Mathematics Curriculum Elaborations K 5. Developed by Janice Novakowski, Jennifer Barker and Sandra Ball. June 2015

Transcription

1 Mathematics Curriculum Elaborations K 5 Developed by Janice Novakowski, Jennifer Barker and Sandra Ball June 2015 Kindergarten number concepts to 10 one- to- one correspondence conservation cardinality stable order counting sequencing 1 10 linking sets to numerals subitizing o ways to make 5 o perceptual subitizing (I see 5.) o conceptual subitizing (I see 4 and 1.) o compare quantities 1 10 o use concrete materials to show ways to make 5 decomposition of numbers to 10 o partitioning to 10 (decomposing and recomposing) o numbers can be arranged and recognized o benchmark of 5 and 10 o making 10 o part part whole thinking o use concrete materials to show ways to make 10 repeating patterns with two or three elements o sorting and classifying using a single attribute o identify patterns in the world o repeating patterns 2-3 elements o identify the core o represent repeating patterns various ways demonstrating an understanding of change in quantity to 10 using concrete materials o generalizing change by adding 1 o describing relationship through change concretely (i.e. how do I get from 4 to 6) equality as a balance and inequality as an imbalance o describe equality as a balance and inequality as an imbalance (i.e. using a pan balance to create a oncrete and visual model of this direct comparative measurement (linear, mass, capacity) o understanding the importance of using a baseline for direct comparison in linear measurement o linear- height, width, length ( i.e. longer than, shorter than, taller than wider than) o mass (i.e. heavier than, lighter than, same as) o capacity (i.e. holds more, holds less) single attributes of 2D shapes and 3D objects o at this level, using specific math terminology to name and identify 2D shapes and 3D objects is not expected o sorting 2 D shapes and 3- D objects using a single attribute o build and describe 3 D objects (i.e. shaped like a can) o explore, create and describe2 D shapes o use positional language, such as beside, on top of, under and in front of the likelihood of familiar, life events o unlikely or likely ( i.e. Could it snow tomorrow?) concrete and pictorial graphs as a visual tool for the class o teachers may con- create concrete and pictorial graphs with their students to model the purpose of graphs and provide opportunities for mathematical discussions (i.e. survey the students as how they got to school and represent the data in a graph and discuss together as a class) Financial Literacy attributes of coins and monetary role play o noticing attributes of the Canadian coins (colour, size, pictures) o identifying the names of the coins o Role play of financial transactions dramatic play such as a restaurant, bakery, or store using whole numbers to combine purchases (i.e. a muffin is $2.00, and a juice is $1.00) integrating the concepts of wants and needs

2 Grade 1 number concepts to 20 counting on and counting back skip counting by 2 and 5 sequence numbers to 20 compare and order numbers to 20 numbers to 20 can be arranged and recognized subitizing base ten ten and some more ways to make 10 o decomposing 10 into parts o numbers to 10 can be arranged and recognized o benchmark of 10 and 20 addition and subtraction to 20 (understanding of operation and process) o decomposing 20 into parts o mental math strategies counting on making 10 doubles o addition and subtraction are related repeating patterns with multiple elements and attributes o identifying sorting rules o repeating patterns with multiple elements/attributes o translated from 1 representation to another o letter coding of pattern o predict an element in repeating patterns with a variety of strategies o patterns using visuals (10 frames, hundred charts) o numerical patterns (i.e. skip counting by 2s or 5s on a hundred chart) direct measurement with non- standard units (non- uniform units are not consistent in size such as children s hands, pencils and uniform are constant in size such as interlocking cubes, standard paper clips) o understanding the importance of using a baseline for direct comparison in linear measurement o using multiple copies of a unit o iteration of a single unit o tiling an area comparison of 2D shapes and 3D objects o sorting 3D objects and 2D shapes using 1 attribute and explain the sorting rule o compare 2D shapes and 3D objects in the environment o use relative positions, using positional language such as up, down, in and out o replicate composite 2D shapes and 3 D objects (i.e. putting 2 triangles together to make a square) concrete graphs using one- to- one correspondence o students create and describe and compare concrete graphs the likelihood of familiar events using comparative language o develop the language of probability (i.e. never, sometimes, always, or more likely, less likely) Financial Literacy identifying the value of coins and monetary exchanges o identifying values of coins (nickels, dimes, quarters, loonies and toonies ) o counting multiples of same denominations (nickels, dimes, looines, and toonies) o money is a medium of exchange o role play financial transactions (i.e. using coins and whole numbers) integrating the concepts of wants and needs demonstrating an understanding of change in quantity to 20 using concrete materials o describe the relationship through change verbally (i.e. I can build 7 and make it 10 by adding 3.) the meaning of equality and inequality o demonstrate and explain the meaning of equality and inequality o record equations symbolically using = and

3 Grade 2 number concepts to 100 o counting skip counting by 2, 5 10 using different starting points increasing and decreasing (forwards and backwards) o quantities to 100 can be arranged and recognized compare and order numbers to 100 benchmarks of 25, 50 and 100 place value understanding of 10s and 1 s understand the relationship of digit places and their value to 99 (i.e. the digit 4 in 49 has the value of 40) decompose 2 digit numbers into 10s and 1s introduction of computational fluency with addition and subtraction to 20 o adding and subtracting numbers to 20 o fluency with math strategies for addition and subtraction (i.e. making or bridging ten, decomposing, related doubles, adding on to find the difference) addition and subtraction to 100 o decomposing numbers to 100 o estimating sums and differences to 100 o using strategies such as looking for a multiples of ten (friendly numbers, i.e , 37 = 35 +2, , = 85), decomposing into 10s and 1s and recomposing (i.e , = 70, 8 +7 = 15, = 85) and compensating (i.e , = 50, 37 2 = 35, =80) o adding up to find the difference o using an open number line, hundred chart, ten frames symbolic representation of equality and inequality direct linear measurement, introducing standard metric units o centimetres and metres o estimating length o measuring and recording length, height, and width using standard units investigating 2D shapes and 3D objects, based on multiple attributes o sorting 2D shapes and 3 D objects using two attributes and explain the sorting rule o describe, compare and construct 2 D shapes including: triangles, squares, rectangles, circles o identify 2D shapes as part of 3D objects pictorial representation of concrete graphs o students collect data, create a concrete graph, and students represent the graph using a pictorial representation using grids, stamps, drawings o one to one correspondence the likelihood of events using comparative language o using comparative language such as certain, uncertain, or more, less or equally likely Financial Literacy- coin combinations to 100 cents and spending and saving o counting simple mixed combinations of coins to a 100 cents o introduction to the concepts of spending and saving integrating the concepts of wants and needs beginning spend choices o role play financial transactions (i.e. using bills and coins) repeating and increasing patterns o exploring more complex repeating patterns (i.e. positional patterns, circular patterns) o identify the core of repeating patterns (i.e. the pattern of the pattern that repeats over and over) o increasing patterns using manipulatives, sounds, actions and numbers (0 to 100) change in quantity using pictorial and symbolic representation o describe the relationship through change numerically (i.e. 6 + # = 10 visualize the change in quantity by using ten frames, hundreds charts etc.)

4 Grade 3 number concepts to 1000 skip counting by any number from any starting point, increasing and decreasing (i.e. forwards and backwards) skip counting is related to multiplication counting patterns are related to place value (i.e. bridging over a century, 698,699, 700, 701) o numbers to 1000 can be arranged and recognized compare and order numbers estimate large quantities o place value 100s, 10s and 1s understand the relationship of digit places and their values to 1000 (i.e. the digit 4 in 342 has the value of 40 or 4 tens) the importance of 0 as a place holder (i.e. in the number 408 the zero indicates there are 0 tens) fraction concepts o fractions are a number that represents an amount or quantity o fractions can represent parts of a region, set or linear model o fraction parts are equal shares or equal- sized portions of a whole or unit o opportunities to explore and create fractions with concrete materials o record pictorial representation of fraction models and connect to symbolic notation computational fluency with addition and subtraction to 20 o adding and subtracting of numbers to 20 o fluency with math strategies for addition and subtraction ( i.e. decomposing, making and bridging ten, related doubles and commutative property o addition and subtraction are related o at the end of Grade 3 most students should be able to recall addition facts to 20 addition and subtraction of numbers to 1000 o use of flexible strategies of computation involving taking apart (i.e. decomposing using friendly numbers and compensating) and combining numbers in a variety of ways o estimate sums and differences of all operations to 1000 multiplication and division concepts o understand concepts of multiplication (i.e. groups of, arrays, repeated addition) o understand concepts of division (i.e. sharing, grouping, repeated subtraction) o multiplication and division are related o opportunities for concrete and pictorial representations of multiplication o use of games to develop opportunities for authentic practice of multiplication computations o looking for patterns in numbers such as a hundred chart to further develop their understanding of multiplication computation o connect multiplication to skip counting o connect multiplication to division and repeated addition o memorization of facts is not intended for this level increasing and decreasing patterns o create patterns using concrete, pictorial and numbers o represent increasing and decreasing patterns in multiple ways o generalizing what makes the pattern increase or decrease (i.e. doubling, adding 2) pattern rules with words and numbers that come from concrete experiences o from a concrete pattern, describe the pattern rule using words and numbers one- step addition and subtraction equations involving an unknown number (e.g.: + 4 = 15) o start unknown (i.e. % + 15 = 20), change unknown ( i.e % = 20), result unknown (i.e = _ ) measurement using standard metric units (linear, mass, and capacity) o linear measurement using standard units (i.e. centimetre, metre, kilometre) o capacity measurements using standard units (i.e. millilitre, litre) o mass measurements using standard units (i.e. gram, kilogram,) o estimation of measurements using standard referents (i.e. If this cup holds 100 millilitres, about how much does this jug hold?) time concepts o understand concepts of time (i.e. second, minute, hour, day, week, month, year) o the relationship between the units of time o telling time in not expected at this level construction of 3D shapes, based on multiple attributes o identify 3 D shapes according to the 2D shapes of the faces and the number of edges and vertices (i.e. construction of nets, skeletons) o describe the attributes of 3 D shapes ( i.e. faces, edges, vertices) o identify 3 D shapes by their mathematical terms (i.e. spheres, cubes, prisms, cones, cylinders) o compare 3 D shapes ( i.e. How are rectangular prisms and cubes same or different? ) o understand the preservation of shape (e.g., the orientation of shape will not change its properties) one- to- one correspondences using bar graphs, pictographs, charts, and tables o students collect data, create a graph, describe, compare and discuss the results o choosing a suitable representation the likelihood of simulated events using comparative language o using comparative language such as certain, uncertain, or more, less or equally likely o develop an understanding of chance (i.e. The toss of a coin creates a chance of landing a head or tail chance. Drawing from a bag, spinners and roll of a die all simulate probability events.) Financial Literacy fluency of coins and bills to $100 and earning and payments o counting mixed combinations of coins and bills up to $100 totaling up a set of coins and bills different ways to use coins and bills to make the same amount o understanding payments can be made in flexible ways (i.e. cash, cheques, credit, electronic transactions, goods and services) o there are different ways of earning money to reach a financial goal (i.e. recycling, bake sales, sell items, walking the neighbour s dog)

5 Grade 4 number concepts to multiples flexible counting strategies whole number benchmarks o numbers to can be arranged and recognized compare and order numbers estimate large quantities o place value 1000s, 100s, 10s and 1s understand the relationship of digit places and their value to decimals to hundredths o fractions and decimals are numbers that represents an amount or quantity o fractions and decimals can represent parts of a region, set or linear model o fractional parts and decimals are equal shares or equal- sized portions of a whole or unit o understand the relationship between fractions and decimals ordering and comparing fractions o comparing and ordering of fractions with common denominators o estimate fractions with benchmarks (e.g., zero, half, whole) o use concrete and visual models addition and subtraction of whole numbers to o use of flexible strategies of computation involving taking apart (i.e. decomposing using friendly numbers and compensating) and combining numbers in a variety of ways o estimate sums and differences to multiplication and division of two- or- three digit numbers by one- digit numbers o understand the relationships between multiplication and division, multiplication and addition, division and subtraction o use the flexible strategies for computation ( i.e. decomposing, distributive principle, commutative principle, repeated addition and repeated subtraction) addition and subtraction using decimals to hundredths o estimate decimal sums and differences o use visual models such as base ten blocks, place value mats, grid paper and number lines computational fluency practice of addition and subtraction facts to 20 o authentic practice, building on previous grade level addition and subtraction facts introduction of computational fluency of multiplication and division facts to 100 o opportunities for concrete and pictorial representations of multiplication o use of games to develop opportunities for authentic practice of multiplication computations o looking for patterns in numbers such as a hundred chart to further develop their understanding of multiplication computation o connect multiplication to skip counting o connect multiplication to division and repeated addition o memorization of facts is not intended for this level o students will become more fluent with these facts o using mental math strategies such as doubling or halving o should be able to recall some familiar multiplication facts by the end of Grade 4 (i.e. 2s, 5s, 10s) increasing and decreasing patterns with the use of tables and charts o change in patterns can be represented in charts, graphs and tables o use words and numbers to describe the increasing and decreasing patterns algebraic relationships o represent and explain one- step equations with an unknown number o describe pattern rules using words and numbers from concrete and pictorial representations one- step equations with an unknown number using all operations o one- step equations for all operations involving an unknown number (e.g.: + 4 = 15) o start unknown (i.e. n + 15 = 20), change unknown ( i.e n = 20), result unknown (i.e = ) regular and irregular polygons o describe and sort regular and irregular polygons based on multiple attributes o investigating polygons; polygons are closed shapes with similar attributes o describe and sort quadrilaterals perimeter of regular and irregular shapes o use geoboards and grid to create, represent, measure and calculate perimeter telling of time o understand how to tell time with analogue and digital clocks using 12- and- 24 hour clocks o concept of am and pm o understand the number of minutes in an hour o understand the concept of using a circle and the notion of fractions in telling time such as half past, quarter to o telling time in five minute intervals o telling time to the nearest minute line symmetry o students use concrete materials such as pattern blocks to create designs that have a mirror image within them one- to- one correspondence and many- to- one correspondence using bar graphs, pictographs, charts, and tables o many- to- one correspondence means that one symbols represents a group or value (i.e. on a bar graph one square may represent 5 cookies) probability experiments o single outcomes (i.e. when you spin using one spinner and it lands on a single colour) o use spinners, roll die, pull objects out of a bag Financial Literacy monetary calculations including making change with amounts to $ and simple financial decisions o monetary calculations including decimal notation in real life contexts and problem based situations o apply a variety of strategies such as counting up, counting back and decomposing to calculate totals and make change o making simple financial decision involving earning, spending, saving and giving

6 Grade 5 number concepts to multiples flexible counting strategies whole number benchmarks o numbers to can be arranged and recognized compare and order numbers estimate large quantities o place value s, s. 1000s, 100s, 10s and 1s understand the relationship of digit places and their value to fractions and decimals to thousandths o two equivalent fractions are two ways to represent the same amount (having the same whole) o comparing and ordering of fractions and decimals o addition and subtraction of decimals to thousandths o estimate decimal sums and differences o estimate fractions with benchmarks (e.g., zero, half, whole) addition and subtraction of whole numbers to o use of flexible strategies of computation involving taking apart (i.e. decomposing using friendly numbers and compensating) and combining numbers in a variety of ways o estimate sums and differences to multiplication and division to three digit numbers including division with remainders o understand the relationships between multiplication and division, multiplication and addition, division and subtraction o use the flexible strategies for computation ( i.e. decomposing, distributive principle, commutative principle, repeated addition and repeated subtraction) o applying the use of multiplication and divisions in real life contexts and problem based situations addition and subtraction using decimals to hundredths o estimate decimal sums and differences o use visual models such as base ten blocks, place value mats, grid paper and number lines application of computational fluency of addition and subtraction facts to 20 o authentic practice, building on previous grade level addition and subtraction facts o apply strategies and their knowledge of addition and subtract facts in real life contexts and problem based situations, as well as when making math to math connections (i.e. when you can annex the zeros and use the knowledge of 8 +7 to find the total) computational fluency of multiplication and division facts to 100 o opportunities for concrete and pictorial representations of multiplication o use of games to develop opportunities for authentic practice of multiplication computations o looking for patterns in numbers such as a hundred chart to further develop their understanding of multiplication computation o connect multiplication to skip counting o connect multiplication to division and repeated addition o memorization of facts is not intended for this level o students will become more fluent with these facts o using mental math strategies such as doubling or halving o should be able to recall some familiar multiplication facts by the end of Grade 5 (i.e. 2s, 3 s, 4 s, 5s, 10s) pattern rules for increasing and decreasing patterns including words, numbers, symbols, and variables algebraic relationships o solve one- step equations with a variable o express a given problem as an equation using symbols (e.g.: 4 + X = 15) measuring time o understand elapsed time and duration o applying concepts of time in real life contexts and problem based situations investigating 3D objects and 2D shapes, based on multiple attributes o describe and sort quadrilaterals o describe and construct rectangular and triangular prisms and pyramids o identify prisms pyramids in the environment area and perimeter of square and rectangles o measure area of squares and rectangles using tiles, geoboards, grid paper o investigate perimeter and area and how they are related but not dependent on each other one- to- one correspondence and many- to- one correspondence using, double bar graphs o many- to- one correspondence means that one symbols represents a group or value (i.e. on a bar graph one square may represent 5 cookies) transformational geometry o single transformations (slide/translation, flip/reflection, turn/rotation) o students use concrete materials with a focus on the motion of transformations probability experiments o predict outcomes of independent events (i.e. when you spin using one spinner and it lands on a single colour) o single outcomes (i.e. when you spin using one spinner and it lands on a single colour) o use spinners, roll die, pull objects out of a bag Financial Literacy monetary calculations including making change to the amount of $1000 and simple financial plans o monetary calculations including making change and decimal notation to $1000 in real life contexts and problem based situations o apply a variety of strategies such as counting up, counting back and decomposing to calculate totals and make change o making simple financial plans towards a financial goal o develop a budget considering income and expenses