Year 4: Block C Three 2-Week Units

Year 4: Block C Three 2-week units

Handling data and measures  Readings from scales  Comparing impact of different scales

 Constructing tables, diagrams, tally charts, pictograms and bar charts

 Collection, organising, presenting and interpreting data to answer related questions  Identifying further questions

 Explaining reasoning using text, diagrams and graphs

 Using standard metric units to estimate, measure and record measurements

 Using ICT

Objectives Units 1 2 3 • Suggest a line of enquiry and the strategy needed to follow it; collect,    organise and interpret selected information to find answers • Answer a question by identifying what data to collect; organise, present, analyse and interpret the data in tables, diagrams, tally charts, pictograms    and bar charts, using ICT where appropriate • Report solutions to puzzles and problems, giving explanations and reasoning    orally and in writing, using diagrams and symbols • Choose and use standard metric units and their abbreviations when estimating, measuring and recording length, weight and capacity; know the    meaning of ‘kilo’, ‘centi’ and ‘milli’ and, where appropriate, use decimal notation to record measurements (e.g. 1.3 m or 0.6 kg) • Interpret intervals and divisions on partially numbered scales and record    readings accurately, where appropriate to the nearest tenth of a unit • Compare the impact of representations where scales have intervals of   differing step size

Speaking and listening objectives for the block

Units Objectives 1 2 3 • Use time, resources and group members efficiently by distributing tasks,    checking progress, making back-up plans

Opportunities to apply mathematics in science

Units Activities 1 2 3

4a Moving and growing: Measure and record relative sizes of bones. Discuss changes over time. Suggest measurements to take to answer questions ü such as ‘Who has the longest arms?’. Choose how to present the results. 4d Solids, liquids and how they can be separated: Observe and measure volumes of liquids, recording them in tables. Explain conservation of  volume of liquids when poured into different containers. 4b Habitats: Sort animals and plants according to own criteria. Select ways of  recording the groupings. 4c Keeping warm: Collect data about cooling liquids over time, e.g. temperature of cooling tea every 15 minutes. Record results in a table.  Make readings from thermometers with different scales.

Key aspects of learning: focus for the block

Enquiry Problem solving Reasoning Creative thinking Information processing Evaluation Self-awareness Managing feeling Social skills Communication Motivation Empathy

Vocabulary problem, solution, calculate, calculation, method, explain, reasoning, reason, predict, pattern, relationship, classify, represent, interpret data, information, survey, questionnaire, graph, chart, table, diagram, horizontal axis, vertical axis, axes, label, title, scale, interval, pictogram, bar chart, tally chart, greatest/least value metric unit, standard unit, millimetre (mm), centimetre (cm), metre (m), kilogram (kg), gram (g), litre (l), millilitre (ml)

Building on previous learning Check that children can already: • consider a question and develop a response by referring to relevant data • make and use lists, tables and simple bar charts to organise and interpret the information • use Venn diagrams or Carroll diagrams to sort data and objects using more than one criterion • recall the relationships between kilometres and metres, metres and centimetres, kilograms and grams, litres and millilitres • choose and use appropriate units to estimate, measure and record length and weight • measure and draw to a suitable degree of accuracy, e.g. measure length to the nearest half centimetre and weight to the nearest half division on the scales Unit 4C1

Learning overview

In this learning overview are suggested assessment opportunities linked to the assessment focuses within the Assessing Pupils’ Progress (APP) guidelines. As you plan your teaching for this unit, draw on these suggestions and alternative methods to help you to gather evidence of attainment or to identify barriers to progress that will inform your planning to meet the needs of particular groups of children. When you make a periodic assessment of children’s learning, this accumulating evidence will help you to determine the level at which they are working.

To gather evidence related to the three Ma1 assessment focuses (problem solving, reasoning and communicating), it is important to give children space and time to develop their own approaches and strategies throughout the mathematics curriculum as well as through the application of skills across the curriculum.

In this unit the illustrated assessment focuses are:

 Ma1, Communicating  Ma3, Measures  Ma4, Processing and representing data

Children undertake enquiries to answer a question that they are given. The enquiry offers a chance to follow through the data- handling cycle: pose a question and answer it by collecting data, and then organising, representing and interpreting it. Children identify possible answers based on their findings. They suggest a further question to explore and revisit the data-handling cycle by collecting further data.

Possible contexts for the enquiry can be found in science, for example in the Qualifications and Curriculum Authority (QCA) scheme of work: Unit 4a: Moving and growing; Unit 4d: Solids, liquids and how they can be separated or Unit 4e: Investigating parachutes.

For example, children explore a hypothesis such as: The bigger the object, the faster it falls. They decide what data to collect to find out more. They consolidate their measurement skills and knowledge as they measure heights of the parachute drop-point above the ground, weights of the objects that they attach to the parachutes, sizes of the parachutes (defined by length of the side of the square forming the parachute), lengths of the parachute strings and times of the falls in seconds. Children choose and use appropriate instruments and units to measure and record lengths to the nearest half-centimetre, weights in grams and kilograms to the nearest half-division on the scales, and timings in seconds.

Assessment focus: Ma3, Measures

Look for children who measure lengths in centimetres to the nearest half-unit. As they weigh objects, look for children reading from simple scales with increments of 5 or 10. Look for evidence of those children who are beginning to read scales with larger increments such as 20, 50 or 100 and who make sensible estimates of values between labelled divisions.

Children organise their measurements by tabulating them. They decide how best to do this. They look for patterns in the data that could support or refute the hypothesis. They consider how to represent the data in a bar chart. They report their findings orally and by showing their charts and tables. They develop further hypotheses, such as: The larger the parachute, the longer the teddy takes to fall or Soft objects fall more slowly. Children evaluate these suggestions, in groups, and make decisions about which are suitable to be pursued.

Assessment focus: Ma1, Communicating

Look for evidence of children who can discuss the data they have collected and represented and use what they find to begin to explain their thinking and how it relates to their original hypothesis. Look for children who listen to and evaluate the explanations of others and can suggest future lines of enquiry.

Children plan what data to collect and how to organise it. They appreciate that they need to make careful choices and to use units of measurement consistently. In groups, they identify the measurements to make and share the work among the group members. They respond to questions such as:

What data do we need to collect? How can we collect the data? How can we represent the data? Is there more than one way to represent the data? Which way would be best? What conclusions can we draw about our hypothesis?

Assessment focus: Ma4, Processing and representing data

Look for children who can decide what data to collect to answer a question and make appropriate choices for recording data. Look for children who consider the scale for a bar chart, for example, children who choose a suitable scale so that data involving large numbers can be displayed on one page. Assessment for learning Objectives Children's learning outcomes are emphasised What are you trying to find out? What information are you aiming to collect? How?

Suggest a line of enquiry and the strategy needed to follow it; collect, organise What do you think the result will be? Why? and interpret selected information to find answers

Why have you chosen to collect that information? What will it tell I can think about an experiment, predict what might happen and decide how I could go you? about finding out whether it is true

Gulab says that most children in our class walk to school. What data would you suggest that he collects to find out whether he is right? What information will you need to collect to answer your question? How will you collect it?

How will you organise your data? How will you display it? Answer a question by identifying what data to collect; organise, present, analyse and interpret the data in tables, diagrams, tally charts, pictograms and bar charts, using ICT where appropriate What titles have you given your graphs? What labels have you put on the axes?

I can collect data and put it in a table to help me explore an idea and find out more about it What does this table tell you? Why did you choose a table to show your information? Why is it easy to interpret?

Look carefully at one of your tables. How did it help you find out more about the data? What have you found out? Does anything surprise you? Why?

Report solutions to puzzles and problems, giving explanations and reasoning What evidence do you have to support your conclusions? orally and in writing, using diagrams and symbols

What other questions could you ask now that you have finished your I can tell people what I have found out and show some graphs to back up my enquiry? conclusions

What would you do differently if you carried out the enquiry again? Estimate the weight of this bag of carrots. And of this tin of soup.

Which units would you use to measure the weight of an orange?

A centimetres Choose and use standard metric units and their abbreviations when estimating, measuring and recording length, weight and capacity; know the meaning of B millilitres 'kilo', 'centi' and 'milli' and, where appropriate, use decimal notation to record measurements (e.g. 1.3 m or 0.6 kg) C grams I can measure lengths, weights, and times to help me find out more about a question I am exploring D kilograms

Which is heavier: 2000 g or 3 kg? Explain how you know.

Can you tell me another way to say or write 8 kilograms? What about 500 grams? Here are some apples. What is the total weight of the apples?

Interpret intervals and divisions on partially numbered scales and record readings accurately, where appropriate to the nearest tenth of a unit

I can measure lengths to the nearest half centimetre, weights in grams and kilograms, and times in seconds

Imagine a centimetre tape measure. The first part has been torn off and it starts at 8 centimetres. How can you use it to make a measurement in centimetres?

Use time, resources and group members efficiently by distributing tasks, How are you going to collect the data? How will you organise the checking progress, making back-up plans tasks? Assessment for learning Objectives Children's learning outcomes are emphasised

I can contribute to a task in my group so that we are all being helpful as we collect data What helped you to collect the data efficiently?

Resource links to existing published material Mathematical challenges for able pupils Key Stages 1 and 2 Activities None currently available Intervention programmes Springboard unit None currently available Supporting children with gaps in their mathematical understanding (Wave 3) Diagnostic focus None currently available

 Year 4 Handling data and measures – Unit 1  Wave 3 addition and subtraction tracking children's learning charts  Wave 3 multiplication and division tracking children's learning charts Unit 4C2

Learning overview

In this learning overview are suggested assessment opportunities linked to the assessment focuses within the Assessing Pupils' Progress (APP) guidelines. As you plan your teaching for this unit, draw on these suggestions and alternative methods to help you to gather evidence of attainment or to identify barriers to progress that will inform your planning to meet the needs of particular groups of children. When you make a periodic assessment of children's learning, this accumulating evidence will help you to determine the level at which they are working.

To gather evidence related to the three Ma1 assessment focuses (problem solving, reasoning and communicating), it is important to give children space and time to develop their own approaches and strategies throughout the mathematics curriculum, as well as through the application of skills across the curriculum.

 Ma1, Problem solving  Ma3, Measures  Ma4, Processing and representing data  Ma4, Interpreting data

In groups, children collect data, measuring where necessary. They work with a range of data, such as shoe size and width of shoe across the widest part of the foot, the number of letters in children's names, the width of their hand spans, the distance around their neck and wrist, data from nutrition panels on cereal packets, and so on.

Assessment focus: Ma3, Measures

Look for evidence of children choosing appropriate units and measuring tools for a range of measurements. For example, look for children who choose a tape measure, a metre stick or 30 cm ruler, according to the length they intend to measure. Look for evidence of children recording longer lengths in metres and centimetres or as decimal fractions of a metre, for example, 3 m 45 cm or 3.45 m. Look for evidence of the range of scales that children can interpret. For example, look for children interpreting measurements on scales with increments of 5, 10, 25, 50 or 100. They might work out a value half-way between labelled divisions, for example, between 12 cm and 13 cm, 80 cm and 90 cm, 200 g and 300 g or 150 ml and 200 ml.

They decide on a suitable question or hypothesis to explore for each data set they work on. For example, 'We think that...boys have larger shoes than girls', '...our neck measurements are twice as long as our wrist measurements', '...girls' names have more letters than boys' names' or '...children in our class would prefer to come to school by car but they usually have to walk'.

Children consider what data to collect and how to collect it. They collect their data and organise it in a table. They choose a Venn or Carroll diagram, or a horizontal or vertical pictogram or bar chart to represent the data. Where appropriate, they use the support of an ICT package. They justify their choice within the group so that they can present their data.

As they construct bar graphs and pictograms, look for evidence of children considering the size of numbers and making decisions about the scale to use. For example, look for those children who use one symbol or one unit on the axis to represent one item where numbers are small and those children who choose to use one symbol or unit to represent two or more items, so that they can represent larger numbers on the page.

Children interpret their diagrams and graphs against their hypothesis or question and draw a conclusion. They respond to questions such as:

What can you tell by comparing these two graphs?

What do you think are the reasons for the differences? Assessment focus: Ma4, Interpreting data

As they compare graphs look for children who are beginning to consider the range of results. Comparing graphs of, for example, shoe sizes for Year 4 and Year 6 they might notice that the most common shoe size in Year 6 is larger than the most common size in Year 4. Some children might also notice if the range of shoe sizes is similar or not, for example, the sizes in Year 4 go from size… to size…, which is five different shoe sizes but in Year 6…

Children present their data in different ways; for example, they change the step size of scales, using steps of 2, 5, 10 and 20, as appropriate. They evaluate the effect of different scales on interpretation of the data. Children look at the way in which others have represented their data and decide as a class which graphs, charts and tables are the most meaningful.

Assessment focus: Ma1, Problem solving

As they collect, process and represent data to solve problems, look for children recognising similarities to previous problems they have solved and the diagrams and graphs they used. Look for children who pose questions and make suggestions about ways to find answers. Look for children trying different approaches to deal with more complex data or larger sets of data. For example look for children who decide to use a Venn or Carroll diagram to record which children drink water or fruit juice when they are thirsty so that they can record who drinks both types and who drinks neither. Look for children choosing a suitable scale to deal with large numbers in their data.

Objectives Children's learning outcomes are emphasised Assessment for learning What are you trying to find out? What information are you aiming to collect? How? Suggest a line of enquiry and the strategy needed to follow it; collect, organise and interpret selected information to find answers Why have you chosen to collect that information? What will it tell you? I can think of a question to ask about some information and organise the information to help me find out more about it Your class has collected data about the distances that children travel to school and the type of transport they use. What questions could you ask to find out more from this data? What information will you need to collect to answer your question? How will you collect it?

How will you display your data? Why have you chosen to do it that Answer a question by identifying what data to collect; organise, present, analyse way? and interpret the data in tables, diagrams, tally charts, pictograms and bar charts, using ICT where appropriate When is a tally chart useful? Think of an example. Why is it useful?

I can choose from tables, diagrams, tally charts, pictograms and bar charts to show data so that they are easy to understand When is a bar chart useful? Think of an example. Why is it useful?

What does this bar chart tell you? Why did you choose a bar chart to show your data? What makes the information in a bar chart easy or difficult to interpret? What have you found out?

What charts or tables will you use to show your results?

Report solutions to puzzles and problems, giving explanations and reasoning Are your results what you expected or were there any surprises? orally and in writing, using diagrams and symbols What evidence do you have to support your conclusions? I can explain how I solved a puzzle using a diagram to help me What other questions could you investigate now that you have answered the original question?

What would you do differently if you carried out the enquiry again? Choose and use standard metric units and their abbreviations when estimating, Estimate the height of the window. And the width of the door. measuring and recording length, weight and capacity; know the meaning of 'kilo', 'centi' and 'milli' and, where appropriate, use decimal notation to record measurements (e.g. 1.3 m or 0.6 kg) Choose the correct answer:

I can measure carefully lengths to the nearest half centimetre so that my measurement is The width of the table is about... accurate 1.5 cm 15 cm 150 cm 1500 cm

In an hour, Meena can walk...

5 mm 5 cm 5 m 5 km

What unit would you use to measure the distance from here to Objectives Children's learning outcomes are emphasised Assessment for learning

Paris? And the length of a shoe?

Can you tell me another way to say or write 2 km? What about 4 m? And 5 cm?

Someone told me that small balls roll further than large balls. What measurements would you make to find out if this is true?

John said to Gemma: 'You can only measure the length of straight lines'. Is he right? How do you know? Robbie collected information about the colours of some bikes. Here are his results.

Colour Number of bikes green 4 red 7 blue 12 pink 3 Interpret intervals and divisions on partially numbered scales and record readings accurately, where appropriate to the nearest tenth of a unit This bar graph shows the information from the table. Fill in all the missing labels. I can use different kinds of rulers and measuring tapes to measure lengths accurately

How did you decide on the scale for this axis?

Which scale helps you to interpret and draw conclusions most Compare the impact of representations where scales have intervals of differing easily? Why? step size [Show two bar charts showing the same data but with different step I can compare graphs with different scales and decide which is the most useful sizes on the scales.]

Tell me how you know that these two charts show the same data. Which chart is better? Why? Use time, resources and group members efficiently by distributing tasks, checking progress, and making back-up plans How are you going to represent your data?

I can contribute to a task in my group so that we are all being helpful as we collect data Why have you decided that this is the best way to represent your data? I can help the group to decide which graph or diagram is a good choice Resource links to existing published material Mathematical challenges for able pupils Key Stages 1 and 2 Activities Resources None currently available Intervention programmes Springboard unit Resources None currently available Supporting children with gaps in their mathematical understanding (Wave 3) Diagnostic focus Resources None currently available

 Wave 3 addition and subtraction tracking children's learning charts  Wave 3 multiplication and division tracking children's learning charts  Wave 3 Resource sheets and index of games booklet

Unit 4C3

Learning overview

In this learning overview are suggested assessment opportunities linked to the assessment focuses within the Assessing Pupils' Progress: Assessment guidelines. As you plan your teaching for this unit, draw on these suggestions and alternative methods to help you to gather evidence of attainment or to identify barriers to progress that will inform your planning to meet the needs of particular groups of children. When you make a periodic assessment of children's learning, this accumulating evidence will help you to determine the level at which they are working.

To gather evidence related to the three Ma1 assessment focuses (problem solving, reasoning and communicating), it is important to give children space and time to develop their own approaches and strategies throughout the mathematics curriculum, as well as through the application of skills across the curriculum.

 Ma1, Communicating  Ma4, Processing and representing data  Ma4, Interpreting data Children undertake one or more of three enquiries:

 What vehicles are very likely to pass the school gate between 10:00 am and 11:00 am? Why? What vehicles would definitely not pass by? Why not? What vehicles would be possible but not very likely? Why? What if it were a different time of day? What if the weather were different?  Does practice improve estimation skills? Children estimate the lengths of five given lines and record the estimate, measured length and difference. They repeat the activity with five more lines to see whether their estimation skills have improved after feedback.  What would children in our class most like to change in the school? Children carry out a survey after preliminary research to whittle down the number of options to a sensible number, for example no more than five. Children identify a hypothesis and decide what data to collect to investigate their hypothesis. They collect the data they need and decide on a suitable representation. In groups, they consider different possibilities for their representation and explain why they have made their choice.

Assessment focus: Ma1, Communicating

As children plan their approach to the problem, look for those who begin to organise their work in a clear and structured way from the start. Look out for children who can explain their hypothesis and thinking, making accurate use of appropriate mathematical vocabulary.

In the first enquiry, children use tallies and bar charts. In the second, they use tables and bar charts to compare the two sets of measurements. In the third, they use a range of tables and charts to show their results, including Venn and Carroll diagrams. They use ICT where appropriate.

As they collect data, look for evidence of how children choose to record their results, for example, keeping a tally or completing a frequency table to record a show of hands. Once they have collected the data, look out for children making sensible decisions about how to represent it, for example in a Venn or Carroll diagram, a bar chart or pictogram. As they work with larger numbers, look for children who choose appropriately from a wider range of scales, for example, with divisions representing 1, 2, 5, 10 or 20.

Children explore the effect of changing the step size on the scale of graphical representations, considering step sizes of 1, 2, 5, 10 and 20 as appropriate. For example, these graphs were produced by the ITP 'Data handling'. The bar charts show the number of gold medals in the 2000 Olympics, first with the vertical axis numbered in 20s from 0 to 100 and then with the vertical axis numbered in 10s from 0 to 40.

Children consider how the differences appear to be greater on the bar chart with the scale numbered in 10s than on the bar chart with the scale numbered in 20s. In groups, children interpret their data and draw conclusions. They decide on the statements of findings that have good evidence to support them. They discuss what further questions they could go on to ask.

Assessment focus: Ma4, Interpreting data

As they interpret a wider range of scales, look for evidence of how accurately children read values, for example, the point halfway between 8 and 10 on a scale that has increments of 2, or the value 17 against a scale that has increments of 5. Look out for children who can estimate and then calculate the size of the whole data set, for example the total number of vehicles that passed the school gates in the hour. Look for children who can draw reasonable conclusions from their enquiry, referring to their data, and any new questions that have arisen.

Objectives Children's learning outcomes are emphasised Assessment for learning What are you trying to find out? What information are you aiming to collect? How? Suggest a line of enquiry and the strategy needed to follow it; collect, organise and interpret selected information to find answers Why have you chosen to collect that information? What will it tell you?

I can think about an investigation, predict what might happen and decide how I Imagine that the class is going to organise a tea party for parents. What could go about finding information, perhaps by doing a survey or taking information would you need to find out? What are the simplest ways that you measurements can find the information?

What information will you need to collect to answer your question? How will you collect it?

Why do you think it is a good idea to tally in fives? Answer a question by identifying what data to collect; organise, present, analyse and interpret the data in tables, diagrams, tally charts, How will you display your data? pictograms and bar charts, using ICT where appropriate What does this graph tell you? Why did you choose this type of graph? What I can collect data in different ways and decide whether to put it in a table, makes the information easy or difficult to interpret? diagram, tally chart, pictogram or bar chart so that it is easy to understand Make up two questions that can be answered using the information in your graph or table or chart.

What were the advantages of using a computer? What have you found out?

What graphs, charts or tables will you use to show your results?

Report solutions to puzzles and problems, giving explanations and Are your results what you expected or were there any surprises? reasoning orally and in writing, using diagrams and symbols

What evidence do you have to support your conclusions? I can tell people what I have found out and show some graphs to back up my conclusions What other questions could you ask now that you have finished your enquiry? Would you use a computer to help you? Why or why not?

What would you do differently if you carried out the enquiry again? Choose and use standard metric units and their abbreviations when Estimate the capacity of this washing-up bowl. And of this bottle. estimating, measuring and recording length, weight and capacity; know the meaning of 'kilo', 'centi' and 'milli' and, where appropriate, use decimal notation to record measurements (e.g. 1.3 m or 0.6 kg) Choose the correct answer. A drinking glass holds about...

I can estimate the length of a line in centimetres and millimetres and then 0.2 litres 2 litres 20 litres 200 litres measure the line to see how close my estimate was What unit would you use to measure the capacity of a watering can? Of an oil tank? Of a coffee cup?

Can you tell me another way to say or write 6 litres? What about 750 millilitres? Objectives Children's learning outcomes are emphasised Assessment for learning

Look at these cards. They have weights in grams or kilograms.

1 5 kg, 500 g, /4 kg, 1.5 kg, 750 g

Put the cards in order from the lightest to the heaviest. How did you order the cards? Why did you put this measurement here?

Here are some children's long jump results. Sue jumped 212 cm.

Draw Sue's long jump result on the graph.

Interpret intervals and divisions on partially numbered scales and record Use the graph to estimate how much further Sam jumped than Jan. readings accurately, where appropriate to the nearest tenth of a unit Harry, Eve and Khalid measured the same objects. Here are Harry's I can use different kinds of rulers and measuring tapes to measure lengths measurements. accurately pencil length – 16 cm computer screen width – 33 cm door width – 77 cm cube length – 1.9 cm ruler width – 3.8 cm room length – 830 cm

Eve wrote her measurements in millimetres. What did she write?

Khalid wrote his measurements in metres. What did he write?

What would you use? Would you use different units for different measurements? Why or why not?

Compare the impact of representations where scales have intervals of How did you decide on the scale for this axis? differing step size

Which scale helps you to interpret and draw conclusions most easily? Why? I can compare graphs with different scales and decide which is the most useful Use time, resources and group members efficiently by distributing tasks, What conclusions have you drawn? checking progress, and making back-up plans

What evidence have you got to back up your conclusions? I can contribute to a task in my group so that we are all being helpful as we collect data I can help the group to decide what we have found out Are your conclusions what you expected?

Resource links to existing published material Mathematical challenges for able pupils Key Stages 1 and 2 Activities None currently available Intervention programmes Springboard unit None currently available Supporting children with gaps in their mathematical understanding (Wave 3) Diagnostic focus Resource None currently available

 Wave 3 addition and subtraction tracking children's learning charts  Wave 3 multiplication and division tracking children's learning charts  Wave 3 Resource sheets and index of games booklet