Grade 2 Mathematical Process

Grade 2 Mathematical Process

• 1.1 Problem Solving
  • 1.1.1 apply developing problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding;
    • Identify numbers as even or odd (2-A.7)
    • Skip-counting stories (2-A.11)
    • Skip-counting puzzles (2-A.12)
    • Addition word problems – one digit (2-E.11)
    • Add three or more one-digit numbers – word problems (2-E.16)
    • Subtraction with pictures (2-F.6)
    • Subtraction word problems – up to 18 (2-F.10)
    • Addition word problems – up to two digits (2-G.9)
    • Add three or more numbers up to two digits – word problems (2-G.14)
    • Subtraction word problems – up to two digits (2-H.9)
    • Fact families (2-K.3)
    • Solve inequalities using addition and subtraction shortcuts (2-K.5)
    • Guess the number (2-N.1)
    • Addition and subtraction word problems – up to 100 (2-X.8)
  • 1.2 Reasoning and Proving
    • 1.2.1 apply developing reasoning skills (e.g., pattern recognition, classification) to make and investigate conjectures (e.g., through discussion with others);
      • Repeating patterns (2-D.1)
      • Growing patterns (2-D.2)
      • Find the next shape in a pattern (2-D.3)
      • Complete a repeating pattern (2-D.4)
      • Make a repeating pattern (2-D.5)
      • Find the next row in a growing pattern (2-D.6)
      • Time patterns (2-P.10)
      • Sort shapes into a Venn diagram (2-Q.10)
      • Count shapes in a Venn diagram (2-Q.11)
    • 1.3 Reflecting
      • 1.3.1 demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by explaining to others why they think their solution is correct);
    • 1.4 Selecting Tools and Computational Strategies
      • 1.4.1 select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
        • Number lines – up to 100 (2-A.4)
        • Hundreds chart (2-A.5)
        • Write addition sentences for arrays: sums to 10 (2-E.18)
        • Write addition sentences for arrays: sums to 25 (2-E.20)
        • Place value models – tens and ones (2-L.1)
        • Place value models – up to hundreds (2-L.2)
        • Place value models – up to thousands (2-L.3)
        • Which shape illustrates the fraction? (2-V.3)
        • Fractions of a group (2-V.5)
        • Compare fractions using models (2-V.7)
        • Add and subtract integers using counters (7-C.2)
      • 1.5 Connecting
        • 1.5.1 make connections among simple mathematical concepts and procedures, and relate mathematical ideas to situations drawn from everyday contexts;
          • Greatest and least – word problems – up to 1,000 (2-B.6)
          • Addition word problems – one digit (2-E.11)
          • Add three or more one-digit numbers – word problems (2-E.16)
          • Subtraction word problems – up to 18 (2-F.10)
          • Addition word problems – up to two digits (2-G.9)
          • Add three or more numbers up to two digits – word problems (2-G.14)
          • Subtraction word problems – up to two digits (2-H.9)
          • Addition word problems – up to three digits (2-I.4)
          • Subtraction word problems – up to three digits (2-J.4)
          • Add and subtract money – up to $1 (2-O.8)
          • Add and subtract money – word problems – up to $1 (2-O.9)
          • Purchases – do you have enough money – up to $1 (2-O.13)
          • Metric units of length: word problems (2-R.10)
          • Shapes of everyday objects I (2-T.7)
          • Shapes of everyday objects II (2-T.8)
          • Perimeter – word problems (2-U.2)
          • Unit fractions: modelling word problems (2-V.4)
          • Fractions of a group: word problems (2-V.6)
          • Addition and subtraction word problems – up to 20 (2-X.3)
          • Addition and subtraction word problems – up to 100 (2-X.8)
        • 1.6 Representing
          • 1.6.1 create basic representations of simple mathematical ideas (e.g., using concrete materials; physical actions, such as hopping or clapping; pictures; numbers; diagrams; invented symbols), make connections among them, and apply them to solve problems;
            • Even or odd numbers on number lines (2-A.9)
            • Addition with pictures – sums to 20 (2-E.7)
            • Write addition sentences to describe pictures – sums to 20 (2-E.8)
            • Addition input/output tables – sums to 20 (2-E.9)
            • Identify repeated addition in arrays: sums to 10 (2-E.17)
            • Write addition sentences for arrays: sums to 10 (2-E.18)
            • Identify repeated addition in arrays: sums to 25 (2-E.19)
            • Write addition sentences for arrays: sums to 25 (2-E.20)
            • Subtraction with pictures (2-F.6)
            • Write subtraction sentences to describe pictures – up to 18 (2-F.7)
            • Subtraction input/output tables – up to 18 (2-F.8)
            • Write addition sentences to describe pictures (2-G.6)
            • Addition input/output tables – up to two digits (2-G.7)
            • Write subtraction sentences to describe pictures – up to two digits (2-H.6)
            • Subtraction input/output tables – up to two digits (2-H.7)
          • 1.7 Communicating
            • 1.7.1 communicate mathematical thinking orally, visually, and in writing, using everyday language, a developing mathematical vocabulary, and a variety of representations.
              • Addition and subtraction terms (1-T.9)
              • Writing numbers up to 100 in words (2-C.3)
              • Writing numbers up to 1,000 in words (2-C.4)
              • Distinguishing ordinal and cardinal numbers (2-C.5)
              • Roman numerals I, V, X, L (2-C.6)
              • Write addition sentences to describe pictures – sums to 20 (2-E.8)
              • Write the addition sentence – one digit (2-E.13)
              • Write addition sentences for arrays: sums to 10 (2-E.18)
              • Write addition sentences for arrays: sums to 25 (2-E.20)
              • Write subtraction sentences to describe pictures – up to 18 (2-F.7)
              • Write the subtraction sentence – up to 18 (2-F.12)
              • Write the addition sentence – up to two digits (2-G.11)
              • Write the subtraction sentence – up to two digits (2-H.11)
              • Write the addition sentence – up to three digits (2-I.6)
              • Write the subtraction sentence – up to three digits (2-J.6)
              • Write addition and subtraction sentences (2-X.12)

2.2 Number Sense and Numeration

• 2.1 Overall Expectations
  • 2.1.1 read, represent, compare, and order whole numbers to 100, and use concrete materials to represent fractions and money amounts to 100¢;
    • Comparing numbers up to 100 (2-B.1)
    • Put numbers up to 100 in order (2-B.3)
    • Greatest and least – word problems – up to 100 (2-B.5)
    • Coin values (2-O.1)
    • Count money – up to $1 (2-O.2)
    • Equivalent amounts of money – up to $1 (2-O.4)
    • Which shape illustrates the fraction? (2-V.3)
    • Fractions of a group (2-V.5)
  • 2.1.2 demonstrate an understanding of magnitude by counting forward to 200 and backwards from 50, using multiples of various numbers as starting points;
    • Counting forward and backward (1-A.11)
    • Counting patterns – up to 100 (2-A.3)
    • Number lines – up to 100 (2-A.4)
  • 2.1.3 solve problems involving the addition and subtraction of one- and two-digit whole numbers, using a variety of strategies, and investigate multiplication and division.
    • Review – add one-digit numbers – sums to 10 (2-E.1)
    • Add one-digit numbers (2-E.5)
    • Review – subtract one-digit numbers – up to 10 (2-F.1)
    • Subtract a one-digit number from a two-digit number up to 18 (2-F.5)
    • Add a two-digit and a one-digit number – without regrouping (2-G.2)
    • Add a two-digit and a one-digit number – with regrouping (2-G.3)
    • Write multiplication sentences for equal groups (2-Y.3)
    • Multiplication tables up to 5 (2-Z.2)
    • Multiplication tables up to 10 (2-Z.5)
    • Divisors and quotients up to 5 (2-AA.1)
    • Divisors and quotients up to 10 (2-AA.2)
  • 2.2 Quantity Relationships
    • 2.2.1 represent, compare, and order whole numbers to 100, including money amounts to 100¢, using a variety of tools (e.g., ten frames, base ten materials, coin manipulatives, number lines, hundreds charts and hundreds carpets);
      • Number lines – up to 100 (2-A.4)
      • Hundreds chart (2-A.5)
      • Comparing numbers up to 100 (2-B.1)
      • Put numbers up to 100 in order (2-B.3)
      • Which picture shows more – up to $1 (2-O.10)
      • Least number of coins (2-O.12)
      • Purchases – do you have enough money – up to $1 (2-O.13)
    • 2.2.2 read and print in words whole numbers to twenty, using meaningful contexts (e.g., storybooks, posters, signs);
      • Writing numbers up to 100 in words (2-C.3)
    • 2.2.3 compose and decompose two-digit numbers in a variety of ways, using concrete materials (e.g., place 42 counters on ten frames to show 4 tens and 2 ones; compose 37¢ using one quarter, one dime, and two pennies) (Sample problem: Use base ten blocks to show 60 in different ways.);
      • Place value models – tens and ones (2-L.1)
      • Regroup tens and ones (2-L.7)
      • Regroup tens and ones – ways to make a number (2-L.8)
      • Convert to/from a number – tens and ones (2-L.9)
      • Equivalent amounts of money – up to $1 (2-O.4)
      • Equivalent amounts of money – up to $5 (2-O.5)
      • Exchanging coins (2-O.6)
      • Comparing groups of coins (2-O.7)
      • Purchases – do you have enough money – up to $1 (2-O.13)
      • How much more to make a dollar? (2-O.15)
      • Making change (2-O.16)
    • 2.2.4 determine, using concrete materials, the ten that is nearest to a given two-digit number, and justify the answer (e.g., use counters on ten frames to determine that 47 is closer to 50 than to 40);
      • Estimate to the nearest ten (2-M.1)
      • Round to the nearest ten (2-M.2)
      • Estimate sums (2-M.5)
    • 2.2.5 determine, through investigation using concrete materials, the relationship between the number of fractional parts of a whole and the size of the fractional parts (e.g., a paper plate divided into fourths has larger parts than a paper plate divided into eighths) (Sample problem: Use paper squares to show which is bigger, one half of a square or one fourth of a square.);
      • Compare fractions using models (2-V.7)
    • 2.2.6 regroup fractional parts into wholes, using concrete materials (e.g., combine nine fourths to form two wholes and one fourth);
    • 2.2.7 compare fractions using concrete materials, without using standard fractional notation (e.g., use fraction pieces to show that three fourths are bigger than one half, but smaller than one whole);
      • Compare fractions using models (2-V.7)
    • 2.2.8 estimate, count, and represent (using the ¢ symbol) the value of a collection of coins with a maximum value of one dollar.
      • Count money – up to $1 (2-O.2)
      • Equivalent amounts of money – up to $1 (2-O.4)
      • Which picture shows more – up to $1 (2-O.10)
      • Purchases – do you have enough money – up to $1 (2-O.13)
      • How much more to make a dollar? (2-O.15)
    • 2.3 Counting
      • 2.3.1 count forward by 1’s, 2’s, 5’s, 10’s, and 25’s to 200, using number lines and hundreds charts, starting from multiples of 1, 2, 5, and 10 (e.g., count by 5’s from 15; count by 25’s from 125);
        • Skip-counting (2-A.1)
        • Skip-counting sequences (2-A.2)
        • Counting patterns – up to 100 (2-A.3)
        • Number lines – up to 100 (2-A.4)
        • Hundreds chart (2-A.5)
        • Skip-counting stories (2-A.11)
        • Skip-counting puzzles (2-A.12)
        • Number lines – up to 1,000 (2-A.13)
        • Counting patterns – up to 1,000 (2-A.14)
      • 2.3.2 count backwards by 1’s from 50 and any number less than 50, and count backwards by 10’s from 100 and any number less than 100, using number lines and hundreds charts (Sample problem: Count backwards from 87 on a hundreds carpet, and describe any patterns you see.);
        • Counting forward and backward (1-A.11)
      • 2.3.3 locate whole numbers to 100 on a number line and on a partial number line (e.g., locate 37 on a partial number line that goes from 34 to 41).
        • Number lines – up to 100 (2-A.4)
        • Even or odd numbers on number lines (2-A.9)
      • 2.4 Operational Sense
        • 2.4.1 solve problems involving the addition and subtraction of whole numbers to 18, using a variety of mental strategies (e.g., “To add 6 + 8, I could double 6 and get 12 and then add 2 more to get 14.”);
          • Review – add one-digit numbers – sums to 10 (2-E.1)
          • Review – ways to make a number – sums to 10 (2-E.2)
          • Review – writing addition sentences – sums to 10 (2-E.3)
          • Add doubles (2-E.4)
          • Add one-digit numbers (2-E.5)
          • Addition with pictures – sums to 20 (2-E.7)
          • Add zero (2-E.10)
          • Addition word problems – one digit (2-E.11)
          • Complete the addition sentence – one digit (2-E.12)
          • Write addition sentences for arrays: sums to 10 (2-E.18)
        • 2.4.2 describe relationships between quantities by using whole-number addition and subtraction (e.g., “If you ate 7 grapes and I ate 12 grapes, I can say that I ate 5 more grapes than you did, or you ate 5 fewer grapes than I did.”);
          • Addition word problems – one digit (2-E.11)
          • Subtraction word problems – up to 18 (2-F.10)
          • Addition word problems – up to two digits (2-G.9)
          • Subtraction word problems – up to two digits (2-H.9)
          • Addition word problems – up to three digits (2-I.4)
          • Subtraction word problems – up to three digits (2-J.4)
          • Addition and subtraction word problems – up to 20 (2-X.3)
          • Addition and subtraction word problems – up to 100 (2-X.8)
        • 2.4.3 represent and explain, through investigation using concrete materials and drawings, multiplication as the combining of equal groups (e.g., use counters to show that 3 groups of 2 is equal to 2 + 2 + 2 and to 3 x 2);
          • Identify repeated addition in arrays: sums to 10 (2-E.17)
          • Write addition sentences for arrays: sums to 10 (2-E.18)
          • Identify repeated addition in arrays: sums to 25 (2-E.19)
          • Write addition sentences for arrays: sums to 25 (2-E.20)
          • Write multiplication sentences for equal groups (2-Y.3)
        • 2.4.4 represent and explain, through investigation using concrete materials and drawings, division as the sharing of a quantity equally (e.g., “I can share 12 carrot sticks equally among 4 friends by giving each person 3 carrot sticks.”);
        • 2.4.5 solve problems involving the addition and subtraction of two-digit numbers, with and without regrouping, using concrete materials (e.g., base ten materials, counters), student-generated algorithms, and standard algorithms;
          • Add a two-digit and a one-digit number – without regrouping (2-G.2)
          • Add a two-digit and a one-digit number – with regrouping (2-G.3)
          • Add two two-digit numbers – without regrouping (2-G.4)
          • Add two two-digit numbers – with regrouping (2-G.5)
          • Subtract a one-digit number from a two-digit number – without regrouping (2-H.2)
          • Subtract a one-digit number from a two-digit number – with regrouping (2-H.3)
          • Subtract two two-digit numbers – without regrouping (2-H.4)
          • Subtract two two-digit numbers – with regrouping (2-H.5)
          • Add and subtract numbers up to 100 (2-X.6)
        • 2.4.6 add and subtract money amounts to 100¢, using a variety of tools (e.g., concrete materials, drawings) and strategies (e.g., counting on, estimating, representing using symbols).
          • Count money – up to $1 (2-O.2)
          • Equivalent amounts of money – up to $1 (2-O.4)
          • Add and subtract money – up to $1 (2-O.8)
          • Add and subtract money – word problems – up to $1 (2-O.9)
          • Which picture shows more – up to $1 (2-O.10)
          • Purchases – do you have enough money – up to $1 (2-O.13)
          • How much more to make a dollar? (2-O.15)
          • Making change (2-O.16)

2.3 Measurement

• 3.1 Overall Expectations
  • 3.1.1 estimate, measure, and record length, perimeter, area, mass, capacity, time, and temperature, using non-standard units and standard units;
    • Match analogue clocks and times (2-P.1)
    • Match digital clocks and times (2-P.2)
    • Match analogue and digital clocks (2-P.3)
    • Read clocks and write times (2-P.4)
    • Time words: o’clock, half, quarter (2-P.5)
    • Relate time units (2-P.11)
    • Months of the year (2-P.14)
    • Number of days in each month (2-P.15)
    • Read a calendar (2-P.16)
    • Long and short (2-R.1)
    • Tall and short (2-R.2)
    • Light and heavy (2-R.3)
    • Holds more or less (2-R.4)
    • Compare size, mass and capacity (2-R.5)
    • Read a thermometer (2-R.6)
    • Measure using a centimetre ruler (2-R.8)
    • Which metric unit of length is appropriate? (2-R.9)
    • Metric units of length: word problems (2-R.10)
    • Which metric unit of mass is appropriate? (2-R.11)
    • Which metric unit of volume is appropriate? (2-R.12)
    • Compare and convert metric units of volume (2-R.13)
    • Compare and convert metric units of mass (2-R.14)
    • Choose the appropriate measuring tool (2-R.15)
    • Select figures with a given area (2-U.4)
  • 3.1.2 compare, describe, and order objects, using attributes measured in non-standard units and standard units.
    • Long and short (2-R.1)
    • Tall and short (2-R.2)
    • Light and heavy (2-R.3)
    • Holds more or less (2-R.4)
    • Compare size, mass and capacity (2-R.5)
    • Compare and convert metric units of volume (2-R.13)
    • Compare and convert metric units of mass (2-R.14)
    • Select two-dimensional shapes (2-S.2)
    • Count sides and vertices (2-S.3)
    • Compare sides and vertices (2-S.4)
    • Select three-dimensional shapes (2-T.2)
    • Count vertices, edges and faces (2-T.3)
    • Compare vertices, edges and faces (2-T.4)
  • 3.2 Attributes, Units, and Measurement Sense
    • 3.2.1 choose benchmarks –in this case, personal referents — for a centimetre and a metre (e.g., “My little finger is about as wide as one centimetre. A really big step is about one metre.”) to help them perform measurement tasks;
    • 3.2.2 estimate and measure length, height, and distance, using standard units (i.e., centimetre, metre) and non-standard units;
      • Measure using a centimetre ruler (2-R.8)
      • Which metric unit of length is appropriate? (2-R.9)
    • 3.2.3 record and represent measurements of length, height, and distance in a variety of ways (e.g., written, pictorial, concrete) (Sample problem: Investigate how the steepness of a ramp affects the distance an object travels. Use cash-register tape for recording distances.);
    • 3.2.4 select and justify the choice of a standard unit (i.e., centimetre or metre) or a nonstandard unit to measure length (e.g., “I needed a fast way to check that the two teams would race the same distance, so I used paces.”);
      • Which metric unit of length is appropriate? (2-R.9)
    • 3.2.5 estimate, measure, and record the distance around objects, using non-standard units (Sample problem: Measure around several different doll beds using string, to see which bed is the longest around.);
    • 3.2.6 estimate, measure, and record area, through investigation using a variety of non-standard units (e.g., determine the number of yellow pattern blocks it takes to cover an outlined shape) (Sample problem: Cover your desk with index cards in more than one way. See if the number of index cards needed stays the same each time.);
    • 3.2.7 estimate, measure, and record the capacity and/or mass of an object, using a variety of non-standard units (e.g., “I used the pan balance and found that the stapler has the same mass as my pencil case.”);
    • 3.2.8 tell and write time to the quarter-hour, using demonstration digital and analogue clocks (e.g., “My clock shows the time recess will start [10:00], and my friend’s clock shows the time recess will end [10:15].”);
      • Match analogue clocks and times (2-P.1)
      • Match digital clocks and times (2-P.2)
      • Match analogue and digital clocks (2-P.3)
      • Read clocks and write times (2-P.4)
      • Time words: o’clock, half, quarter (2-P.5)
    • 3.2.9 construct tools for measuring time intervals in non-standard units (e.g., a particular bottle of water takes about five seconds to empty);
    • 3.2.10 describe how changes in temperature affect everyday experiences (e.g., the choice of clothing to wear);
    • 3.2.11 use a standard thermometer to determine whether temperature is rising or falling (e.g., the temperature of water, air).
      • Read a thermometer (2-R.6)
    • 3.3 Measurement Relationships
      • 3.3.1 describe, through investigation, the relationship between the size of a unit of area and the number of units needed to cover a surface (Sample problem: Compare the numbers of hexagon pattern blocks and triangle pattern blocks needed to cover the same book.);
        • Area (2-U.3)
        • Create figures with a given area (2-U.5)
      • 3.3.2 compare and order a collection of objects by mass and/or capacity, using non-standard units (e.g., “The coffee can holds more sand than the soup can, but the same amount as the small pail.”);
        • Holds more or less (2-R.4)
      • 3.3.3 determine, through investigation, the relationship between days and weeks and between months and years.
        • Days of the week (2-P.13)
        • Months of the year (2-P.14)

2.4 Geometry and Spatial Sense

• 4.1 Overall Expectations
  • 4.1.1 identify two-dimensional shapes and three-dimensional figures and sort and classify them by their geometric properties;
    • Name the two-dimensional shape (2-S.1)
    • Select two-dimensional shapes (2-S.2)
    • Count sides and vertices (2-S.3)
    • Compare sides and vertices (2-S.4)
    • Name the three-dimensional shape (2-T.1)
    • Select three-dimensional shapes (2-T.2)
    • Count vertices, edges and faces (2-T.3)
    • Compare vertices, edges and faces (2-T.4)
  • 4.1.2 compose and decompose two-dimensional shapes and three-dimensional figures;
    • Identify shapes traced from solids (2-T.5)
    • Identify faces of three-dimensional shapes (2-T.6)
    • Nets of three-dimensional figures (4-P.6)
  • 4.1.3 describe and represent the relative locations of objects, and represent objects on a map.
    • Left, middle and right (1-O.3)
    • Top, middle and bottom (1-O.4)
    • Location in a grid (1-O.5)
  • 4.2 Geometric Properties
    • 4.2.1 distinguish between the attributes of an object that are geometric properties (e.g., number of sides, number of faces) and the attributes that are not geometric properties (e.g., colour, size, texture), using a variety of tools (e.g., attribute blocks, geometric solids, connecting cubes);
    • 4.2.2 identify and describe various polygons (i.e., triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons) and sort and classify them by their geometric properties (i.e., number of sides or number of vertices), using concrete materials and pictorial representations (e.g., “I put all the figures with five or more vertices in one group, and all the figures with fewer than five vertices in another group.”);
      • Name the two-dimensional shape (1-M.1)
      • Count sides and vertices (1-M.3)
      • Compare sides and vertices (1-M.4)
      • Name the two-dimensional shape (2-S.1)
      • Select two-dimensional shapes (2-S.2)
      • Count sides and vertices (2-S.3)
      • Compare sides and vertices (2-S.4)
    • 4.2.3 identify and describe various three-dimensional figures (i.e., cubes, prisms, pyramids) and sort and classify them by their geometric properties (i.e., number and shape of faces), using concrete materials (e.g., “I separated the figures that have square faces from the ones that don’t.”);
      • Name the three-dimensional shape (1-N.2)
      • Count vertices, edges and faces (1-N.5)
      • Compare vertices, edges and faces (1-N.6)
      • Count sides and vertices (2-S.3)
      • Compare sides and vertices (2-S.4)
      • Name the three-dimensional shape (2-T.1)
      • Select three-dimensional shapes (2-T.2)
      • Count vertices, edges and faces (2-T.3)
      • Compare vertices, edges and faces (2-T.4)
    • 4.2.4 create models and skeletons of prisms and pyramids, using concrete materials (e.g., cardboard; straws and modelling clay), and describe their geometric properties (i.e., number and shape of faces, number of edges);
      • Identify shapes traced from solids (1-N.7)
      • Count sides and vertices (2-S.3)
      • Count vertices, edges and faces (2-T.3)
      • Identify faces of three-dimensional shapes (2-T.6)
      • Nets of three-dimensional figures (4-P.6)
    • 4.2.5 locate the line of symmetry in a two-dimensional shape (e.g., by paper folding; by using a Mira).
      • Symmetry (2-S.7)
    • 4.3 Geometric Relationships
      • 4.3.1 compose and describe pictures, designs, and patterns by combining two-dimensional shapes (e.g., “I made a picture of a flower from one hexagon and six equilateral triangles.”);
      • 4.3.2 compose and decompose two-dimensional shapes (Sample problem: Use Power Polygons to show if you can compose a rectangle from two triangles of different sizes.);
      • 4.3.3 cover an outline puzzle with two-dimensional shapes in more than one way;
      • 4.3.4 build a structure using three-dimensional figures, and describe the two-dimensional shapes and three-dimensional figures in the structure (e.g., “I used a box that looks like a triangular prism to build the roof of my house.”).
    • 4.4 Location and Movement
      • 4.4.1 describe the relative locations (e.g., beside, two steps to the right of) and the movements of objects on a map (e.g., “The path shows that he walked around the desk, down the aisle, and over to the window.”);
        • Left, middle and right (1-O.3)
        • Top, middle and bottom (1-O.4)
        • Location in a grid (1-O.5)
      • 4.4.2 draw simple maps of familiar settings, and describe the relative locations of objects on the maps (Sample problem: Draw a map of the classroom, showing the locations of the different pieces of furniture.);
      • 4.4.3 create and describe symmetrical designs using a variety of tools (e.g., pattern blocks, tangrams, paper and pencil).

2.5 Patterning and Algebra

• 5.1 Overall Expectations
  • 5.1.1 identify, describe, extend, and create repeating patterns, growing patterns, and shrinking patterns;
    • Repeating patterns (2-D.1)
    • Growing patterns (2-D.2)
    • Find the next shape in a pattern (2-D.3)
    • Complete a repeating pattern (2-D.4)
    • Make a repeating pattern (2-D.5)
    • Find the next row in a growing pattern (2-D.6)
  • 5.1.2 demonstrate an understanding of the concept of equality between pairs of expressions, using concrete materials, symbols, and addition and subtraction to 18.
    • Complete the addition sentence – one digit (2-E.12)
    • Balance addition equations – one digit (2-E.14)
    • Complete the subtraction sentence – up to 18 (2-F.11)
    • Balance subtraction equations – up to 18 (2-F.13)
    • Ways to make a number using addition (2-G.8)
    • Complete the addition sentence – up to two digits (2-G.10)
    • Balance addition equations – up to two digits (2-G.12)
    • Ways to make a number using subtraction (2-H.8)
    • Complete the subtraction sentence – up to two digits (2-H.10)
    • Balance subtraction equations – up to two digits (2-H.12)
    • Related addition facts (2-K.1)
    • Related subtraction facts (2-K.2)
    • Fact families (2-K.3)
    • Addition and subtraction – ways to make a number – up to 20 (2-X.2)
    • Addition and subtraction – balance equations – up to 20 (2-X.4)
  • 5.2 Patterns and Relationships
    • 5.2.1 identify and describe, through investigation, growing patterns and shrinking patterns generated by the repeated addition or subtraction of 1’s, 2’s, 5’s, 10’s, and 25’s on a number line and on a hundreds chart (e.g., the numbers 90, 80, 70, 60, 50, 40, 30, 20, 10 are in a straight line on a hundreds chart);
      • Skip-counting (2-A.1)
      • Skip-counting sequences (2-A.2)
      • Counting patterns – up to 100 (2-A.3)
      • Hundreds chart (2-A.5)
    • 5.2.2 identify, describe, and create, through investigation, growing patterns and shrinking patterns involving addition and subtraction, with and without the use of calculators (e.g., 3 + 1 = 4, 3 + 2 = 5, 3 + 3 = 6, …);
      • Addition input/output tables – sums to 20 (2-E.9)
      • Subtraction input/output tables – up to 18 (2-F.8)
      • Addition input/output tables – up to two digits (2-G.7)
      • Subtraction input/output tables – up to two digits (2-H.7)
      • Addition input/output tables – up to three digits (2-I.3)
      • Subtraction input/output tables – up to three digits (2-J.3)
      • Input/output tables – write the rule – up to 20 (2-X.5)
      • Input/output tables – write the rule – up to 100 (2-X.10)
    • 5.2.3 identify repeating, growing, and shrinking patterns found in real-life contexts (e.g., a geometric pattern on wallpaper, a rhythm pattern in music, a number pattern when counting dimes);
    • 5.2.4 represent a given growing or shrinking pattern in a variety of ways (e.g., using pictures, actions, colours, sounds, numbers, letters, number lines, bar graphs) (Sample problem: Show the letter pattern A, AA, AAA, AAAA, … by clapping or hopping.);
      • Growing patterns (2-D.2)
      • Find the next row in a growing pattern (2-D.6)
    • 5.2.5 create growing or shrinking patterns (Sample problem: Create a shrinking pattern using cut-outs of pennies and/or nickels, starting with 20 cents.);
    • 5.2.6 create a repeating pattern by combining two attributes (e.g., colour and shape; colour and size) (Sample problem: Use attribute blocks to make a train that shows a repeating pattern involving two attributes.);
      • Repeating patterns (2-D.1)
      • Complete a repeating pattern (2-D.4)
      • Make a repeating pattern (2-D.5)
    • 5.2.7 demonstrate, through investigation, an understanding that a pattern results from repeating an operation (e.g., addition, subtraction) or making a repeated change to an attribute (e.g., colour, orientation).
  • 5.3 Expressions and Equality
    • 5.3.1 demonstrate an understanding of the concept of equality by partitioning whole numbers to 18 in a variety of ways, using concrete materials (e.g., starting with 9 tiles and adding 6 more tiles gives the same result as starting with 10 tiles and adding 5 more tiles);
      • Review – ways to make a number – sums to 10 (2-E.2)
      • Balance addition equations – one digit (2-E.14)
      • Balance subtraction equations – up to 18 (2-F.13)
      • Ways to make a number using addition (2-G.8)
      • Balance addition equations – up to two digits (2-G.12)
      • Ways to make a number using subtraction (2-H.8)
      • Balance subtraction equations – up to two digits (2-H.12)
      • Addition and subtraction – ways to make a number – up to 20 (2-X.2)
    • 5.3.2 represent, through investigation with concrete materials and pictures, two number expressions that are equal, using the equal sign (e.g., “I can break a train of 10 cubes into 4 cubes and 6 cubes. I can also break 10 cubes into 7 cubes and 3 cubes. This means 4 + 6 = 7 + 3.”);
      • Balance addition equations – one digit (2-E.14)
      • Balance subtraction equations – up to 18 (2-F.13)
      • Balance addition equations – up to two digits (2-G.12)
      • Balance subtraction equations – up to two digits (2-H.12)
      • Balance addition equations – up to three digits (2-I.7)
      • Balance subtraction equations – up to three digits (2-J.7)
      • Addition and subtraction – balance equations – up to 20 (2-X.4)
      • Addition and subtraction – balance equations – up to 100 (2-X.9)
    • 5.3.3 determine the missing number in equations involving addition and subtraction to 18, using a variety of tools and strategies (e.g., modelling with concrete materials, using guess and check with and without the aid of a calculator) (Sample problem: Use counters to determine the missing number in the equation 6 + 7 = __ + 5.);
      • Complete the addition sentence – one digit (2-E.12)
      • Balance addition equations – one digit (2-E.14)
      • Complete the subtraction sentence – up to 18 (2-F.11)
      • Balance subtraction equations – up to 18 (2-F.13)
      • Complete the addition sentence – up to two digits (2-G.10)
      • Balance addition equations – up to two digits (2-G.12)
      • Complete the subtraction sentence – up to two digits (2-H.10)
      • Balance subtraction equations – up to two digits (2-H.12)
      • Complete the addition sentence – up to three digits (2-I.5)
      • Balance addition equations – up to three digits (2-I.7)
      • Complete the subtraction sentence – up to three digits (2-J.5)
      • Balance subtraction equations – up to three digits (2-J.7)
      • Addition and subtraction – balance equations – up to 20 (2-X.4)
      • Addition and subtraction – balance equations – up to 100 (2-X.9)
    • 5.3.4 identify, through investigation, and use the commutative property of addition (e.g., create a train of 10 cubes by joining 4 red cubes to 6 blue cubes, or by joining 6 blue cubes to 4 red cubes) to facilitate computation with whole numbers (e.g., “I know that 9 + 8 + 1 = 9 + 1 + 8. Adding becomes easier because that gives 10 + 8 = 18.”);
      • Related addition facts (2-K.1)
      • Related subtraction facts (2-K.2)
      • Fact families (2-K.3)
      • Solve inequalities using addition and subtraction shortcuts (2-K.5)
    • 5.3.5 identify, through investigation, the properties of zero in addition and subtraction (i.e., when you add zero to a number, the number does not change; when you subtract zero from a number, the number does not change).
      • Add zero (2-E.10)
      • Subtract zero/all (2-F.9)

2.6 Data Management and Probability

• 6.1 Overall Expectations
  • 6.1.1 collect and organize categorical or discrete primary data and display the data, using tally charts, concrete graphs, pictographs, line plots, simple bar graphs, and other graphic organizers, with labels ordered appropriately along horizontal axes, as needed;
    • Create line plots (2-Q.5)
    • Create pictographs (2-Q.7)
  • 6.1.2 read and describe primary data presented in tally charts, concrete graphs, pictographs, line plots, simple bar graphs, and other graphic organizers;
    • Interpret bar graphs (2-Q.2)
    • Which bar graph is correct? (2-Q.3)
    • Interpret line plots (2-Q.4)
    • Interpret pictographs (2-Q.6)
    • Interpret line graphs (2-Q.8)
    • Which line graph is correct? (2-Q.9)
    • Count shapes in a Venn diagram (2-Q.11)
    • Venn diagrams with three circles (2-Q.12)
  • 6.1.3 describe probability in everyday situations and simple games.
    • More, less and equally likely (2-W.1)
    • Certain, probable, unlikely and impossible (2-W.2)
  • 6.2 Collection and Organization of Data
    • 6.2.1 demonstrate an ability to organize objects into categories, by sorting and classifying objects using two attributes simultaneously (e.g., sort attribute blocks by colour and shape at the same time);
      • Sort shapes into a Venn diagram (2-Q.10)
      • Venn diagrams with three circles (2-Q.12)
    • 6.2.2 gather data to answer a question, using a simple survey with a limited number of responses (e.g., What is your favourite season?; How many letters are in your first name?);
    • 6.2.3 collect and organize primary data (e.g., data collected by the class) that is categorical or discrete (i.e., that can be counted, such as the number of students absent), and display the data using one-to-one correspondence in concrete graphs, pictographs, line plots, simple bar graphs, and other graphic organizers (e.g., tally charts, diagrams), with appropriate titles and labels and with labels ordered appropriately along horizontal axes, as needed (Sample problem: Record the number of times that specific words are used in a simple rhyme or poem.).
      • Record data with tally charts, picture graphs, tables (1-P.1)
    • 6.3 Data Relationships
      • 6.3.1 read primary data presented in concrete graphs, pictographs, line plots, simple bar graphs, and other graphic organizers (e.g., tally charts, diagrams), and describe the data using mathematical language (e.g., “Our bar graph shows that 4 more students walk to school than take the bus.”);
        • Interpret bar graphs (2-Q.2)
        • Interpret line plots (2-Q.4)
        • Interpret pictographs (2-Q.6)
        • Interpret line graphs (2-Q.8)
      • 6.3.2 pose and answer questions about class-generated data in concrete graphs, pictographs, line plots, simple bar graphs, and tally charts (e.g., Which is the least favourite season?);
      • 6.3.3 distinguish between numbers that represent data values (e.g., “I have 4 people in my family.”) and numbers that represent the frequency of an event (e.g., “There are 10 children in my class who have 4 people in their family.”);
      • 6.3.4 demonstrate an understanding of data displayed in a graph (e.g., by telling a story, by drawing a picture), by comparing different parts of the data and by making statements about the data as a whole (e.g., “I looked at the graph that shows how many students were absent each month. More students were away in January than in September.”).
        • Interpret bar graphs (2-Q.2)
        • Which bar graph is correct? (2-Q.3)
        • Interpret line plots (2-Q.4)
        • Interpret pictographs (2-Q.6)
        • Interpret line graphs (2-Q.8)
        • Which line graph is correct? (2-Q.9)
      • 6.4 Probability
        • 6.4.1 describe probability as a measure of the likelihood that an event will occur, using mathematical language (i.e., impossible, unlikely, less likely, equally likely, more likely, certain) (e.g., “If I take a new shoe out of a box without looking, it’s equally likely that I will pick the left shoe or the right shoe.”);
          • More, less and equally likely (2-W.1)
          • Certain, probable, unlikely and impossible (2-W.2)
        • 6.4.2 describe the probability that an event will occur (e.g., getting heads when tossing a coin, landing on red when spinning a spinner), through investigation with simple games and probability experiments and using mathematical language (e.g., “I tossed 2 coins at the same time, to see how often I would get 2 heads. I found that getting a head and a tail was more likely than getting 2 heads.”) (Sample problem: Describe the probability of spinning red when you spin a spinner that has one half shaded yellow, one fourth shaded blue, and one fourth shaded red. Experiment with the spinner to see if the results are what you expected.).
          • More, less and equally likely (2-W.1)
          • Certain, probable, unlikely and impossible (2-W.2)