Grade 1 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;
- 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);
  - 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;
    - 1.5 Connecting
      - 1.5.1 make connections among simple mathematical concepts and procedures, and relate mathematical ideas to situations drawn from everyday contexts;
        
        Ordinal numbers (1-A.21)
        
        Addition word problems – sums up to 10 (1-D.5)
        
        Addition sentences for word problems – sums up to 10 (1-D.6)
        
        Addition word problems – sums up to 18 (1-D.9)
        
        Addition sentences for word problems – sums up to 18 (1-D.10)
        
        Addition sentences for word problems – sums up to 20 (1-D.13)
        
        Add three numbers – word problems (1-E.10)
        
        Subtraction word problems – numbers up to 10 (1-H.6)
        
        Subtraction sentences for word problems – numbers up to 10 (1-H.7)
        
        Subtraction word problems – numbers up to 18 (1-H.10)
        
        Subtraction sentences for word problems – numbers up to 18 (1-H.11)
        
        Relate addition and subtraction sentences (1-I.1)
        
        Fractions – word problems (1-L.6)
        
        Shapes of everyday objects I (1-N.9)
        
        Shapes of everyday objects II (1-N.10)
        
        Read a thermometer (1-Q.7)
        
        Which metric unit of length is appropriate? (1-Q.9)
        
        Metric units of length: word problems (1-Q.10)
        
        Which metric unit of mass is appropriate? (1-Q.11)
        
        Coin values (1-R.1)
        
        Count nickels and dimes (1-R.2)
        
        Addition and subtraction word problems (1-T.6)
        
        Match analogue clocks and times (1-W.1)
        
        Match analogue and digital clocks (1-W.3)
        
        Read clocks and write times (1-W.4)
        
        M. or P.M. (1-W.5)
        
        Times of everyday events (1-W.6)
        
        Compare clocks (1-W.7)
        
        Time and clocks: word problems (1-W.8)
        
        Seasons of the year (1-W.9)
        
        Days of the week (1-W.10)
        
        Months of the year (1-W.11)
        
        Read a calendar (1-W.12)
      - 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;
        
        Counting by twos, fives and tens with pictures (1-A.9)
        
        Number lines (1-A.12)
        
        Counting on the hundred chart (1-A.13)
        
        Hundred chart (1-A.14)
        
        Even or odd (1-A.15)
        
        Even or odd numbers on number lines (1-A.17)
        
        Add with pictures – sums up to 10 (1-B.1)
        
        Subtract with pictures – numbers up to 10 (1-F.1)
        
        Simple fractions: what fraction does the shape show? (1-L.3)
        
        Simple fractions: parts of a group (1-L.5)
        
        Sort shapes into a Venn diagram (1-V.1)
        
        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.
        
        Writing numbers in words (1-A.22)
        
        Roman numerals I, V, X (1-A.23)
        
        Sort shapes into a Venn diagram (1-V.1)

1.2 Number Sense and Numeration

2.1 Overall Expectations
- 2.1.1 read, represent, compare, and order whole numbers to 50, and use concrete materials to investigate fractions and money amounts;
- 2.1.2 demonstrate an understanding of magnitude by counting forward to 100 and backwards from 20;
- 2.1.3 solve problems involving the addition and subtraction of single-digit whole numbers, using a variety of strategies.
- 2.2 Quantity Relationships
  - 2.2.1 represent, compare, and order whole numbers to 50, using a variety of tools (e.g., connecting cubes, ten frames, base ten materials, number lines, hundreds charts) and contexts (e.g., real-life experiences, number stories);
  - 2.2.2 read and print in words whole numbers to ten, using meaningful contexts (e.g., storybooks, posters);
    - Names of numbers – up to 20 (K-D.10)
    - Writing numbers in words (1-A.22)
  - 2.2.3 demonstrate, using concrete materials, the concept of conservation of number (e.g., 5 counters represent the number 5, regardless whether they are close together or far apart);
  - 2.2.4 relate numbers to the anchors of 5 and 10 (e.g., 7 is 2 more than 5 and 3 less than 10);
  - 2.2.5 identify and describe various coins (i.e., penny, nickel, dime, quarter, $1 coin, $2 coin), using coin manipulatives or drawings, and state their value (e.g., the value of a penny is one cent; the value of a toonie is two dollars);
  - 2.2.6 represent money amounts to 20¢, through investigation using coin manipulatives;
    - Coin values (1-R.1)
    - Count nickels and dimes (1-R.2)
  - 2.2.7 estimate the number of objects in a set, and check by counting (e.g., “I guessed that there were 20 cubes in the pile. I counted them and there were only 17 cubes. 17 is close to 20.”);
    - Estimate to the nearest ten (1-K.1)
  - 2.2.8 compose and decompose numbers up to 20 in a variety of ways, using concrete materials (e.g., 7 can be decomposed using connecting cubes into 6 and 1, or 5 and 2, or 4 and 3);
  - 2.2.9 divide whole objects into parts and identify and describe, through investigation, equal-sized parts of the whole, using fractional names (e.g., halves; fourths or quarters).
    - Equal parts (1-L.1)
    - Halves, thirds and fourths (1-L.2)
  - 2.3 Counting
    - 2.3.1 demonstrate, using concrete materials, the concept of one-to-one correspondence between number and objects when counting;
    - 2.3.2 count forward by 1’s, 2’s, 5’s, and 10’s to 100, using a variety of tools and strategies (e.g., move with steps; skip count on a number line; place counters on a hundreds chart; connect cubes to show equal groups; count groups of pennies, nickels, or dimes);
    - 2.3.3 count backwards by 1’s from 20 and any number less than 20 (e.g., count backwards from 18 to 11), with and without the use of concrete materials and number lines;
      - Counting forward and backward (1-A.11)
    - 2.3.4 count backwards from 20 by 2’s and 5’s, using a variety of tools (e.g., number lines, hundreds charts);
      - Sequences – count up and down by 1, 2, 3, 5 and 10 (1-A.20)
    - 2.3.5 use ordinal numbers to thirty-first in meaningful contexts (e.g., identify the days of the month on a calendar).
      - Ordinal numbers (1-A.21)
    - 2.4 Operational Sense
      - 2.4.1 solve a variety of problems involving the addition and subtraction of whole numbers to 20, using concrete materials and drawings (e.g., pictures, number lines) (Sample problem: Miguel has 12 cookies. Seven cookies are chocolate. Use counters to determine how many cookies are not chocolate.);
        
        Add with pictures – sums up to 10 (1-B.1)
        
        Addition sentences using number lines – sums up to 10 (1-B.3)
        
        Addition word problems – sums up to 10 (1-D.5)
        
        Addition sentences using number lines – sums up to 18 (1-D.8)
        
        Addition word problems – sums up to 18 (1-D.9)
        
        Add three numbers – word problems (1-E.10)
        
        Subtract with pictures – numbers up to 10 (1-F.1)
        
        Subtraction sentences using number lines – numbers up to 10 (1-F.3)
        
        Subtraction word problems – numbers up to 10 (1-H.6)
        
        Subtraction sentences using number lines – numbers up to 18 (1-H.9)
        
        Subtraction word problems – numbers up to 18 (1-H.10)
        
        Addition and subtraction facts – numbers up to 10 (1-T.4)
        
        Addition and subtraction facts – numbers up to 18 (1-T.5)
        
        Addition and subtraction word problems (1-T.6)
        
        Add and subtract integers using counters (7-C.2)
      - 2.4.2 solve problems involving the addition and subtraction of single-digit whole numbers, using a variety of mental strategies (e.g., one more than, one less than, counting on, counting back, doubles);
        
        Adding zero (1-B.4)
        
        Adding 1 (1-C.1)
        
        Adding 2 (1-C.2)
        
        Adding 3 (1-C.3)
        
        Adding 4 (1-C.4)
        
        Adding 5 (1-C.5)
        
        Adding 6 (1-C.6)
        
        Adding 7 (1-C.7)
        
        Adding 9 (1-C.8)
        
        Adding 8 (1-C.9)
        
        Adding 0 (1-C.10)
        
        Make a number using addition – sums up to 10 (1-D.3)
        
        Complete the addition sentence – sums up to 10 (1-D.4)
        
        Make a number using addition – sums up to 20 (1-D.12)
        
        Add doubles (1-E.1)
        
        Add using doubles plus one (1-E.2)
        
        Add using doubles minus one (1-E.3)
        
        Add three numbers – use doubles (1-E.4)
        
        Complete the addition sentence – make ten (1-E.5)
        
        Add three numbers – make ten (1-E.6)
        
        Subtract zero and all (1-F.4)
        
        Subtracting 1 (1-G.1)
        
        Subtracting 2 (1-G.2)
        
        Subtracting 3 (1-G.3)
        
        Subtracting 4 (1-G.4)
        
        Subtracting 5 (1-G.5)
        
        Subtracting 6 (1-G.6)
        
        Subtracting 7 (1-G.7)
        
        Subtracting 8 (1-G.8)
        
        Subtracting 9 (1-G.9)
        
        Subtracting 0 (1-G.10)
        
        Make a number using subtraction – numbers up to 10 (1-H.4)
        
        Complete the subtraction sentence (1-H.5)
        
        Make a number using subtraction – numbers up to 20 (1-H.12)
        
        Subtract doubles (1-I.2)
      - 2.4.3 add and subtract money amounts to 10¢, using coin manipulatives and drawings.
        
        Coin values (1-R.1)
        
        Count nickels and dimes (1-R.2)
        
        Equivalent groups of coins (1-R.3)
        
        Exchanging coins (1-R.4)

1.3 Measurement

3.1 Overall Expectations
- 3.1.1 estimate, measure, and describe length, area, mass, capacity, time, and temperature, using non-standard units of the same size;
- 3.1.2 compare, describe, and order objects, using attributes measured in non-standard units.
- 3.2 Attributes, Units, and Measurement Sense
  - 3.2.1 demonstrate an understanding of the use of non-standard units of the same size (e.g., straws, index cards) for measuring (Sample problem: Measure the length of your desk in different ways; for example, by using several different non-standard units or by starting measurements from opposite ends of the desk. Discuss your findings.);
    - Measure using objects (1-Q.6)
  - 3.2.2 estimate, measure (i.e., by placing nonstandard units repeatedly, without overlaps or gaps), and record lengths, heights, and distances (e.g., a book is about 10 paper clips wide; a pencil is about 3 toothpicks long);
    - Measure using objects (1-Q.6)
  - 3.2.3 construct, using a variety of strategies, tools for measuring lengths, heights, and distances in non-standard units (e.g., footprints on cash register tape or on connecting cubes);
  - 3.2.4 estimate, measure (i.e., by minimizing overlaps and gaps), and describe area, through investigation using non-standard units (e.g., “It took about 15 index cards to cover my desk, with only a little bit of space left over.”);
  - 3.2.5 estimate, measure, and describe the capacity and/or mass of an object, through investigation using non-standard units (e.g., “My journal has the same mass as 13 pencils.” “The juice can has the same capacity as 4 pop cans.”);
  - 3.2.6 estimate, measure, and describe the passage of time, through investigation using nonstandard units (e.g., number of sleeps; number of claps; number of flips of a sand timer);
  - 3.2.7 read demonstration digital and analogue clocks, and use them to identify benchmark times (e.g., times for breakfast, lunch, dinner; the start and end of school; bedtime) and to tell and write time to the hour and half-hour in everyday settings;
  - 3.2.8 name the months of the year in order, and read the date on a calendar;
    - Months of the year (1-W.11)
    - Read a calendar (1-W.12)
  - 3.2.9 relate temperature to experiences of the seasons (e.g., “In winter, we can skate because it’s cold enough for there to be ice.”).
- 3.3 Measurement Relationships
  - 3.3.1 compare two or three objects using measurable attributes (e.g., length, height, width, area, temperature, mass, capacity), and describe the objects using relative terms (e.g., taller, heavier, faster, bigger, warmer; “If I put an eraser, a pencil, and a metre stick beside each other, I can see that the eraser is shortest and the metre stick is longest.”);
  - 3.3.2 compare and order objects by their linear measurements, using the same non-standard unit (Sample problem: Using a length of string equal to the length of your forearm, work with a partner to find other objects that are about the same length.);
  - 3.3.3 use the metre as a benchmark for measuring length, and compare the metre with non-standard units (Sample problem: In the classroom, use a metre stick to find objects that are taller than one metre and objects that are shorter than one metre.);
  - 3.3.4 describe, through investigation using concrete materials, the relationship between the size of a unit and the number of units needed to measure length (Sample problem: Compare the numbers of paper clips and pencils needed to measure the length of the same table).

1.4 Geometry and Spatial Sense

4.1 Overall Expectations
- 4.1.1 identify common two-dimensional shapes and three-dimensional figures and sort and classify them by their attributes;
- 4.1.2 compose and decompose common two-dimensional shapes and three-dimensional figures;
- 4.1.3 describe the relative locations of objects using positional language.
- 4.2 Geometric Properties
  - 4.2.1 identify and describe common two-dimensional shapes (e.g., circles, triangles, rectangles, squares) and sort and classify them by their attributes (e.g., colour; size; texture; number of sides), using concrete materials and pictorial representations (e.g., “I put all the triangles in one group. Some are long and skinny, and some are short and fat, but they all have three sides.”);
  - 4.2.2 trace and identify the two-dimensional faces of three-dimensional figures, using concrete models (e.g., “I can see squares on the cube.”);
    - Identify shapes traced from solids (1-N.7)
    - Identify faces of three-dimensional shapes (1-N.8)
  - 4.2.3 identify and describe common three-dimensional figures (e.g., cubes, cones, cylinders, spheres, rectangular prisms) and sort and classify them by their attributes (e.g., colour; size; texture; number and shape of faces), using concrete materials and pictorial representations (e.g., “I put the cones and the cylinders in the same group because they all have circles on them.”);
  - 4.2.4 describe similarities and differences between an everyday object and a three-dimensional figure (e.g., “A water bottle looks like a cylinder, except the bottle gets thinner at the top.”);
    - Shapes of everyday objects I (1-N.9)
    - Shapes of everyday objects II (1-N.10)
  - 4.2.5 locate shapes in the environment that have symmetry, and describe the symmetry.
    - Symmetry (1-M.7)
  - 4.3 Geometric Relationships
    - 4.3.1 compose patterns, pictures, and designs, using common two-dimensional shapes (Sample problem: Create a picture of a flower using pattern blocks.);
    - 4.3.2 identify and describe shapes within other shapes (e.g., shapes within a geometric design);
    - 4.3.3 build three-dimensional structures using concrete materials, and describe the two-dimensional shapes the structures contain;
    - 4.3.4 cover outline puzzles with two-dimensional shapes (e.g., pattern blocks, tangrams) (Sample problem: Fill in the outline of a boat with tangram pieces.).
  - 4.4 Location and Movement
    - 4.4.1 describe the relative locations of objects or people using positional language (e.g., over, under, above, below, in front of, behind, inside, outside, beside, between, along);
    - 4.4.2 describe the relative locations of objects on concrete maps created in the classroom (Sample problem: Work with your group to create a map of the classroom in the sand table, using smaller objects to represent the classroom objects. Describe where the teacher’s desk and the bookshelves are located.);
    - 4.4.3 create symmetrical designs and pictures, using concrete materials (e.g., pattern blocks, connecting cubes, paper for folding), and describe the relative locations of the parts.

1.5 Patterning and Algebra

5.1 Overall Expectations
- 5.1.1 identify, describe, extend, and create repeating patterns;
- 5.1.2 demonstrate an understanding of the concept of equality, using concrete materials and addition and subtraction to 10.
- 5.2 Patterns and Relationships
  - 5.2.1 identify, describe, and extend, through investigation, geometric repeating patterns involving one attribute (e.g., colour, size, shape, thickness, orientation);
  - 5.2.2 identify and extend, through investigation, numeric repeating patterns (e.g., 1, 2, 3, 1, 2, 3, 1, 2, 3, …);
  - 5.2.3 describe numeric repeating patterns in a hundreds chart;
    - Counting on the hundred chart (1-A.13)
    - Hundreds chart (2-A.5)
  - 5.2.4 identify a rule for a repeating pattern (e.g., “We’re lining up boy, girl, boy, girl, boy, girl.”);
    - Shape patterns (1-S.3)
  - 5.2.5 create a repeating pattern involving one attribute (e.g., colour, size, shape, sound) (Sample problem: Use beads to make a string that shows a repeating pattern involving one attribute.);
  - 5.2.6 represent a given repeating pattern in a variety of ways (e.g., pictures, actions, colours, sounds, numbers, letters) (Sample problem: Make an ABA, ABA, ABA pattern using actions like clapping or tapping.).
    - Make a pattern (1-S.6)
  - 5.3 Expressions and Equality
    - 5.3.1 create a set in which the number of objects is greater than, less than, or equal to the number of objects in a given set;
    - 5.3.2 demonstrate examples of equality, through investigation, using a “balance” model (Sample problem: Demonstrate, using a pan balance, that a train of 7 attached cubes on one side balances a train of 3 cubes and a train of 4 cubes on the other side.);
    - 5.3.3 determine, through investigation using a “balance” model and whole numbers to 10, the number of identical objects that must be added or subtracted to establish equality (Sample problem: On a pan balance, 5 cubes are placed on the left side and 8 cubes are placed on the right side. How many cubes should you take off the right side so that both sides balance?).

1.6 Data Management and Probability

6.1 Overall Expectations
- 6.1.1 collect and organize categorical primary data and display the data using concrete graphs and pictographs, without regard to the order of labels on the horizontal axis;
  - Record data with tally charts, picture graphs, tables (1-P.1)
  - Which bar graph is correct? (1-P.4)
- 6.1.2 read and describe primary data presented in concrete graphs and pictographs;
- 6.1.3 describe the likelihood that everyday events will happen.
  - More, less and equally likely (1-U.1)
  - Certain, probable, unlikely and impossible (1-U.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 one attribute (e.g., colour, size), and by describing informal sorting experiences (e.g., helping to put away groceries) (Sample problem: Sort a collection of attribute blocks by colour. Re-sort the same collection by shape.);
  - 6.2.2 collect and organize primary data (e.g., data collected by the class) that is categorical (i.e., that can be organized into categories based on qualities such as colour or hobby), and display the data using one-to-one correspondence, prepared templates of concrete graphs and pictographs (with titles and labels), and a variety of recording methods (e.g., arranging objects, placing stickers, drawing pictures, making tally marks) (Sample problem: Collect and organize data about the favourite fruit that students in your class like to eat.).
    - Record data with tally charts, picture graphs, tables (1-P.1)
    - Create pictographs (2-Q.7)
  - 6.3 Data Relationships
    - 6.3.1 read primary data presented in concrete graphs and pictographs, and describe the data using comparative language (e.g., more students chose summer than winter as their single favourite season);
    - 6.3.2 pose and answer questions about collected data (Sample problem: What was the most popular fruit chosen by the students in your class?).
    - 6.4 Probability
      - 6.4.1 describe the likelihood that everyday events will occur, using mathematical language (i.e., impossible, unlikely, less likely, more likely, certain) (e.g., “It’s unlikely that I will win the contest shown on the cereal box.”).
        
        More, less and equally likely (1-U.1)
        
        Certain, probable, unlikely and impossible (1-U.2)