Grade 5. Mathematical Process

1.1 Problem Solving
- 1.1.1 develop, select, and apply 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 develop and apply reasoning skills (e.g., classification, recognition of relationships, use of counter-examples) to make and investigate conjectures and construct and defend arguments;
  - 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 comparing and adjusting strategies used, by explaining why they think their results are reasonable, by recording their thinking in a math journal);
  - 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 mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, sports);
        
        Add and subtract whole numbers: word problems (5-B.2)
        
        Estimate sums and differences: word problems (5-B.9)
        
        Multiply by one-digit numbers: word problems (5-C.2)
        
        Multiply numbers ending in zeroes: word problems (5-C.5)
        
        Estimate products: word problems (5-C.9)
        
        Multiply by 2-digit numbers: word problems (5-C.14)
        
        Multiply three or four numbers: word problems (5-C.16)
        
        Division facts to 12: word problems (5-D.2)
        
        Divide by one-digit numbers: word problems (5-D.4)
        
        Estimate quotients: word problems (5-D.7)
        
        Divide numbers ending in zeroes: word problems (5-D.10)
        
        Divisibility rules: word problems (5-E.4)
        
        Add and subtract decimals: word problems (5-G.2)
        
        Multiply decimals and whole numbers: word problems (5-H.4)
        
        Add and subtract money: word problems (5-I.2)
        
        Multiply money amounts with decimals: word problems (5-I.4)
        
        Divide money amounts with decimals: word problems (5-I.5)
        
        Fractions of a whole: word problems (5-J.4)
        
        Fractions of a number: word problems (5-J.8)
        
        Add and subtract fractions with like denominators: word problems (5-L.4)
        
        Add and subtract mixed numbers with like denominators: word problems (5-L.6)
        
        Add three or more fractions: word problems (5-L.9)
        
        Add, subtract, multiply and divide whole numbers: word problems (5-N.2)
        
        Add, subtract and multiply decimals: word problems (5-N.6)
        
        Multi-step word problems (5-O.1)
        
        Word problems with extra or missing information (5-O.2)
        
        Number sequences: word problems (5-P.8)
        
        Write variable equations: word problems (5-R.4)
      - 1.6 Representing
        
        1.6.1 create a variety of representations of mathematical ideas (e.g., by using physical models, pictures, numbers, variables, diagrams, graphs, onscreen dynamic representations), make connections among them, and apply them to solve problems;
        
        Model decimals and fractions (5-F.2)
        
        Compare decimals on number lines (5-F.9)
        
        Compare decimals and fractions on number lines (5-F.15)
        
        Show fractions: fraction bars (5-J.1)
        
        Show fractions: area models (5-J.2)
        
        Graph and compare fractions on number lines (5-K.6)
        
        Add and subtract fractions with like denominators using number lines (5-L.2)
        
        Multiply unit fractions by whole numbers using number lines (5-M.1)
        
        Multiply unit fractions by whole numbers using models (5-M.2)
        
        Multiply fractions by whole numbers using number lines (5-M.5)
        
        Multiply fractions by whole numbers using models (5-M.6)
        
        Multiply fractions by whole numbers: input/output tables (5-M.9)
        
        Write variable expressions (5-R.1)
        
        Write variable equations: word problems (5-R.4)
        
        Complete a table for a two-variable relationship (5-R.7)
        
        Complete a table from a graph (5-R.8)
        
        Graph a two-variable relationship (5-R.9)
        
        Write a two-variable equation (5-R.10)
        
        1.7 Communicating
        
        1.7.1 communicate mathematical thinking orally, visually, and in writing, using everyday language, a basic mathematical vocabulary, and a variety of representations, and observing basic mathematical conventions.
        
        Word names for numbers (5-A.4)
        
        Even or odd: arithmetic rules (5-A.7)
        
        Prime and composite numbers (5-E.1)
        
        Model decimals and fractions (5-F.2)
        
        Convert decimals between standard and expanded form (5-F.5)
        
        Compare decimals on number lines (5-F.9)
        
        Convert decimals between standard and expanded form using fractions (5-F.14)
        
        Compare decimals and fractions on number lines (5-F.15)
        
        Graph and compare fractions on number lines (5-K.6)
        
        Multiply unit fractions by whole numbers using models (5-M.2)
        
        Multiply fractions by whole numbers using models (5-M.6)
        
        Write numerical expressions (5-N.3)
        
        Objects on a coordinate plane (5-Q.1)
        
        Write variable expressions (5-R.1)
        
        Write variable expressions: word problems (5-R.2)
        
        Graph a two-variable relationship (5-R.9)
        
        Is it a polygon? (5-W.1)
        
        Parallel, perpendicular and intersecting lines (5-W.4)
        
        Classify triangles (5-W.7)
        
        Classify quadrilaterals (5-W.13)
        
        Identify three-dimensional figures (5-Y.1)

5.2 Number Sense and Numeration

2.1 Overall Expectations
- 2.1.1 read, represent, compare, and order whole numbers to 100 000, decimal numbers to hundredths, proper and improper fractions, and mixed numbers;
- 2.1.2 demonstrate an understanding of magnitude by counting forward and backwards by 0.01;
  - Decimal number lines (5-F.8)
- 2.1.3 solve problems involving the multiplication and division of multi-digit whole numbers, and involving the addition and subtraction of decimal numbers to hundredths, using a variety of strategies;
- 2.1.4 demonstrate an understanding of proportional reasoning by investigating whole-number rates.
  - Unit rates and equivalent rates (6-P.6)
- 2.2 Quantity Relationships
  - 2.2.1 represent, compare, and order whole numbers and decimal numbers from 0.01 to 100 000, using a variety of tools (e.g., number lines with appropriate increments, base ten materials for decimals);
  - 2.2.2 demonstrate an understanding of place value in whole numbers and decimal numbers from 0.01 to 100 000, using a variety of tools and strategies (e.g., use numbers to represent 23 011 as 20 000 + 3000 + 0 + 10 + 1; use base ten materials to represent the relationship between 1, 0.1, and 0.01) (Sample problem: How many thousands cubes would be needed to make a base ten block for 100 000?);
  - 2.2.3 read and print in words whole numbers to ten thousand, using meaningful contexts (e.g., newspapers, magazines);
    - Word names for numbers (5-A.4)
  - 2.2.4 round decimal numbers to the nearest tenth, in problems arising from real-life situations;
    - Round decimals (5-F.7)
  - 2.2.5 represent, compare, and order fractional amounts with like denominators, including proper and improper fractions and mixed numbers, using a variety of tools (e.g., fraction circles, Cuisenaire rods, number lines) and using standard fractional notation;
  - 2.2.6 demonstrate and explain the concept of equivalent fractions, using concrete materials (e.g., use fraction strips to show that 3/4 is equal to 9/12);
  - 2.2.7 demonstrate and explain equivalent representations of a decimal number, using concrete materials and drawings (e.g., use base ten materials to show that three tenths [0.3] is equal to thirty hundredths [0.30]);
    - Equivalent decimals (5-F.6)
  - 2.2.8 read and write money amounts to $1000 (e.g., $455.35 is 455 dollars and 35 cents, or four hundred fifty-five dollars and thirty-five cents);
  - 2.2.9 solve problems that arise from real-life situations and that relate to the magnitude of whole numbers up to 100 000 (Sample problem: How many boxes hold 100 000 sheets of paper, if one box holds 8 packages of paper, and one package of paper contains 500 sheets of paper?).
  - 2.3 Counting
    - 2.3.1 count forward by hundredths from any decimal number expressed to two decimal places, using concrete materials and number lines (e.g., use base ten materials to represent 2.96 and count forward by hundredths: 2.97, 2.98, 2.99, 3.00, 3.01…; “Two and ninety-six hundredths, two and ninety-seven hundredths, two and ninety-eight hundredths, two and ninety-nine hundredths, three, three and one hundredth…”) (Sample problem: What connections can you make between counting by hundredths and measuring lengths in centimetres and metres?).
      - Decimal number lines (5-F.8)
    - 2.4 Operational Sense
      - 2.4.1 solve problems involving the addition, subtraction, and multiplication of whole numbers, using a variety of mental strategies (e.g., use the commutative property: 5 x 18 x 2 = 5 x 2 x 18, which gives 10 x 18 = 180);
        
        Add and subtract whole numbers up to millions (5-B.1)
        
        Add and subtract whole numbers: word problems (5-B.2)
        
        Complete addition and subtraction sentences (5-B.3)
        
        Fill in the missing digits (5-B.4)
        
        Choose numbers with a particular sum or difference (5-B.5)
        
        Properties of addition (5-B.6)
        
        Inequalities with addition and subtraction (5-B.7)
        
        Multiplication patterns over increasing place values (5-C.3)
        
        Multiply numbers ending in zeroes (5-C.4)
        
        Multiply numbers ending in zeroes: word problems (5-C.5)
        
        Properties of multiplication (5-C.6)
        
        Choose numbers with a particular product (5-C.7)
        
        Multiply by 2-digit numbers: complete the missing steps (5-C.12)
        
        Multiply 2-digit numbers by 2-digit numbers (5-C.13)
        
        Multiply by 2-digit numbers: word problems (5-C.14)
        
        Multiply three or four numbers (5-C.15)
        
        Multiply three or four numbers: word problems (5-C.16)
        
        Inequalities with multiplication (5-C.19)
        
        Divide by one-digit numbers: word problems (5-D.4)
        
        Divide by one-digit numbers: interpret remainders (5-D.5)
        
        Division patterns over increasing place values (5-D.8)
        
        Divide numbers ending in zeroes (5-D.9)
        
        Divide numbers ending in zeroes: word problems (5-D.10)
        
        Choose numbers with a particular quotient (5-D.11)
      - 2.4.2 add and subtract decimal numbers to hundredths, including money amounts, using concrete materials, estimation, and algorithms (e.g., use 10 x 10 grids to add 2.45 and 3.25);
        
        Add and subtract decimal numbers (5-G.1)
        
        Add and subtract decimals: word problems (5-G.2)
        
        Choose decimals with a particular sum or difference (5-G.3)
        
        Complete the addition or subtraction sentence (5-G.4)
        
        Inequalities with decimal addition and subtraction (5-G.5)
        
        Add and subtract money amounts (5-I.1)
        
        Add and subtract money: word problems (5-I.2)
      - 2.4.3 multiply two-digit whole numbers by two-digit whole numbers, using estimation, student-generated algorithms, and standard algorithms;
        
        Estimate products (5-C.8)
        
        Estimate products: word problems (5-C.9)
        
        Box multiplication (5-C.10)
        
        Lattice multiplication (5-C.11)
        
        Multiply by 2-digit numbers: complete the missing steps (5-C.12)
        
        Multiply 2-digit numbers by 2-digit numbers (5-C.13)
        
        Multiply by 2-digit numbers: word problems (5-C.14)
      - 2.4.4 divide three-digit whole numbers by one-digit whole numbers, using concrete materials, estimation, student-generated algorithms, and standard algorithms;
        
        Divide by one-digit numbers (5-D.3)
        
        Divide by one-digit numbers: word problems (5-D.4)
        
        Estimate quotients (5-D.6)
        
        Estimate quotients: word problems (5-D.7)
      - 2.4.5 multiply decimal numbers by 10, 100, 1000, and 10 000, and divide decimal numbers by 10 and 100, using mental strategies (e.g., use a calculator to look for patterns and generalize to develop a rule);
        
        Multiply a decimal by a power of ten (5-H.2)
        
        Divide by powers of ten (5-H.6)
        
        Decimal division patterns over increasing place values (5-H.7)
      - 2.4.6 use estimation when solving problems involving the addition, subtraction, multiplication, and division of whole numbers, to help judge the reasonableness of a solution (Sample problem: Mori used a calculator to add 7.45 and 2.39. The calculator display showed 31.35. Explain why this result is not reasonable, and suggest where you think Mori made his mistake.).
        
        Estimate sums and differences of whole numbers (5-B.8)
        
        Estimate sums and differences: word problems (5-B.9)
        
        Estimate products (5-C.8)
        
        Estimate products: word problems (5-C.9)
        
        Estimate quotients (5-D.6)
        
        Estimate quotients: word problems (5-D.7)
      - 2.5 Proportional Relationships
        
        2.5.1 describe multiplicative relationships between quantities by using simple fractions and decimals (e.g., “If you have 4 plums and I have 6 plums, I can say that I have 1 1/2 or 1.5 times as many plums as you have.”);
        
        2.5.2 determine and explain, through investigation using concrete materials, drawings, and calculators, the relationship between fractions (i.e., with denominators of 2, 4, 5, 10, 20, 25, 50, and 100) and their equivalent decimal forms (e.g., use a 10 x 10 grid to show that 2/5 = 40/100, which can also be represented as 0.4);
        
        Model decimals and fractions (5-F.2)
        
        Convert fractions to decimals (5-F.12)
        
        Convert decimals to fractions (5-F.13)
        
        Equivalent fractions (5-K.3)
        
        Patterns of equivalent fractions (5-K.4)
        
        Write fractions in lowest terms (5-K.5)
        
        2.5.3 demonstrate an understanding of simple multiplicative relationships involving whole-number rates, through investigation using concrete materials and drawings (Sample problem: If 2 books cost $6, how would you calculate the cost of 8 books?).
        
        Multiply money amounts: word problems (5-I.3)
        
        Divide money amounts with decimals: word problems (5-I.5)

5.3 Measurement

3.1 Overall Expectations
- 3.1.1 estimate, measure, and record perimeter, area, temperature change, and elapsed time, using a variety of strategies;
- 3.1.2 determine the relationships among units and measurable attributes, including the area of a rectangle and the volume of a rectangular prism.
  - Area of squares and rectangles (5-Z.3)
  - Volume of rectangular prisms made of unit cubes (5-Z.6)
- 3.2 Attributes, Units, and Measurement Sense
  - 3.2.1 estimate, measure (i.e., using an analogue clock), and represent time intervals to the nearest second;
    - Elapsed time (5-U.3)
    - Find start and end times: word problems (5-U.4)
  - 3.2.2 estimate and determine elapsed time, with and without using a time line, given the durations of events expressed in minutes, hours, days, weeks, months, or years (Sample problem: You are travelling from Toronto to Montreal by train. If the train departs Toronto at 11:30 a.m. and arrives in Montreal at 4:56 p.m., how long will you be on the train?);
    - Elapsed time (5-U.3)
    - Find start and end times: word problems (5-U.4)
  - 3.2.3 measure and record temperatures to determine and represent temperature changes over time (e.g., record temperature changes in an experiment or over a season) (Sample problem: Investigate the relationship between weather, climate, and temperature changes over time in different locations.);
    - Read a thermometer (3-V.1)
  - 3.2.4 estimate and measure the perimeter and area of regular and irregular polygons, using a variety of tools (e.g., grid paper, geoboard, dynamic geometry software) and strategies.
  - 3.3 Measurement Relationships
    - 3.3.1 select and justify the most appropriate standard unit (i.e., millimetre, centimetre, decimetre, metre, kilometre) to measure length, height, width, and distance, and to measure the perimeter of various polygons;
      - Choose the appropriate metric unit of measure (5-V.1)
    - 3.3.2 solve problems requiring conversion from metres to centimetres and from kilometres to metres (Sample problem: Describe the multiplicative relationship between the number of centimetres and the number of metres that represent a length. Use this relationship to convert 5.1 m to centimetres.);
      - Compare and convert metric units of length (5-V.2)
    - 3.3.3 solve problems involving the relationship between a 12-hour clock and a 24-hour clock (e.g., 15:00 is 3 hours after 12 noon, so 15:00 is the same as 3:00 p.m.);
      - Time zones – 24-hour time (5-U.7)
      - Schedules – 24-hour time (5-U.9)
    - 3.3.4 create, through investigation using a variety of tools (e.g., pattern blocks, geoboard, grid paper) and strategies, two-dimensional shapes with the same perimeter or the same area (e.g., rectangles and parallelograms with the same base and the same height) (Sample problem: Using dot paper, how many different rectangles can you draw with a perimeter of 12 units? with an area of 12 square units?);
    - 3.3.5 determine, through investigation using a variety of tools (e.g., concrete materials, dynamic geometry software, grid paper) and strategies (e.g., building arrays), the relationships between the length and width of a rectangle and its area and perimeter, and generalize to develop the formulas [i.e., Area = length x width; Perimeter = (2 x length) + (2 x width)];
    - 3.3.6 solve problems requiring the estimation and calculation of perimeters and areas of rectangles (Sample problem: You are helping to fold towels, and you want them to stack nicely. By folding across the length and/or the width, you fold each towel a total of three times. You want the shape of each folded towel to be as close to a square as possible. Does it matter how you fold the towels?);
    - 3.3.7 determine, through investigation, the relationship between capacity (i.e., the amount a container can hold) and volume (i.e., the amount of space taken up by an object), by comparing the volume of an object with the amount of liquid it can contain or displace (e.g., a bottle has a volume, the space it takes up, and a capacity, the amount of liquid it can hold) (Sample problem: Compare the volume and capacity of a thin-walled container in the shape of a rectangular prism to determine the relationship between units for measuring capacity [e.g., millilitres] and units for measuring volume [e.g., cubic centimetres].);
    - 3.3.8 determine, through investigation using stacked congruent rectangular layers of concrete materials, the relationship between the height, the area of the base, and the volume of a rectangular prism, and generalize to develop the formula (i.e., Volume = area of base x height) (Sample problem: Create a variety of rectangular prisms using connecting cubes. For each rectangular prism, record the area of the base, the height, and the volume on a chart. Identify relationships.);
      - Volume of rectangular prisms made of unit cubes (5-Z.6)
    - 3.3.9 select and justify the most appropriate standard unit to measure mass (i.e., milligram, gram, kilogram, tonne).
      - Choose the appropriate metric unit of measure (5-V.1)
      - Compare and convert metric units of mass (5-V.3)

5.4 Geometry and Spatial Sense

4.1 Overall Expectations
- 4.1.1 identify and classify two-dimensional shapes by side and angle properties, and compare and sort three-dimensional figures;
- 4.1.2 identify and construct nets of prisms and pyramids;
  - Nets of three-dimensional figures (5-Y.3)
- 4.1.3 identify and describe the location of an object, using the cardinal directions, and translate two-dimensional shapes.
  - Coordinate planes as maps (5-Q.3)
- 4.2 Geometric Properties
  - 4.2.1 distinguish among polygons, regular polygons, and other two-dimensional shapes;
  - 4.2.2 distinguish among prisms, right prisms, pyramids, and other three-dimensional figures;
    - Identify three-dimensional figures (5-Y.1)
    - Count vertices, edges and faces (5-Y.2)
  - 4.2.3 identify and classify acute, right, obtuse, and straight angles;
    - Types of angles (5-W.5)
  - 4.2.4 measure and construct angles up to 90º, using a protractor;
    - Measure angles with a protractor (5-W.6)
  - 4.2.5 identify triangles (i.e., acute, right, obtuse, scalene, isosceles, equilateral), and classify them according to angle and side properties;
    - Classify triangles (5-W.7)
  - 4.2.6 construct triangles, using a variety of tools (e.g., protractor, compass, dynamic geometry software), given acute or right angles and side measurements (Sample problem: Use a protractor, ruler, and pencil to construct a scalene triangle with a 30° angle and a side measuring 12 cm.).
    - Measure angles with a protractor (5-W.6)
    - Classify triangles (5-W.7)
  - 4.3 Geometric Relationships
    - 4.3.1 identify prisms and pyramids from their nets;
      - Nets of three-dimensional figures (5-Y.3)
    - 4.3.2 construct nets of prisms and pyramids, using a variety of tools (e.g., grid paper, isometric dot paper, Polydrons, computer application).
      - Nets of three-dimensional figures (5-Y.3)
    - 4.4 Location and Movement
      - 4.4.1 locate an object using the cardinal directions (i.e., north, south, east, west) and a coordinate system (e.g., “If I walk 5 steps north and 3 steps east, I will arrive at the apple tree.”);
        
        Objects on a coordinate plane (5-Q.1)
        
        Coordinate planes as maps (5-Q.3)
      - 4.4.2 compare grid systems commonly used on maps (i.e., the use of numbers and letters to identify an area; the use of a coordinate system based on the cardinal directions to describe a specific location);
        
        Objects on a coordinate plane (5-Q.1)
        
        Coordinate planes as maps (5-Q.3)
      - 4.4.3 identify, perform, and describe translations, using a variety of tools (e.g., geoboard, dot paper, computer program);
        
        Reflection, rotation and translation (5-X.3)
      - 4.4.4 create and analyse designs by translating and/or reflecting a shape, or shapes, using a variety of tools (e.g., geoboard, grid paper, computer program) (Sample problem: Identify translations and/or reflections that map congruent shapes onto each other in a given design.).
        
        Reflection, rotation and translation (5-X.3)

5.5 Patterning and Algebra

5.1 Overall Expectations
- 5.1.1 determine, through investigation using a table of values, relationships in growing and shrinking patterns, and investigate repeating patterns involving translations;
- 5.1.2 demonstrate, through investigation, an understanding of the use of variables in equations.
- 5.2 Patterns and Relationships
  - 5.2.1 create, identify, and extend numeric and geometric patterns, using a variety of tools (e.g., concrete materials, paper and pencil, calculators, spreadsheets);
  - 5.2.2 build a model to represent a number pattern presented in a table of values that shows the term number and the term;
    - Complete a table for a two-variable relationship (5-R.7)
    - Complete a table from a graph (5-R.8)
  - 5.2.3 make a table of values for a pattern that is generated by adding or subtracting a number (i.e., a constant) to get the next term, or by multiplying or dividing by a constant to get the next term, given either the sequence (e.g., 12, 17, 22, 27, 32, …) or the pattern rule in words (e.g., start with 12 and add 5 to each term to get the next term);
    - Complete a table for a two-variable relationship (5-R.7)
    - Complete a table from a graph (5-R.8)
  - 5.2.4 make predictions related to growing and shrinking geometric and numeric patterns (Sample problem: Create growing L’s using tiles. The first L has 3 tiles, the second L has 5 tiles, the third L has 7 tiles, and so on. Predict the number of tiles you would need to build the 10th L in the pattern.);
    - Number sequences: word problems (5-P.8)
    - Number sequences: mixed review (5-P.9)
  - 5.2.5 extend and create repeating patterns that result from translations, through investigation using a variety of tools (e.g., pattern blocks, dynamic geometry software, dot paper).
  - 5.3 Variables, Expressions, and Equations
    - 5.3.1 demonstrate, through investigation, an understanding of variables as changing quantities, given equations with letters or other symbols that describe relationships involving simple rates (e.g., the equations C = 3 x n and 3 x n = C both represent the relationship between the total cost (C), in dollars, and the number of sandwiches purchased (n), when each sandwich costs $3);
    - 5.3.2 demonstrate, through investigation, an understanding of variables as unknown quantities represented by a letter or other symbol (e.g., 12 = 5 + __ or 12 = 5 + s can be used to represent the following situation: “I have 12 stamps altogether and 5 of them are from Canada. How many are from other countries?”);
    - 5.3.3 determine the missing number in equations involving addition, subtraction, multiplication, or division and one- or two-digit numbers, 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: What is the missing number in the equation 8 = 88 ÷ __?).
      - Complete the addition or subtraction sentence (5-G.4)
      - Solve equations with whole numbers (5-R.5)

5.6 Data Management and Probability

6.1 Overall Expectations
- 6.1.1 collect and organize discrete or continuous primary data and secondary data and display the data using charts and graphs, including broken-line graphs;
- 6.1.2 read, describe, and interpret primary data and secondary data presented in charts and graphs, including broken-line graphs;
- 6.1.3 represent as a fraction the probability that a specific outcome will occur in a simple probability experiment, using systematic lists and area models.
  - Probability of one event (6-FF.2)
- 6.2 Collection and Organization of Data
  - 6.2.1 distinguish between discrete data (i.e., data organized using numbers that have gaps between them, such as whole numbers, and often used to represent a count, such as the number of times a word is used) and continuous data (i.e., data organized using all numbers on a number line that fall within the range of the data, and used to represent measurements such as heights or ages of trees);
  - 6.2.2 collect data by conducting a survey or an experiment (e.g., gather and record air temperature over a two-week period) to do with themselves, their environment, issues in their school or community, or content from another subject, and record observations or measurements;
  - 6.2.3 collect and organize discrete or continuous primary data and secondary data and display the data in charts, tables, and graphs (including broken-line graphs) that have appropriate titles, labels (e.g., appropriate units marked on the axes), and scales that suit the range and distribution of the data (e.g., to represent precipitation amounts ranging from 0 mm to 50 mm over the school year, use a scale of 5 mm for each unit on the vertical axis and show months on the horizontal axis), using a variety of tools (e.g., graph paper, simple spreadsheets, dynamic statistical software);
  - 6.2.4 demonstrate an understanding that sets of data can be samples of larger populations (e.g., to determine the most common shoe size in your class, you would include every member of the class in the data; to determine the most common shoe size in Ontario for your age group, you might collect a large sample from classes across the province);
  - 6.2.5 describe, through investigation, how a set of data is collected (e.g., by survey, measurement, observation) and explain whether the collection method is appropriate.
- 6.3 Data Relationships
  - 6.3.1 read, interpret, and draw conclusions from primary data (e.g., survey results, measurements, observations) and from secondary data (e.g., precipitation or temperature data in the newspaper, data from the Internet about heights of buildings and other structures), presented in charts, tables, and graphs (including broken-line graphs);
  - 6.3.2 calculate the mean for a small set of data and use it to describe the shape of the data set across its range of values, using charts, tables, and graphs (e.g., “The data values fall mainly into two groups on both sides of the mean.”; “The set of data is not spread out evenly around the mean.”);
  - 6.3.3 compare similarities and differences between two related sets of data, using a variety of strategies (e.g., by representing the data using tally charts, stem-and-leaf plots, double bar graphs, or broken-line graphs; by determining measures of central tendency [i.e., mean, median, and mode]; by describing the shape of a data set across its range of values).
- 6.4 Probability
  - 6.4.1 determine and represent all the possible outcomes in a simple probability experiment (e.g., when tossing a coin, the possible outcomes are heads and tails; when rolling a number cube, the possible outcomes are 1, 2, 3, 4, 5, and 6), using systematic lists and area models (e.g., a rectangle is divided into two equal areas to represent the outcomes of a coin toss experiment);
    - Combinations (5-T.7)
  - 6.4.2 represent, using a common fraction, the probability that an event will occur in simple games and probability experiments (e.g., “My spinner has four equal sections and one of those sections is coloured red. The probability that I will land on red is 1/4.”);
    - Probability of one event (6-FF.2)
  - 6.4.3 pose and solve simple probability problems, and solve them by conducting probability experiments and selecting appropriate methods of recording the results (e.g., tally chart, line plot, bar graph).
    - Find the probability (5-T.5)
    - Make predictions (5-T.6)