to enlarge and reduce shapes. They will apply the language and notation of bearing to describe direction and position.

48 KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students be know understand able to do Resources

Represents the rule for a pattern Investigate arithmetical number patterns, for Skills: number, mental, written calculators example, 2,4,6,8.. and geometrical patterns, for arithmetic. example, 2, 4, 8, 16. paper, rulers, pencils

Use mental calculations and/or calculator. different examples of table and graphs Uses the mathematical language of Solve equations Skills: number, mental, written arithmetic. algebra to solve simple problems Analyses pattern and function using Investigate when there are two interrelated Skills:-identify a process, think logically, words, tables and graphs. quantities, then the value of the 1st quantity explain determines the value of the 2nd quantity, for Peer assessment example, investigate the number of large shapes which can be made from different numbers of small triangles. Measurement Learners will understand that a range of procedures exists to measure different attributes of objects and events, for example, the use of formulas for finding area, perimeter and volume. They will be able to decide on the level of accuracy required for measuring and using decimal and fraction notation when precise measurements are necessary. To demonstrate their understanding of angles as a measure of rotation, the learners will be able to measure and construct angles. KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students be know understand able to do Resources

Estimates, measure and compares Estimate and measure real objects Skills: measure, explain, solve Rulers, pencils objects using standard units of problems. measurement Make up and solve expressions boxes, blocks, containers, measuring cylinders,

49 Reads and interprets scale on a range Fill a box with blocks, record and find the Skills: measure, explain, solve protractors, of measuring instruments volume. problems, use formulae Schedules/timetables

Investigate making and using a formula to find volume of boxes: (V = L x W x H).

Estimate and measure capacity and volume using litres and milliliters

Solve problems, for example, share drinks among all their classmates and guess how much drink they need.

Measure and constructs angles in Exploring measuring angles to an accurate Show me how you measure degrees using a protractor degree.

Selects and uses an appropriate Use different measurement tools to perform Skills: measure, think logically. standard measuring tool and unit of different tasks and be able o select the correct measurement for different situations one? Self asessment

Uses timetables and schedules in real- Using timetables to organise work/Create your Explaining how to read different life situations own timetable schedules

Creates own schedule for Exhibition Shape and Space Learners will understand the properties of regular and irregular polyhedra. They will understand the properties of 2D shapes and understand that 2D representations of 3D objects can be used to visualize and solve problems in the real world, for example, through the use of drawing and modelling. Learners will develop their understanding of the use of scale (ratio) to enlarge and reduce shapes. They will apply the language and notation of bearing to describe direction and position. KNOW: What will the students UNDERSTAND: What will the students SKILLS: What will the students be know understand able to do Resources

50 Analyses, describes and classifies 2D Analyze and compare properties of real 2D and Skills: problem solve, analyse. geometric shapes. paper, and 3D shapes using geometric 3D shapes found in the classroom, for example, pencils, scissors, vocabulary look at corners in the room and discuss , ‘Are protractors, they similar or not ? Are the ceiling and floor corners similar? rulers. Make models and generalize links among them Investigate and discuss vocabulary of sides, Sets of 2D shapes, symmetry, sections, vertical and horizontal including equilateral, isosceles, scalene, right- Investigate how many ways they can draw a cube, for example, make 3D shapes using angled triangles, sticks, noting number of sides and angles quadrilateral, regular & irregular polygons, Describes lines and angles using Drawing shapes using Google sketch Able to describe different types of lines Geostrips or Meccano geometric vocabulary pieces, centimeter squared Identifies and uses scale to enlarge or Scale drawings Creates display boards showing scale paper, mirror, rulers, reduce shapes drawings geoboards and pegs

Creates and models how a 2D net Net drawings Skills: problem solve, analyse converts into a 3D shapes and vice What shape do you think this is? Using knowledge of shapes teaches to another class Data handling Learners will collect, organize and display data for the purposes of valid interpretation and communication. They will be able to use the mode, median, mean and range to summarize a set of data. They will create and manipulate an electronic database for their own purposes, including setting up spreadsheets and using simple formulas to create graphs. Learners will understand that probability can be expressed on a scale (0–1 or 0%–100%) and that the probability of an event can be predicted theoretically. Represents and expresses probability Probability charts Skills: problem solve, analyse Half/one/two centimetre & on a scale two millimetre squared Understands how to collect, present Make different charts Skills: data collection paper of graphs, and interpret information calculator, a simple Make distance tables from journey information Skills: organise data computer graphing on a map. programme/ database spreadsheet. . . Use and interpret timetables for journeys Skills: organise data flashcards of the

51 Understand how to calculate the Use knowledge of fractions, decimals and language of probability chance of events occurring. percentage to calculate the chance of things such as likely, no chance happening. Decimals, squared paper, Identifies, describes and explains the Data collected by students rulers, pencils, charts, range, mode, median and mean in a Whiteboards, Markers, set of data Graph paper Collects,Data Handlingdisplays and interprets data usingLearners a variety will continue of graphs to work with 2D and 3D shapes, developing the understanding that shapes are classified and named according to their properties. They will understand that examples of symmetry and transformations can be found in their immediate environment. Learners will interpret, create and use simple Designsdirections a surveyand specific and systematically vocabulary to describeStudent paths, data regions, positions and boundaries of theirResearch immediate skills environment. collects,KNOW: organizes What will and the displays students data in UNDERSTAND: What will the students SKILLS: What will the students be Resources aknow variety of ways understand able to do ATTITUDES: What attitudes will be developed? Know: Understand: Able to Do: Clipboards Poster paper How to design a survey, collect, Understand that data analysis and - Identifies, describes and discusses represent and interpret data. probability are useful in everyday life. ideas about probability using (predicting the weather, gambling, vocabulary such as fair, unfair, likely, How to interpret tables, charts and marketing) unlikely, probably, always, graphs. sometimes, rarely and never. Apply the concepts of Form, Function and How to identify, describe and Connection. - Collect, interpret and present data express chance in everyday life. using different types of tables, charts and graphs. E.g. pictographs, tally marks, bar graphs, pie charts and living graphs.

- Design a survey.

- Describe, sort and label objects by attributes.

- Represent the relationship between objects using a Venn tree and/or Carroll diagram. 52