British Columbia Curriculum K-9 Alignment with Mathletics

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BC Kindergarten 02

BC Grade 1 04

BC Grade 2 07

BC Grade 3 10

BC Grade 4 14

BC Grade 5 20

BC Grade 6 25

BC Grade 7 28

BC Grade 8 31

BC Grade 9 36 British Columbia Curriculum K-9 Alignment with Mathletics

Mathletics and the British Columbia Curriculum K-9

At Mathletics, we are committed to providing students, teachers and schools with high-quality learning resources that align with current curricula. Our Content and Curriculum Team has created grade-level courses that specifically follow the British Columbia Curriculum K–9 (first implemented for the 2016-2017 school year). The Big Ideas, Curricular Competencies and Content of the curriculum are supported with more than 1200 adaptive practice activities, as well as a range of eBooks, videos and interactives. You can be assured that students have access to relevant and targeted content. This document maps Mathletics activities to the content (and elaborations) of the curriculum. All of the activities mapped to a particular grade level in this document are included as ‘core’ activities in the topics of the Mathletics course for that grade level. In some topics, a few additional activities from the prior grade level have been included as ‘core’ activities in the course in order to support the learning of the grade level. The ‘Something Easier’ section for each topic generally includes activities from the related topic of the prior grade level.

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1 © 3P Learning British Columbia Curriculum K-9 Alignment with Mathletics

BC Kindergarten

Big Ideas

• Numbers represent quantities that can be decomposed into smaller parts. • One-to-one correspondence and a sense of 5 and 10 are essential for fluency with numbers. • Repeating elements in patterns can be identified. • Objects have attributes that can be described, measured, and compared. • Familiar events can be described as likely or unlikely and compared.

Content Elaborations Activities • counting: o one-to-one correspondence o conservation Count to 5 o cardinality How Many? o stable order counting Dot Display number o sequencing 1-10 Concept of Zero concepts to 10 o linking sets to numerals Order Numbers to 10 o subitizing Ordinal Numbers • using counting collections made of local materials More, Less or the Same to 10 • counting to 10 in more than one language, including local First Peoples language or languages • perceptual subitizing (e.g., I see 5) • conceptual subitizing (e.g., I see 4 and 1) • comparing quantities, 1-10 ways to make 5 Picture Graphs: More or Less • using concrete materials to show ways to make 5 • Traditional First Peoples counting methods involved using fingers to count to 5 and for groups of 5. • decomposing and recomposing quantities to 10 • Numbers can be arranged and recognized. • benchmarks of 5 and 10 Adding to Make 5 and 10 decomposition • making 10 of numbers to 10 Add and Subtract Using • part-part-whole thinking Graphs • using concrete materials to show ways to make 10 • whole-class number talks • sorting and classifying using a single attribute • identifying patterns in the world repeating • repeating patterns with 2-3 elements patterns with • identifying the core Complete the Pattern two or three • representing repeating patterns in various ways Hot or Cold? elements • noticing and identifying repeating patterns in First Peoples and local art and textiles, including beadwork and beading, and frieze work in borders change in • generalizing change by adding 1 or 2 Adding to Make 5 and 10 quantity to 10, • modeling and describing number relationships through change (eg., using concrete build and change tasks - begin with four cubes, what do you need to Add and Subtract Using materials do to change it to six? to change it to 3?) Graphs

BC Kindergarten

Content Elaborations Activities equality as a • modeling equality as balanced and inequality as imbalanced using balance and concrete and visual models (e.g., using a pan balance with cubes on Balancing Objects inequality as an each side to show equal and not equal) Balancing Act imbalance • fish drying and sharing Everyday Length • understanding the importance of using a baseline for direct direct Comparing Length comparison in linear measurement comparative Everyday Mass • linear height, width, length (e.g., longer than, shorter than, taller than, measurement How Full? wider than) (e.g., linear, • mass (e.g., heavier than, lighter than, same as) Which Holds More? mass, capacity) • capacity (e.g., holds more, holds less) Filling Fast! Comparing Volume • At this level, using specific math terminology to name and identify 2D shapes and 3D objects is not expected. single attributes • sorting 2D shapes and 3D objects using a single attribute Same and Different of 2D shapes • building and describing 3D objects (e.g., shaped like a can) Where is it? and 3D objects • exploring, creating, and describing 2D shapes Following Directions • using positional language, such as beside, on top of, under, and in front of • creating concrete and pictorial graphs to model the purpose of concrete or graphs and provide opportunities for mathematical discussions (e.g., Read Graphs pictorial graphs survey the students about how they got to school, then represent the as a visual tool Comparing groups of objects data in a graph and discuss together as a class). likelihood of • using the language of probability, such as unlikely or likely (e.g., Will it Happen? familiar life Could it snow tomorrow?) events Most Likely and Least Likely • noticing attributes of Canadian coins (colour, size, pictures) financial literacy • identifying the names of coins — attributes • role-playing financial transactions, such as in a restaurant, bakery, of coins, and or store, using whole numbers to combine purchases (e.g., a muffin Under review financial role- is $2.00 and a juice is $1.00), and integrating the concept of wants play and needs • token value (e.g., wampum bead/trade beads for furs)

3 © 3P Learning British Columbia Curriculum K-9 Alignment with Mathletics

BC Grade 1

Big Ideas

• Numbers to 20 represent quantities that can be decomposed into 10s and 1s. • Addition and subtraction with numbers to 10 can be modelled concretely, pictorially, and symbolically to develop computational fluency. • Repeating elements in patterns can be identified. • Objects and shapes have attributes that can be described, measured, and compared. • Concrete graphs help us to compare and interpret data and show one-to-one correspondence.

Content Elaborations Activities • counting: o counting on and counting back o skip-counting by 2 and 5 o sequencing numbers to 20 Counting Up to 20 o comparing and ordering numbers to 20 Counting Back Within 20 o Numbers to 20 can be arranged and recognized. Before, After and Between to 20 o subitizing Order Numbers to 20 number o base 10 More, Less or the Same to 20 concepts to 20 o 10 and some more • books published by Native Northwest: Learn to Count, by various How Many Dots? artists; Counting Wild Bears, by Gryn White; We All Count, by Making Teen Numbers Jason Adair; We All Count, by Julie Flett (nativenorthwest.com) Matching Numbers to 10 using counting collections made of local materials; counting in Matching Numbers to 20 different languages; different First Peoples counting systems (e.g., Tsimshian) • Tlingit Math Book • decomposing 10 into parts • Numbers to 10 can be arranged and recognized. • benchmarks of 10 and 20 Adding to Make 5 and 10 ways to make 10 • Traditional First Peoples counting methods involved using fingers Add and Subtract Using Graphs to count to 5 and for groups of 5. • traditional songs/singing and stories

BC Grade 1

Content Elaborations Activities Model Addition Adding to 5 Adding to Ten Adding In Any Order Commutative Property of Addition Addictive Addition Add 3 Numbers Using Bonds to 10 • decomposing 20 into parts Add 3 Single Digit Numbers addition and • mental math strategies: Doubles and Near Doubles subtraction o counting on Model Subtraction to 20 o making 10 Subtracting From 5 (understanding o doubles of operation and • Addition and subtraction are related. Subtracting from Ten process) • whole-class number talks Subtracting from 20 • nature scavenger hunt in Kaska Counting Book Simple Subtraction All about Ten All about Twenty Fact Families: Add and Subtract Adding to 10 Word Problems Add and Subtract Problems Related Facts 1 Problems: Addition and Subtraction • identifying sorting rules • repeating patterns with multiple elements/attributes • translating patterns from one representation to another (e.g., an orange-blue pattern could be translated to a circle-square Sort It repeating pattern) Complete the Pattern patterns • letter coding of pattern Simple Patterns with multiple • predicting an element in repeating patterns using a variety of elements and Missing it! strategies attributes Colour Patterns • patterns using visuals (ten-frames, hundred charts) Pattern Error • investigating numerical patterns (e.g., skip-counting by 2s or 5s on a hundred chart) • beading using 3–5 colours change in quantity to 20, • verbally describing a change in quantity (e.g., I can build 7 and Composing numbers to 10 concretely and make it 10 by adding 3) Composing Numbers to 20 verbally

meaning of • demonstrating and explaining the meaning of equality and Composing numbers to 10 equality and inequality inequality • recording equations symbolically, using = and ≠ Composing Numbers to 20

5 © 3P Learning British Columbia Curriculum K-9 Alignment with Mathletics

BC Grade 1

Content Elaborations Activities • Non-uniform units are not consistent in size (e.g., children’s hands, pencils); uniform units are consistent in size (e.g., interlocking cubes, standard paper clips). • understanding the importance of using a baseline for direct comparison in linear measurement direct • using multiple copies of a unit measurement • iterating a single unit for measuring (e.g., to measure the Measuring Length with Blocks with non- length of a string with only one cube, a student iterates the Compare Length standard units cube over and over, keeping track of how many cubes long (non-uniform and the string is) uniform) • tiling an area • rope knots at intervals • using body parts to measure • book: An Anishnaabe Look at Measurement, by Rhonda Hopkins and Robin King-Stonefish • hand/foot tracing for mitten/moccasin making • sorting 3D objects and 2D shapes using one attribute, and explaining the sorting rule comparison of • comparing 2D shapes and 3D objects in the environment Match the Solid 1 2D shapes and • describing relative positions, using positional language (e.g., Collect Simple Shapes 3D objects up and down, in and out) Left or Right? • replicating composite 2D shapes and 3D objects (e.g., putting two triangles together to make a square) concrete graphs, Comparing groups of objects using one-to-one • creating, describing, and comparing concrete graphs correspondence Picture Graphs: More or Less likelihood of • using the language of probability (e.g., never, sometimes, familiar life always, more likely, less likely) events, using Chance Gauge • cycles (Elder or knowledge keeper to speak about comparative ceremonies and life events) language • identifying values of coins (nickels, dimes, quarters, loonies, and toonies) • counting multiples of the same denomination (nickels, financial literacy dimes, loonies, and toonies) — values of coins, • Money is a medium of exchange. Under review and monetary • role-playing financial transactions (e.g., using coins and exchanges whole numbers), integrating the concept of wants and needs • trade games, with understanding that objects have variable value or worth (shells, beads, furs, tools)

BC Grade 2

Big Ideas

• Numbers to 100 represent quantities that can be decomposed into 10s and 1s. • Development of computational fluency in addition and subtraction with numbers to 100 requires an understanding of place value. • The regular change in increasing patterns can be identified and used to make generalizations. • Objects and shapes have attributes that can be described, measured, and compared. • Concrete items can be represented, compared, and interpreted pictorially in graphs.

Content Elaborations Activities 1 to 30 Reading Numbers to 30 1st to 31st Counting forward Counting Backward • counting: o skip-counting by 2, 5, and 10: Going Up - using different starting points Going Down - increasing and decreasing (forward and backward) Before, After & Between to 100 • Quantities to 100 can be arranged and recognized: Arranging Numbers o comparing and ordering numbers to 100 Number Lines number o benchmarks of 25, 50, and 100 Number Line Order concepts to 100 o place value: Count by 2s, 5s and 10s - understanding of 10s and 1s Odd or Even - understanding the relationship between digit places and Place Value 1 their value, to 99 (e.g., the digit 4 in 49 has the value of 40) Making Numbers Count - decomposing two-digit numbers into 10s and 1s Making Big Numbers Count • even and odd numbers 1 More, 2 Less 1 More, 10 Less Greater or Less to 100 Repartition Two-digit Numbers Nearest Ten? benchmarks of 25, 50, and 100 Complements to 10, 20, 50 • seating arrangements at ceremonies/feasts and personal Complements to 50 and 100 referents Addition Facts All about Ten addition and All about Twenty subtractiton • adding and subtracting numbers to 20 Fact Families: Add and Subtract facts to 20 • fluency with math strategies for addition and subtraction Doubles and Halves to 10 (introduction of (e.g., making or bridging 10, decomposing, identifying related computational doubles, adding on to find the difference) Add 3 Numbers Using Bonds to 10 strategies) Doubles and Halves to 20 Related Facts 1 Problems: Addition and Subtraction 7 © 3P Learning British Columbia Curriculum K-9 Alignment with Mathletics

BC Grade 2

Content Elaborations Activities • decomposing numbers to 100 • estimating sums and differences to 100 Subtract Tens • using strategies such as looking for multiples of 10, 10 More, 10 Less friendly numbers (e.g., 48 + 37, 37 = 35 + 2, 48 + 2, 50 + Adding to 2-digit numbers 35 = 85), decomposing into 10s and 1s and recomposing Mental Addition addition and (e.g., 48 + 37, 40 + 30 = 70, 8 +7 = 15, 70 +15 = 85), and Mental Subtraction subtraction to compensating (e.g., 48 + 37, 48 +2 = 50, 37 – 2 = 35, Repartition to Subtract/Decompose 100 50 + 35 = 80) numbers to subtract • adding up to find the difference Partition Puzzles 1 • using an open number line, hundred chart, ten-frames Bar Model Problems 1 • using addition and subtraction in real-life contexts and Bar Model Problems 2 problem-based situations Add 3 Numbers: Bonds to Multiples of 10 • whole-class number talks Complete the Pattern Simple Patterns • exploring more complex repeating patterns (e.g., Missing it! positional patterns, circular patterns) Colour Patterns • identifying the core of repeating patterns (e.g., the pattern Pattern Error repeating and of the pattern that repeats over and over) Count by Twos increasing • increasing patterns using manipulatives, sounds, actions, patterns and numbers (0 to 100) Counting by Twos • Métis finger weaving Count by Fives • First Peoples head/armband patterning Counting by Fives • online video and text: Small Number Counts to 100 Count by Tens Counting by Tens Counting on a 100 grid change in quantity, • numerically describing a change in quantity (e.g., for 6 + n using pictorial = 10, visualize the change in quantity by using ten-frames, Under review and symbolic hundred charts, etc.) representation symbolic representation Composing numbers to 10 Under review of equality and Composing Numbers to 20 inequality direct linear • centimetres and metres measurement, • estimating length Ordering Length (cm) introducing • measuring and recording length, height, and width, using standard metric How Long is That? standard units units • sorting 2D shapes and 3D objects, using two attributes, and explaining the sorting rule Sort It multiple • describing, comparing, and constructing 2D shapes, Match the Object attributes of 2D including triangles, squares, rectangles, circles Collect the Polygons shapes and 3D • identifying 2D shapes as part of 3D objects objects • usin g traditional northwest coast First Peoples shapes Count Sides and Corners (ovoids, U, split U, and local art shapes) reflected in the Relate Shapes and Solids natural environment © 3P Learning 8 British Columbia Curriculum K-9 Alignment with Mathletics

BC Grade 2

Content Elaborations Activities

pictorial Comparing groups of objects representation • collecting data, creating a concrete graph, and representing the Picture Graphs: More or Less of concrete graph, using a pictorial representation through grids, stamps, graphs, using drawings Picture Graphs: Single-Unit one-to-one • one-to-one correspondence Scale correspondence Tallies likelihood of familiar life • using comparative language (e.g., certain, uncertain; more, less, or events, using Chance Gauge equally likely) comparative language financial literacy — coin • counting simple mixed combinations of coins to 100 cents combinations to • introduction to the concepts of spending and saving, integrating the Skip Counting with Coins 100 cents, and concepts of wants and needs spending and • role-playing financial transactions (e.g., using bills and coins) saving

9 © 3P Learning British Columbia Curriculum K-9 Alignment with Mathletics

BC Grade 3

Big Ideas

• Fractions are a type of number that can represent quantities. • Development of computational fluency in addition, subtraction, multiplication, and division of whole numbers requires flexible decomposing and composing. • Regular increases and decreases in patterns can be identified and used to make generalizations. • Standard units are used to describe, measure, and compare attributes of objects’ shapes. • The likelihood of possible outcomes can be examined, compared, and interpreted.

Content Elaborations Activities • counting: Count Forward Patterns o skip-counting by any number from any starting point, increasing and Count Backward Patterns decreasing (i.e., forward and backward) Counting up in 4s o Skip-counting is related to multiplication. Counting up in 6s o investigating place-value based counting patterns (e.g., counting by 10s, 100s; bridging over a century; noticing the role of zero as Counting up in 7s a placeholder 698, 699, 700, 701; noticing the predictability of our Counting up in 8s number system) Model Numbers number • Numbers to 1000 can be arranged and recognized: Which is Bigger? concepts to o comparing and ordering numbers 1000 Which is Smaller? o estimating large quantities Compare Numbers to 20 • place value: Compare Numbers to 50 o 100s, 10s, and 1s Compare Numbers to 100 o understanding the relationship between digit places and their values, to 1000 (e.g., the digit 4 in 342 has the value of 40 or 4 tens) Place Value 2 o understanding the importance of 0 as a place holder (e.g., in the Place Value Partitioning number 408, the zero indicates that there are 0 tens) Understanding Place Value 1 • instructional resource: Math in a Cultural Context, by Jerry Lipka Nearest Hundred? Halves Is it Half? • Fractions are numbers that represent an amount or quantity. Halves and Quarters • Fractions can represent parts of a region, set, or linear model. Shade fractions • Fraction parts are equal shares or equal-sized portions of a whole or Thirds and Sixths unit. Counting with Fractions on a • Provide opportunities to explore and create fractions with concrete fraction Number Line materials. concepts Model Fractions • recording pictorial representations of fraction models and connecting to symbolic notation Part-Whole Rods 1 • equal partitioning Uneven partitioned shapes 1 • equal sharing, pole ratios as visual parts, medicine wheel, seasons Uneven partitioned shapes 2 Partition into Equal Parts Fraction Fruit Sets 1 Fraction Fruit Sets 2

BC Grade 3

Content Elaborations Activities Add 3 Numbers: Bonds to Multiples of 10 Add 3 Numbers: Bonds to 100 • using flexible computation strategies, involving taking Jump Add and Subtract apart (e.g., decomposing using friendly numbers and Split Add and Subtract compensating) and combining numbers in a variety of ways, Bump Add and Subtract addition and Compensation - Add regrouping subtraction to Compensation - Subtract • estimating sums and differences of all operations to 1000 1000 Magic Symbols 1 • using addition and subtraction in real-life contexts and Partition Puzzles 2 problem-based situations Pyramid Puzzles 1 • whole-class number talks Pyramid Puzzles 2 Estimate Sums Estimate Differences Addition Facts • adding and subtracting of numbers to 20 addition and All about Ten • demonstrating fluency with math strategies for addition and subtraction All about Twenty subtraction (e.g., decomposing, making and bridging 10, Fact Families: Add and Subtract facts to 20 related doubles, and commutative property) Add 3 Numbers Using Bonds to 10 (emerging • Addition and subtraction are related. Doubles and Halves to 10 computational • At the end of Grade 3, most students should be able to Doubles and Halves to 20 fluency) recall addition facts to 20. Related Facts 1 Problems: Addition and Subtraction Share the Treasure Groups Divide Into Equal Groups Fill the Jars Grouping in Twos • understanding concepts of multiplication (e.g., groups of, Dividing Twos arrays, repeated addition) Grouping in Fives • understanding concepts of division (e.g., sharing, grouping, Dividing Fives repeated subtraction) Grouping in Tens • Multiplication and division are related. Dividing Tens • Provide opportunities for concrete and pictorial Grouping in Threes representations of multiplication. Dividing Threes • Use games to develop opportunities for authentic practice of multiplication Frog Jump Multiplication multiplication computations. Frog Jump Division and division • looking for patterns in numbers, such as in a hundred Grouping in Fours concepts chart, to further develop understanding of multiplication Dividing Fours computation Grouping in Sixes • Connect multiplication to skip-counting. Dividing Sixes • Connect multiplication to division and repeated addition. Grouping in Sevens • Memorization of facts is not intended for this level. Dividing Sevens • fish drying on rack; sharing of food resources in First Peoples Grouping in Eights communities Dividing Eights Grouping in Nines Dividing Nines Multiplication Arrays Arrays 2 Model multiplication to 5 x 5 Arrays 1 11 © 3P Learning British Columbia Curriculum K-9 Alignment with Mathletics

BC Grade 3

Content Elaborations Activities • creating patterns using concrete, pictorial, and numerical increasing and representations Increasing Patterns decreasing • representing increasing and decreasing patterns in multiple ways Decreasing Patterns patterns • generalizing what makes the pattern increase or decrease (e.g., Pick the Next Number doubling, adding 2) pattern rules • from a concrete pattern, describing the pattern rule using words and using words numbers and numbers, • predictability in song rhythm and patterns Describing Patterns based on • Share examples of local First Peoples art with the class, and ask concrete students to notice patterns in the artwork. experiences Composing additions to 20 one-step Missing Numbers addition and • start unknown (e.g., n + 15 = 20 or + 15 = 20) Complements to 10, 20, 50 subtraction • change unknown (e.g., 12 + n = 20 or 12 + = 20) Missing Values equations with • result unknown (e.g., 6 + 13 = n or 6 + 13 = ) Complements to 50 and 100 an unknown • investigating even and odd numbers number Odd or Even Odd and Even Numbers 1 Metres and Kilometres Kilometre Conversions Perimeter of Shapes • linear measurements, using standard units (e.g., centimetre, metre, Bigger or smaller shape kilometre) Equal Areas • capacity measurements, using standard units (e.g., millilitre, litre) measurement, • Introduce concepts of perimeter, area, and circumference (the distance Area of Shapes using standard around); use of formula and pi to calculate not intended — the focus is Using a Litre units (linear, on the concepts. mass, and Ordering Volumes (l) • area measurement, using square units (standard and non-standard) capacity) Litre Conversions • mass measurements, using standard units (e.g., gram, kilogram) • estimation of measurements, using standard referents (e.g., If this cup Milliliters and Liters holds 100 millilitres, about how much does this jug hold?) How Heavy? How Heavy is it? Ordering Mass (g) Kilogram Conversions • understanding concepts of time (e.g., second, minute, hour, day, week, Months of the Year month, year) Months After and Before • understanding the relationships between units of time 1st to 31st time concepts • Telling time is not expected at this level. • estimating time, using environmental references and natural daily/ Days and Dates seasonal cycles, temperatures based on weather systems, traditional Time Conversions: Whole calendar Numbers 1

BC Grade 3

Content Elaborations Activities

• identifying 3D objects according to the 2D shapes of the faces Collect the Objects and the number of edges and vertices (e.g., construction of nets, skeletons) What Prism am I? • describing the attributes of 3D objects (e.g., faces, edges, What Pyramid am I? vertices) Prisms and Pyramids construction of • identifying 3D objects by their mathematical terms (e.g., sphere, Faces, Edges, and Vertices 1 3D objects cube, prism, cone, cylinder) • comparing 3D objects (e.g., How are rectangular prisms and How Many Faces? cubes the same or different?) How many Edges? • understanding the preservation of shape (e.g., the orientation of a How many corners? shape will not change its properties) • jingle dress bells, bentwood box, birch bark baskets, pithouses Faces, Edges and Vertices one-to-one Picture Graphs: More or Less correspondence • collecting data, creating a graph, and describing, comparing, and Picture Graphs: Single-Unit Scale with bar graphs, discussing the results Tallies pictographs, • choosing a suitable representation charts, and Analysing data tables Interpreting Data Tables • using comparative language (e.g., certain, uncertain; more, less, likelihood of or equally likely) simulated • developing an understanding of chance (e.g., tossing a coin Chance Gauge events, using creates a 50-50 chance of landing a head or tail; drawing from Chance Dial comparative a bag, using spinners, and rolling dice all simulate probability Fair Games language events) • story: The Snowsnake Game • counting mixed combinations of coins and bills up to $100: o totalling up a set of coins and bills o using different combinations of coins and bills to make the financial literacy same amount — fluency with • understanding that payments can be made in flexible ways (e.g., coins and bills cash, cheques, credit, electronic transactions, goods and services) Everyday Money to 100 dollars, • understanding that there are different ways of earning money to and earning and reach a financial goal (e.g., recycling, holding bake sales, selling payment items, walking a neighbour’s dog) • Using pictures of First Peoples trade items (e.g., dentalium shells, dried fish, or tools when available) with the values indicated on the back, have students play a trading game.

13 © 3P Learning British Columbia Curriculum K-9 Alignment with Mathletics

BC Grade 4

Big Ideas

• Fractions and decimals are types of numbers that can represent quantities. • Development of computational fluency and multiplicative thinking requires analysis of patterns and relations in multiplication and division. • Regular changes in patterns can be identified and represented using tools and tables. • Polygons are closed shapes with similar attributes that can be described, measured, and compared. • Analyzing and interpreting experiments in data probability develops an understanding of chance.

Content Elaborations Activities Going Up Going Down Before, After & Between to 100 Multiples Counting up in 4s Counting up in 6s Counting up in 7s • counting: Counting up in 8s o multiples Expanding Numbers o flexible counting strategies Place Value - Thousands

o whole number benchmarks Place Value 3 number • Numbers to 10 000 can be arranged and recognized: concepts to o comparing and ordering numbers Partition and Rename 2/ 10 000 o estimating large quantities Understanding Place Value 2 • place value: (CAN) o 1000s, 100s, 10s, and 1s Which Is Greater? o understanding the relationship between digit places and their value, Which Is Less? to 10 000 Smallest and largest numbers Put in Order 1 Descending Order Missing Numbers 1 Missing Numbers 2 Greater Than or Less Than? Greater Than or Less Than 1 Nearest Thousand? • Fractions and decimals are numbers that represent an amount or quantity. • Fractions and decimals can represent parts of a region, set, or linear decimals to Decimals from Words to Digits 1 model. hundredths • Fractional parts and decimals are equal shares or equal-sized Decimals on the Number Line portions of a whole or unit. • understanding the relationship between fractions and decimals

BC Grade 4

Content Elaborations Activities • comparing and ordering of fractions with common Compare Fractions 1a ordering and denominators Compare Fractions 1b comparing • estimating fractions with benchmarks (e.g., zero, half, whole) Comparing Fractions 1 fractions • using concrete and visual models • equal partitioning Compare Fractions 2 Add 3 Numbers: Bonds to Multiples of 10 Add 3 Numbers: Bonds to 100 Jump Add and Subtract Split Add and Subtract Bump Add and Subtract Compensation - Add Compensation - Subtract Magic Symbols 1 Partition Puzzles 2 Estimate Sums Estimate Differences Add Two 2-Digit Numbers • using flexible computation strategies, involving taking Add Three 2-Digit Numbers apart (e.g., decomposing using friendly numbers and Columns that Add compensating) and combining numbers in a variety of ways, Add 3-Digit Numbers addition and regrouping Add Three 1-Digit Numbers subtraction • estimating sums and differences to 10 000 to 10 000 • using addition and subtraction in real-life contexts and Add Two 2-Digit Numbers: Regroup problem-based situations Add Three 2-Digit Numbers: Regroup • whole-class number talks Add 3-Digit Numbers: Regroup Add Multi-Digit Numbers 1 Add Three 3-Digit Numbers: Regroup Adding Colossal Columns Subtract Numbers 3-Digit Differences Subtract Numbers: Regroup 2-Digit Differences: Regroup 3-Digit Differences: 1 Regrouping 3-Digit Differences: 2 Regroupings 3-Digit Differences with Zeros Columns that Subtract Subtracting Colossal Columns

15 © 3P Learning British Columbia Curriculum K-9 Alignment with Mathletics

BC Grade 4

Content Elaborations Activities Multiplication Properties Arithmetic Laws Multiply Multiples of 10 • understanding the relationships between multiplication and Multiply 3 single-digit numbers multiplication division, multiplication and addition, division and subtraction Grid Methods 1 and division of • using flexible computation strategies (e.g., decomposing, Multiply: 1-Digit Number two- or three- distributive principle, commutative principle, repeated addition Multiply: 1-Digit Number, Regroup digit numbers and repeated subtraction) by one-digit • using multiplication and division in real-life contexts and problem- Halve it! numbers based situations Divide: 1-Digit Divisor 1 • whole-class number talks Divide: 1-Digit Divisor 2 Bar model × ÷ Problems: Times and Divide Multiply and Divide Problems 1 • estimating decimal sums and differences addition and • using visual models, such as base 10 blocks, place-value mats, Decimal Complements subtraction of grid paper, and number lines Subtract Decimals 1 decimals to • using addition and subtraction in real-life contexts and problem- hundredths based situations Magic Symbols 2 • whole-class number talks Addition Facts All about Ten addition and All about Twenty subtraction • Provide opportunities for authentic practice, building on previous Fact Families: Add and Subtract facts to 20 grade-level addition and subtraction facts. Doubles and Halves to 10 (developing • flexible use of mental math strategies computational Add 3 Numbers Using Bonds to 10 fluency) Doubles and Halves to 20 Related Facts 1 Problems: Addition and Subtraction

BC Grade 4

Content Elaborations Activities Groups Grouping in Twos Grouping in Fives Grouping in Tens Grouping in Threes Grouping in Fours Grouping in Sixes Grouping in Sevens Grouping in Eights Grouping in Nines • Provide opportunities for concrete and pictorial Multiplication Problems 1 representations of multiplication. • building computational fluency Divide Into Equal Groups • Use games to provide opportunities for authentic Dividing Twos practice of multiplication computations. Dividing Fives • looking for patterns in numbers, such as in a hundred Dividing Tens chart, to further develop understanding of multiplication multiplication and division computation Dividing Threes facts to 100 (introductory • Connect multiplication to skip-counting. Dividing Fours computational strategies) • Connecting multiplication to division and repeated Dividing Sixes addition. • Memorization of facts is not intended for this level. Dividing Sevens • Students will become more fluent with these facts. Dividing Eights • using mental math strategies, such as doubling or Dividing Nines halving Multiplication Arrays • Students should be able to recall the following multiplication facts by the end of Grade 4 (2s, 5s, 10s). Arrays 2 Model multiplication to 5 × 5 Arrays 1 Frog Jump Multiplication Frog Jump Division Times Tables Multiplication Grids Multiplication Turn-Abouts Related Facts 2 Fact Families: Multiply and Divide Missing Numbers: × and ÷ facts • Change in patterns can be represented in charts, increasing and graphs, and tables. Skip Counting decreasing patterns, • using words and numbers to describe increasing and Counting on a 100 grid using tables and charts decreasing patterns Describing Patterns • fish tockss in lakes, life expectancies

17 © 3P Learning British Columbia Curriculum K-9 Alignment with Mathletics

BC Grade 4

Content Elaborations Activities • representing and explaining one-step equations with an unknown number algebraic • describing pattern rules, using words and numbers from Composing Numbers to 20 relationships concrete and pictorial representations among quantities Composing additions to 20 • planning a camping or hiking trip; planning for quantities and materials needed per individual and group over time one-step • one-step equations for all operations involving an unknown equations with number (e.g., + 4 = 15, 15 – = 11) Missing Numbers an unknown • start unknown (e.g., n + 15 = 20; 20 – 15 = ) Missing Values number, using all • change unknown (e.g., 12 + n = 20) Find the Missing Number 1 operations • result unknown (e.g., 6 + 13 = )

• understanding how to tell time with analog and digital clocks, Tell Time to the Hour (UK) using 12- and 24-hour clocks Hour Times • understanding the concept of a.m. and p.m. Tell Time to the Hour • understanding the number of minutes in an hour how to tell time • understanding the concepts of using a circle and of using Tell Time to the Half Hour (UK) with analog and fractions in telling time (e.g., half past, quarter to) Half Hour Times digital clocks, • telling time in five-minute intervals using 12- and Tell Time to the Half Hour • telling time to the nearest minute 24-hour clocks Quarter To and Quarter Past • First Peoples use of numbers in time and seasons, represented by seasonal cycles and moon cycles (e.g., how position of sun, Five Minute Times moon, and stars is used to determine times for traditional What is the Time? activities, navigation) 24 Hour Time • describing and sorting regular and irregular polygons based on multiple attributes regular and • investigating polygons (polygons are closed shapes with similar Collect the Polygons irregular polygons attributes) • Yup’ik border patterns Measuring Length perimeter of Perimeter of Shapes • using geoboards and grids to create, represent, measure, and regular and Perimeter: Squares and Rectangles calculate perimeter irregular shapes Perimeter: Triangles 2 Perimeter: Triangles 1 • using concrete materials such as pattern blocks to create designs that have a mirror image within them • First Peoples art, borders, birchbark biting, canoe building • Visit a structure designed by First Peoples in the local Symmetry line symmetry community and have the students examine the symmetry, Symmetry or Not? balance, and patterns within the structure, then replicate simple models of the architecture focusing on the patterns they noted in the original.

BC Grade 4

Content Elaborations Activities Picture Graphs: More or Less Picture Graphs: Single-Unit Scale Picture Graphs: with scale & half one-to-one symbols correspondence • many-to-one correspondence: one symbol represents Pictographs and many-to-one a group or value (e.g., on a bar graph, one square may Making Picture Graphs: With correspondence, represent five cookies) Scale using bar graphs and pictographs Tallies Analysing data Bar Graphs 1 Bar Graphs 2 • predicting single outcomes (e.g., when you spin using one spinner and it lands on a single colour) probability experiments • using spinners, rolling dice, pulling objects out of a bag Fair Games • recording results using tallies • Dene/Kaska hand games, Lahal stick games • making monetary calculations, including decimal notation in real-life contexts and problem-based financial literacy — Everyday Money situations monetary calculations, • applying a variety of strategies, such as counting up, How much Change? including making change counting back, and decomposing, to calculate totals and Who’s got the Money? with amounts to 100 make change dollars and making Money • making simple financial decisions involving earning, simple financial decisions spending, saving, and giving Money Problems: Four Operations • equitable trade rules

19 © 3P Learning British Columbia Curriculum K-9 Alignment with Mathletics

BC Grade 5

Big Ideas

•s Numberdescribe quantities that can be represented by equivalent fractions. • Computational fluency and flexibility with numbers extend to operations with larger (multi-digit) numbers. • Identified regularities in number patterns can be expressed in tables. • Closed shapes have area and perimeter that can be described, measured, and compared. • Data represented in graphs can be used to show many-to-one correspondence.

Content Elaborations Activities • counting: o multiples o flexible counting strategies o whole number benchmarks Increasing Patterns • Numbers to 1 000 000 can be arranged and recognized: Decreasing Patterns o comparing and ordering numbers Multiples o number estimating large quantities Numbers in Words concepts to • place value: Understanding Place Value 3 1 000 000 o 100 000s, 10 000s, 1000s, 100s, 10s, and 1s Rounding Numbers o understanding the relationship between digit places and Place Value to Millions their value, to 1 000 000 Numbers from Words to Digits 1 • First Peoples use unique counting systems (e.g., Tsimshian use of three counting systems, for animals, people and things; Tlingit counting for the naming of numbers e.g., 10 = two hands, 20 = one person) Decimals from Words to Digits 2 decimals to Under Review Decimals to Fractions 1 thousandths Decimals to Fractions 2 Equivalent Fractions on a Number Line 1 Equivalent Fractions on a Number Line 2 Equivalent Fraction Wall 1 equivalent Under Review Equivalent Fraction Wall 2 fractions The Equivalent Fraction Selecting Equivalent Fractions Simplify Fractions Comparing Fractions 2 Arranging Fractions • Two equivalent fractions are two ways to represent the same Compare Fractions 1a amount (having the same whole). Compare Fractions 1b whole- • comparing and ordering of fractions and decimals Compare Fractions 2 number, • addition and subtraction of decimals to thousandths Comparing Fractions 1 fraction, • estimating decimal sums and differences Decimals on a Number Line and decimal • estimating fractions with benchmarks (e.g., zero, half, whole) benchmarks Comparing Decimals 1 • equal partitioning Comparing Decimals Decimal Order Decimal Order 1 Nearest Whole Number © 3P Learning 20 British Columbia Curriculum K-9 Alignment with Mathletics

BC Grade 5

Content Elaborations Activities Add 3 Numbers: Bonds to Multiples of 10 Add 3 Numbers: Bonds to 100 Jump Add and Subtract Split Add and Subtract Bump Add and Subtract • using flexible computation strategies involving Compensation - Add taking apart (e.g., decomposing using friendly Compensation - Subtract numbers and compensating) and combining addition and Magic Symbols 1 numbers in a variety of ways, regrouping subtraction of whole Partition Puzzles 2 • estimating sums and differences to 10 000 numbers to 1 000 000 • using addition and subtraction in real-life Estimate Sums contexts and problem-based situations Estimate Differences • whole-class number talks Estimation: Add and Subtract Add Multi-Digit Numbers 1 Adding Colossal Columns Add Multi-Digit Numbers 2 Subtracting Colossal Columns Column Subtraction Multiplication Properties Arithmetic Laws Multiply Multiples of 10 Multiply 3 single-digit numbers Grid Methods 1 Multiply: 1-Digit Number Multiply: 1-Digit Number, Regroup Halve it! Divide: 1-Digit Divisor 1 • understanding the relationships between Divide: 1-Digit Divisor 2 multiplication and division, multiplication and Remainders by Arrays addition, and division and subtraction Remainders by Tables multiplication and • using flexible computation strategies (e.g., Divide: 1-Digit Divisor, Remainder division to three digits, decomposing, distributive principle, commutative Estimate Quotients including division with principle, repeated addition, repeated subtraction) remainders Bar model × ÷ • using multiplication and division in real-life Problems: Times and Divide contexts and problem-based situations Multiply and Divide Problems 1 • whole-class number talks Estimation: Multiply and Divide Multiply More Multiples of 10 Mental Methods Multiplication 1 Grid Methods 2 Grid Methods 3 Multiply 2 Digits Area Model Long Multiplication Estimate Products Mental Methods Division Mental Methods Division 1

21 © 3P Learning British Columbia Curriculum K-9 Alignment with Mathletics

BC Grade 5

Content Elaborations Activities Adding Decimals • estimating decimal sums and differences Add Decimals 2 addition and • using visual models such as base 10 blocks, place-value Subtract Decimals 2 subtraction of mats, grid paper, and number lines Adding and Subtracting Decimals decimals to • using addition and subtraction in real-life contexts and thousandths problem-based situations Decimal Complements • whole-class number talks Estimate Decimal Sums 1 Estimate Decimal Differences 1 Addition Facts • Provide opportunities for authentic practice, building on All about Ten addition and previous grade-level addition and subtraction facts. All about Twenty subtraction facts • applying strategies and knowledge of addition and subtraction Fact Families: Add and Subtract to 20 (extending facts in real-life contexts and problem-based situations, as Doubles and Halves to 10 computational well as when making math-to-math connections (e.g., for 800 Add 3 Numbers Using Bonds to 10 fluency) + 700, you can annex the zeros and use the knowledge of 8 + Doubles and Halves to 20 7 to find the total) Related Facts 1 Problems: Addition and Subtraction • Provide opportunities for concrete and pictorial representations of multiplication. Multiplication Arrays • Use games to provide opportunities for authentic practice of Arrays 2 multiplication computations. Model multiplication to 5 × 5 • looking for patterns in numbers, such as in a hundred chart, to Arrays 1 multiplication further develop understanding of multiplication computation Frog Jump Multiplication and division facts • Connect multiplication to skip-counting. Frog Jump Division to 100 (emerging • Connect multiplication to division and repeated addition. computational • Memorization of facts is not intended this level. Times Tables fluency) • Students will become more fluent with these facts. Multiplication Grids • using mental math strategies such as doubling and halving, Multiplication Turn-Abouts annexing, and distributive property Related Facts 2 • Students should be able to recall many multiplication facts by Fact Families: Multiply and Divide the end of Grade 5 (e.g., 2s, 3s, 4s, 5s, 10s). Missing Numbers: × and ÷ facts • developing computational fluency with facts to 100 rules for increasing and decreasing Describing Patterns patterns with Under Review Number Sequences Up to 1 Million words, numbers, Table of Values symbols, and variables one-step • solving one-step equations with a variable Missing Numbers: Variables equations with • expressing a given problem as an equation, using symbols Solve Equations: Multiply, Divide 1 variables (e.g., 4 + x = 15) Write an Equation: Word Problems

BC Grade 5

Content Elaborations Activities Bigger or smaller shape area measurement of Equal Areas Under Review squares and rectangles Area of Shapes Area: Squares and Rectangles • measuring area of squares and rectangles, using tiles, geoboards, grid paper • investigating perimeter and area and how they are relationships between related to but not dependent on each other Under Review area and perimeter • use traditional dwellings • Invite a local Elder or knowledge keeper to talk about traditional measuring and estimating techniques for hunting, fishing, and building. Time Conversions: Whole Numbers 1 Time Conversions: Whole Numbers 2 • understanding elapsed time and duration Time Conversions: Simple Fractions • applying concepts of time in real-life contexts and Time Conversions: Simple Decimals duration, using problem-based situations What Time Will it Be? measurement of time • daily and seasonal cycles, moon cycles, tides, Time Mentals journeys, events Elapsed Time Using Timetables Time Zones

• investigating 3D objects and 2D shapes, based on Collect the Objects multiple attributes What Pyramid am I? classification of prisms • describing and sorting quadrilaterals Prisms and Pyramids and pyramids • describing and constructing rectangular and Naming 3D Objects triangular prisms Collect the Shapes 2 • identifying prisms in the environment Collect More Shapes • single transformations (slide/translation, flip/ reflection, turn/rotation) single transformations • using concrete materials with a focus on the motion Flip, Slide, Turn of transformations • weaving, cedar baskets, designs Picture Graphs: More or Less Picture Graphs: Single-Unit Scale one-to-one Picture Graphs: with scale & half correspondence • many-to-one correspondence: one symbol represents symbols and many-to-one a group or value (e.g., on a bar graph, one square Pictographs correspondence, using may represent five cookies) Making Picture Graphs: With Scale double bar graphs Analysing data Bar Graphs 1 Bar Graphs 2

23 © 3P Learning British Columbia Curriculum K-9 Alignment with Mathletics

BC Grade 5

Content Elaborations Activities • predicting outcomes of independent events (e.g., when you spin using a spinner and it lands on a single colour) Possible Outcomes probability experiments, • predicting single outcomes (e.g., when you spin using a Counting Techniques 1 single events or outcomes spinner and it lands on a single colour) Introductory probability • using spinners, rolling dice, pulling objects out of a bag Find the Probability • representing single outcome probabilities using fractions • making monetary calculations, including making change and decimal notation to $1000 in real-life contexts and financial literacy— problem-based situations monetary calculations, • applying a variety of strategies, such as counting up, including making change Budgeting counting back, and decomposing, to calculate totals and with amounts to 1000 make change Money Problems: Four Operations dollars and developing • making simple financial plans to meet a financial goal simple financial plans • developing a budget that takes into account income and expenses

BC Grade 6

Big Ideas

• Mixed numbers and decimal numbers represent quantities that can be decomposed into parts and wholes. • Computational fluency and flexibility with numbers extend to operations with whole numbers and decimals. • Linear relations can be identified and represented using expressions with variables and line graphs and can be used to form generalizations. • Properties of objects and shapes can be described, measured, and compared using volume, area, perimeter, and angles. • Data from the results of an experiment can be used to predict the theoretical probability of an event and to compare and interpret.

Content Elaborations Activities Place Value to Billions Numbers from Words to Digits 2 Numbers from Words to Digits 3 Comparing Numbers Equal, Less or Greater than? small to large • place value from thousandths to billions, operations with Rounding Numbers numbers thousandths to billions Decimals from Words to Digits 1 (thousandths to • numbers used in science, medicine, technology, and media Decimal Place Value billions) • compare, order, estimate Decimals to Fractions 1 Comparing Decimals Decimal Order Decimal Order 1 Nearest Whole Number Rounding Decimals 1 multiplication Times Tables and division Multiplication Grids facts to 100 • mental math strategies (e.g., the double-double strategy to Multiplication Turn-Abouts (developing multiply 23 × 4) Related Facts 2 computational Fact Families: Multiply and Divide fluency) Missing Numbers: × and ÷ facts order of • includes the use of brackets, but excludes exponents Order of Operations 1 (BEDMAS) operations with • quotients can be rational numbers whole numbers Word Problems with Letters Multiples Least Common Multiple factors and Venn Diagram 1 multiples • prime and composite numbers, divisibility rules, factor trees, prime Factors — greatest factor phrase (e.g., 300 = 2² × 3 × 5² ) Find the Factor common • using graphic organizers (e.g., Venn diagrams) to compare factor and Greatest Common Factor numbers for common factors and common multiples least common Fit the Conditions 1 multiple Prime or Composite? Product of Prime Factors Prime Factoring

BC Grade 6

Content Elaborations Activities What fraction is Shaded 1 What Mixed Number Is Shaded? Identifying Fractions on a Number Line • using benchmarks, number line, and Identifying Fractions Beyond 1 common denominators to compare Mixed and Improper Fractions on a Number Line improper fractions Make Fair Shares and mixed and order, including whole numbers numbers • using pattern blocks, Cuisenaire Rods, Improper Fraction to Mixed Numeral fraction strips, fraction circles, grids Mixed to Improper Fractions • birchbark biting Converting Mixed and Improper Compare Fractions 2 Comparing Fractions 1 Arranging Fractions • comparing numbers, comparing Simplify Ratios: 2 Whole numbers introduction to quantities, equivalent ratios Equivalent Ratios ratios • part-to-part ratios and part-to-whole Word Problems: Ratio ratios Ratio Word Problems Modelling Percentages • using base 10 blocks, geoboard, Percents to Fractions whole-number 10×10 grid to represent whole number Percentages to Fractions (with and without simplification) percents and percents Fractions to Percentages (Non-Calculator) percentage • finding missing part (whole or percentage) Percents and Decimals discounts Match Decimals and Percentages 1 • 50% = = 0.5 = 50:100 Mixed decimal, percentage and fraction conversions 2 Percent of a Number (Mental) Multiply Decimals: 10, 100, 1000 Divide Decimals: 10, 100, 1000 Multiply Decimals and Powers of 10 • 0.125 × 3 or 7.2 ÷ 9 Divide Decimals by Powers of 10 100 1000 multiplication and • using base 10 block array Multiply Decimal by Whole Number division of decimals • birchbark biting Multiply Decimals: Area Model Multiply Decimals 1 Divide Decimal by Whole Number Estimate Decimal Operations • limited to discrete points in the first increasing and quadrant Describing Patterns decreasing • visual patterning (e.g., colour tiles) Table of Values patterns, using • Take 3 add 2 each time, 2n + 1, and 1 Increasing Patterns expressions, more than twice a number all describe Decreasing Patterns tables, and graphs the pattern 3, 5, 7, … as functional • graphing data on First Peoples Count Backward Patterns relationships language loss, effects of language Pattern Rules and Tables intervention one-step equations • preservation of equality (e.g., using a Missing Numbers: Variables with whole-number balance, algebra tiles) Solve Equations: Multiply, Divide 1 coefficients and solutions • 3x = 12, x + 5 = 11 Write an Equation: Word Problems © 3P Learning 26 British Columbia Curriculum K-9 Alignment with Mathletics

BC Grade 6

Content Elaborations Activities Perimeter Detectives 1 perimeter • A complex shape is a group of shapes with of complex Perimeter Detectives 2 shapes no holes (e.g., use colour tiles, pattern blocks, tangrams). Perimeter: Triangles 1 • grid paper explorations area of triangles, • deriving formulas Area: Triangles parallelograms, and • making connections between area of trapezoids parallelogram and area of rectangle Area: Parallelograms (Metric) • birchbark biting • straight, acute, right, obtuse, reflex Equal Angles • constructing and identifying; include examples Comparing Angles from local environment Right Angle Relation angle measurement and • estimating using 45°, 90°, and 180° as classification reference angles What Type of Angle 2? • angles of polygons Classifying Angles • Small Number stories: Small Number and the Measuring Angles Skateboard Park Estimating Angles • using cubes to build 3D objects and determine their volume Volume of Solids and Prisms - 1 cm³ blocks • referents and relationships between units (e.g., volume and capacity cm³, m³, mL, L) How many Blocks? • the number of coffee mugs that hold a litre Capacity Word Problems • berry baskets, seaweed drying • scalene, isosceles, equilateral Triangles: Acute, Right, Obtuse triangles • right, acute, obtuse Triangle - Tasters • classified regardless of orientation • plotting points on Cartesian plane using whole-number ordered pairs • translation(s), rotation(s), and/or reflection(s) on a single 2D shape combinations of Transformations • limited to first quadrant transformations Coordinate Graphs: 1st Quadrant • transforming, drawing, and describing image • Use shapes in First Peoples art to integrate printmaking (e.g., Inuit, Northwest coastal First Nations, frieze work) • table of values, data set; creating and Line Graphs: Reading line graphs interpreting a line graph from a given set of data Graphing from a Table of Values • single-outcome probability events (e.g., spin a spinner, roll a die, toss a coin) single-outcome Possible Outcomes • listing all possible outcomes to determine Counting Techniques 1 probability, both theoretical probability theoretical and Introductory probability experimental • comparing experimental results with theoretical expectation Find the Probability • Lahal stick games • informed decision making on saving and financial literacy — purchasing Budgeting simple budgeting and consumer math • How many weeks of allowance will it take to Money Problems: Four Operations buy a bicycle? 27 © 3P Learning British Columbia Curriculum K-9 Alignment with Mathletics

BC Grade 7

Big Ideas

• Decimals, fractions, and percents are used to represent and describe parts and wholes of numbers. • Computational fluency and flexibility with numbers extend to operations with integers and decimals. • Linear relations can be represented in many connected ways to identify regularities and make generalizations. • The constant ratio between the circumference and diameter of circles can be used to describe, measure, and compare spatial relationships. • Data from circle graphs can be used to illustrate proportion and to compare and interpret.

Content Elaborations Activities Times Tables Missing Numbers: × and ÷ facts Multiplying by 10, 100, 1000 Dividing by 10, 100, 1000 Multiply Multiples of 10 Multiply More Multiples of 10 Multiply 3 single-digit numbers multiplication and Arithmetic Laws division facts to • When multiplying 214 by 5, we can multiply by 10, Estimate Products 100 (extending then divide by 2 to get 1070. Mental Methods Multiplication 1 computational fluency Mental Methods Multiplication 2 Mental Methods Multiplication 3 Multiply 2 Digits Area Model Estimate Quotients Mental Methods Division Mental Methods Division 1 Mental Methods Division 2 Mental Methods Division 3 Integers on a Number Line Ordering Integers (Number Line) Comparing Integers Negative or Positive? • addition, subtraction, multiplication, division, and Integers: Add and Subtract order of operations operations with integers More with Integers • concretely, pictorially, symbolically (addition, subtraction, • order of operations includes the use of brackets, Add Integers multiplication, excludes exponents Integers: Subtraction division, and order of • using two-sided counters Adding Integers: Positive, Negative or Zero operations) • 9 – (–4) = 13 because –4 is 13 away from +9 Integers: Multiplication and Division • extending whole-number strategies to decimals Multiplying and Dividing Integers Order of Operations 1 (BEDMAS) Integers: Order of Operations (BEDMAS) Identifying Errors in Applying the Order of Operations © 3P Learning 28 British Columbia Curriculum K-9 Alignment with Mathletics

BC Grade 7

Content Elaborations Activities Adding Decimals Subtract Decimals 2 Adding and Subtracting Decimals Decimal Complements operations with Multiply Decimals: 10, 100, 1000 decimals (addition, Multiply Decimal by Whole Number subtraction, • includes the use of brackets, but Multiply Decimals: Area Model multiplication, excludes exponents Decimal by Decimal division, and order Multiply Decimals 1 of operations Divide Decimal by Whole Number Divide Decimal by Decimal Estimate Decimal Sums 1 Estimate Decimal Differences 1 Estimate Decimal Operations Decimals to Fractions 2 Fractions to Decimals Fractions to Decimals 2 Fraction to Terminating Decimal Modelling Percentages • conversions, equivalency, and Percentages to Fractions (with and without simplification) terminating versus repeating decimals, Common Fractions as Percentages relationships place value, and benchmarks Fractions to Percentages (Non-Calculator) between decimals, • comparing and ordering decimals and Fractions to Percentages (Calculator) fractions, ratios, fractions using the number line Mixed decimal, percentage and fraction conversions and percents 1 • = 0.5 = 50% = 50:100 Match Decimals and Percentages 2 Calculating Percentages (Mental) • shoreline cleanup Percentage of an amount using Fractions (<100%) Percentage of an amount using Decimals (calculator) Quantities to Percentages (no units) Quantities to Percentages (with units) What percentage? Complementary Percentages • four quadrants, limited to integral coordinates • 3n + 2; values increase by 3 starting discrete linear from Table of Values relations, using - intercept of 2 y Graphing from a Table of Values expressions, tables, • deriving relation from the graph or and graphs table of values Reading Values from a Line • Small Number stories: Small Number and the Old Canoe, Small Number Counts to 100

BC Grade 7

Content Elaborations Activities two-step equations • solving and verifying 3x + 4 = 16 with whole-number • modelling the preservation of equality (e.g., using balance, coefficients, pictorial representation, algebra tiles) I am Thinking of a Number! constants, and • spirit canoe trip pre-planning and calculations solutions • Small Number stories: Small Number and the Big Tree • constructing circles given radius, diameter, area, or circumference • finding relationships between radius, diameter, circumference, and area to develop C = π x d formula Labelling Circles circumference and • applying A = π x r x r formula to find the area given radius Calculate circumference of circles area of circles or diameter Area: Circles 1 • drummaking, dreamcatcher making, stories of Area: Annulus SpiderWoman (Dene, Cree, Hopi, Tsimshian), basket making, quill box making (Note: Local protocols should be considered when choosing an activity.) • volume = area of base x height • bentwood boxes, wiigwaasabak and mide-wiigwaas (birch volume of rectangular Volume: Rectangular Prisms 1 bark scrolls) prisms and cylinders • Exploring Math through Haida Legends: Culturally Volume: Cylinders Responsive Mathematics • origin, four quadrants, integral coordinates, connections to linear relations, transformations Cartesian coordinates Number Plane • overlaying coordinate plane on medicine wheel, beading on and graphing dreamcatcher, overlaying coordinate plane on Coordinate Graphs traditional maps • four quadrants, integral coordinates Transformations • translation(s), rotation(s), and/or reflection(s) on a single 2D combinations of Transformations: Coordinate Plane shape; combination of successive transformations of 2D transformations shapes; tessellations Horizontal and Vertical Change • First Peoples art, jewelry making, birchbark biting Rotations: Coordinate Plane • constructing, labelling, and interpreting circle graphs • translating percentages displayed in a circle graph into Sector Graphs circle graphs quantities and vice versa Sector Graph Angles • visual representations of tidepools or traditional meals on Creating a Sector Graph plates Relative Frequency experimental • experimental probability, multiple trials (e.g., toss two coins, Complementary Events probability with two roll two dice, spin a spinner twice, or a combination thereof) independent events • dice games Fair Games Dice and Coins Percentage Change: Increase and financial literacy— • financial percentage calculations Decrease financial percentage • sales tax, tips, discount, sale price GST Profit and Loss

BC Grade 8

Big Ideas

• Number represents, describes, and compares the quantities of ratios, rates, and percents. • Computational fluency and flexibility extend to operations with fractions. • Discrete linear relationships can be represented in many connected ways and used to identify and make generalizations. • The relationship between surface area and volume of 3D objects can be used to describe, measure, and compare spatial relationships. • Analyzing data by determining averages is one way to make sense of large data sets and enables us to compare and interpret

Content Elaborations Activities

perfect squares and • using colour tiles, pictures, or multi-link cubes Square Roots cubes • building the number or using prime factorization Square Roots 1 • finding the cube root of 125 Estimating Square Roots Estimating Cube Roots square and cube roots • finding the square root of 16 169 Prime Factoring • estimating the square root of 30 Square and Cube Roots Percentages greater than 100% to Mixed Numerals Percentages to Decimals • A worker’s salary increased 122% in three years. If Mixed numerals to Percentages greater her salary is now $93,940, what was it originally? than 100% percents less than 1 1 Decimals to percentages and greater than 100 • What is % of 1 billion? 2 Decimal to Percentage (decimal and fractional • The population of Vancouver increased by 3.25%. Percentage of a Quantity percents) What is the population if it was approximately 603,500 people last year? What percentage? • beading Percentage Word Problems Complementary Percentages Percentage Change: Increase and Decrease

BC Grade 8

Content Elaborations Activities Simplify Ratios: 2 Whole numbers Simplify Ratios: 3 Whole Numbers Simplify Ratios: Fractions Simplify Ratios: Mixed Numbers Simplify Ratios: Decimals Equivalent Ratios Ratio Word Problems: Ratio • two-term and three-term ratios, real-life examples Dividing a Quantity into a Ratio and problems Ratio Word Problems numerical proportional • A string is cut into three pieces whose lengths form Scale Measurement a ratio of 3:5:7. If the string was 105 cm long, how Floor Plans reasoning (rates, ratio, long are the pieces? Unitary Method proportions, and percent) • creating a cedar drum box of proportions that use Rates Word Problems ratios to create differences in pitch and tone Distance Travelled • paddle making Average Speed Time Taken Travel Graphs Rates Calculations Converting Rates Wages and Salaries Working Overtime Commission Piecework and Royalties Add: Common Denominator Add: No Common Denominator Add Like Mixed Numbers Add Unlike Mixed Numbers Subtract: Common Denominator Subtract: No Common Denominator One Take Fraction Subtract Like Mixed Numbers • includes the use of brackets, but excludes exponents Subtract Unlike Mixed Numbers • using pattern blocks or Cuisenaire Rods Mixed Numerals 1 9 4 Unit Fractions • simplifying ÷ × 7 − Fraction of an Amount operations with fractions 2 6 ( 5 ) (addition, subtraction, Multiply Fraction by Whole Number 1 1 1 Multiply Fraction by Fraction multiplication, division, • drumming and song: , , , whole notes, 2 4 8 Multiply Two Fractions 1 and order of operations) dot bars, rests = one beat Multiplying Fractions • changing tempos of traditional songs dependent on Multiply Mixed Numbers context of use Estimate Products with Fractions • proportional sharing of harvests based on family size Fraction Word Problems More Fraction Problems Using Reciprocals Divide by a Unit Fraction Divide Whole Number by Fraction Divide Fractions Visual Model Divide Fractions by Fractions 1 Dividing Fractions Divide Mixed Numbers © 3P Learning 32 British Columbia Curriculum K-9 Alignment with Mathletics

BC Grade 8

Content Elaborations Activities Pattern Rules and Tables • two-variable discrete linear relations discrete linear relations Find the Pattern Rule • expressions, table of values, and graphs (extended to larger Coordinate Graphs • scale values (e.g., tick marks on axis represent numbers, limited to 5 units instead of 1) Graphing from a Table of Values integers) • four quadrants, integral coordinates Reading Values from a Line Determining a Rule for a Line Writing Algebraic Expressions Algebra Tiles Recognising Like Terms expressions- writing Like Terms: Add, Subtract • using an expression to describe a relationship and evaluating using Like Terms: Add and Subtract • evaluating 0.5n - 3n + 25 if n = 14 substitution Algebraic Multiplication Algebraic Division Simple Substitution Complex Substitution • solving and verifying 3x - 4 = -12 two-step equations with • modelling the preservation of equality Solve Equations: Multiply, Divide 2 integer coefficients, (e.g., using a balance, manipulatives, algebra tiles, Solving Simple Equations constants, and solutions diagrams) Solve Two-Step Equations • spirit canoe journey calculations Nets • exploring strategies to determine the surface area Surface Area: Rectangular Prisms surface area and volume and volume of a regular solid using objects, a net, Surface Area: Triangular Prisms 1 of regular solids, including 3D design software Surface Area: Triangular Prisms triangular and other right • volume = area of the base × height Surface Area: Cylinders prisms and cylinders • surface area = sum of the areas of Volume: Rectangular Prisms 1 each side Volume of Triangular prisms Volume: Cylinders Hypotenuse of a Right Triangle Pythagoras: Find a Short Side • modelling the Pythagorean theorem (integers only) • finding a missing side of a right triangle Pythagoras: Find a short side • deriving the Pythagorean theorem (rounding needed) Pythagorean theorem • constructing canoe paths and landings given current Pythagoras: Find a Short Side on a river (decimal values) • First Peoples constellations Pythagorean Theorem Pythagoras and Perimeter Pythagorean Triads

BC Grade 8

Content Elaborations Activities • top, front, and side views of 3D objects • matching a given net to the 3D object it represents • drawing and interpreting top, front, and construction, views, and side views of 3D objects Teacher directed nets of 3D objects • constructing 3D objects with nets • using design software to create 3D objects from nets • bentwood boxes, lidded baskets, packs Mode Mean The Median Median central tendency • mean, median, and mode Mode from Frequency Table Mean from Frequency Table Median from Frequency Table Which Measure of Central Tendency? • solving and verifying 3x - 4 = -12 two-step equations with • modelling the preservation of equality Solve Equations: Multiply, Divide 2 integer coefficients, (e.g., using a balance, manipulatives, Solving Simple Equations constants, and solutions algebra tiles, diagrams) Solve Two-Step Equations • spirit canoe journey calculations Nets • exploring strategies to determine the Surface Area: Rectangular Prisms surface area and volume surface area and volume of a regular solid Surface Area: Triangular Prisms 1 of regular solids, including using objects, a net, 3D design software Surface Area: Triangular Prisms triangular and other right • volume = area of the base × height Surface Area: Cylinders prisms and cylinders • surface area = sum of the areas of Volume: Rectangular Prisms 1 each side Volume of Triangular prisms Volume: Cylinders Hypotenuse of a Right Triangle • modelling the Pythagorean theorem Pythagoras: Find a Short Side (integers only) • finding a missing side of a right triangle Pythagoras: Find a short side (rounding needed) • deriving the Pythagorean theorem Pythagorean theorem Pythagoras: Find a Short Side (decimal values) • constructing canoe paths and landings given current on a river Pythagorean Theorem • First Peoples constellations Pythagoras and Perimeter Pythagorean Triads

BC Grade 8

Content Elaborations Activities • top, front, and side views of 3D objects • matching a given net to the 3D object it represents construction, views, • drawing and interpreting top, front, and side and nets of 3D views of 3D objects Teacher directed objects • constructing 3D objects with nets • using design software to create 3D objects from nets • bentwood boxes, lidded baskets, packs Mode Mean The Median Median central tendency • mean, median, and mode Mode from Frequency Table Mean from Frequency Table Median from Frequency Table Which Measure of Central Tendency? • with two independent events: sample space (e.g., using tree diagram, table, Dice and Coins graphic organizer) theoretical Probability Tables probability with two • rolling a 5 on a fair die and flipping Probability With Replacement independent events 1 1 1 Venn Diagrams a head on a fair coin is 6 × 2 = 12 • deciding whether a spinner in a game is fair • coupons, proportions, unit price, products financial literacy— and services Best Buy best buys • proportional reasoning strategies (e.g., unit rate, equivalent fractions given prices and quantities)

BC Grade 9

Big Ideas

• The principles and processes underlying operations with numbers apply equally to algebraic situations and can be described and analyzed. • Computational fluency and flexibility with numbers extend to operations with rational numbers. • Continuous linear relationships can be identified and represented in many connected ways to identify regularities and make generalizations. • Similar shapes have proportional relationships that can be described, measured, and compared. • Analyzing the validity, reliability, and representation of data enables us to compare and interpret.

Content Elaborations Activities Add: Common Denominator Add: No Common Denominator No Common Denominator Common Denominator Add Like Mixed Numbers Add Unlike Mixed Numbers Subtract: Common Denominator Subtract: No Common Denominator One Take Fraction Subtract Like Mixed Numbers Subtract Unlike Mixed Numbers Mixed Numerals Add Mixed Numbers: Same Sign operations with • includes brackets and exponents Subtract Mixed Numbers: Signs Differ rational numbers 3 1 1 5 • simplifying Unit Fractions (addition, (- 4 ) ÷ 5 + ((− 3 ) × (− 2 )) subtraction, Fraction of an Amount multiplication, 4 ² • simplifying 1 - 2 Multiply Fraction by Whole Number division, and order ( 5 ) Multiply Two Fractions 1 of operations) • paddle making Multiplying Fractions Multiply Mixed Numbers Operations with Fractions Divide Mixed Numbers with Signs Estimate Products with Fractions Fraction Word Problems More Fraction Problems Order of Operations 1 (BEDMAS) Exponent form to numbers Order of Operations 2 (PEDMAS) Identifying Errors in Applying the Order of Operations Integers: Order of Operations (BEDMAS) Integers: Operations Order

BC Grade 9

Content Elaborations Activities • includes variable bases Exponents • 27 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128 ; Powers of Integers n4 = n × n × n × n

0 Exponent notation • exponent laws (e.g., 6 = 1; m1 = m; n5 × n³ = n8 ; Exponent Notation and Algebra 5 7 ³ 5 exponents and y 4 m m Properties of Exponents = y ; 5n 5³ × n³ 125n³; = ; 3 ( ) = = n Simplifying with Exponent Laws 1 exponent laws with y ( ) n5 whole-number 4 Multiplication with exponents ² 8 exponents and (3 ) = 3 ) Exponent Laws and Algebra • limited to whole-number exponents and whole-number Exponent Laws with Brackets exponent outcomes when simplified Multiplication and Division with Exponents The Zero Exponent • ( 3²) does not equal -3² - Zero Exponent and Algebra • 3x (x - 4) = 3x² - 12x Expanding Brackets Expanding with Negatives • variables, degree, number of terms, and coefficients, Expand then Simplify including the constant term Expanding Binomial Products • (x² + 2x - 4) + (2x² - 3x - 4) Special Binomial Products operations with Factoring polynomials, of • (5x - 7) - (2x + 3) Grouping in Pairs degree less than or • 2n(n + 7) equal to 2 Factoring Quadratics 1 15k² - 10k • Factoring Quadratics 2 5k Simplifying Algebraic Fractions by • using algebra tiles Factoring Algebraic Fractions 3 Factoring and Fractions 1 Graphing from a Table of Values Horizontal and Vertical Lines Determining a Rule for a Line y = ax Conversion Graphs • two-variable continuous linear relations; includes two-variable rational coordinates Linear Modelling linear relations, • horizontal and vertical lines Breakeven Point using graphing, • graphing relation and analyzing interpolation, and Slope of a Line • interpolating and extrapolating approximate values extrapolation Gradient • spirit canoe journey predictions and daily checks Gradients for Real Intercepts Equation of a Line 1 Equation from Point and Gradient Which Straight Line? 37 © 3P Learning British Columbia Curriculum K-9 Alignment with Mathletics

BC Grade 9

Content Elaborations Activities Solving Simple Equations Equations with Fractions Equations: Variables, Both Sides • includes distribution, variables on both sides of the equation, and collecting like terms Equations with Grouping Symbols • includes rational coefficients, constants, and Equations with Fractions 2 multi-step one-variable solutions Checking Solutions linear equations 2 • solving and verifying 1 + 2x = 3 - (x + 6) Find the Mistake 3 Substitution in Formulae • solving symbolically and pictorially Real Formulae Rearranging the Equation Equations to Solve Problems Metres and Kilometres Centimetres and Metres Converting cm and mm Converting Units of Length Operations with Length Simplify Ratios: 2 Whole numbers Simplify Ratios: 3 Whole Numbers • scale diagrams, similar triangles and polygons, Simplify Ratios: Fractions linear unit conversions Simplify Ratios: Mixed Numbers • limited to metric units Simplify Ratios: Decimals • drawing a diagram to scale that represents an enlargement or reduction of a given 2D shape Equivalent Ratios spatial proportional • solving a scale diagram problem by applying Ratio reasoning the properties of similar triangles, including Word Problems: Ratio measurements Dividing a Quantity into a Ratio • integration of scale for First Peoples mural work, use of traditional design in current First Ratio Word Problems Peoples fashion design, use of similar triangles Solve Proportions to create longhouses/models Similar Figures 1 Similar Figures Scale Factor Scale Scale Measurement Floor Plans Using Similar Triangles 1 Similar Triangles

BC Grade 9

Content Elaborations Activities Data Types Methods of Data Sampling Mode The Mean Median Data Extremes and Range • population versus sample, bias, ethics, sampling techniques, Mode from Frequency Table misleading stats Mean from Frequency Table • analyzing a given set of data (and/or its representation) and Median from Frequency Table statistics in society identifying potential problems related to bias, use of language, ethics, cost, time and timing, privacy, or cultural sensitivity Frequency Histograms • using First Peoples data on water quality, Statistics Canada Mode from Stem and Leaf Plot data on income, health, housing, population Median from Stem and Leaf Plot Stem and Leaf Plots with Range Double Stem and Leaf Plots Calculating Interquartile Range Box-and-Whisker Plots 1 Box-and-Whisker Plots 2 Skewness of Data Successive Discounts Simple Interest financial literacy — • banking, simple interest, savings, planned purchases Purchase Options simple budgets and • creating a budget/plan to host a First Peoples event transactions Compound Interest Compound Interest by Formula Depreciation

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