Ontario

5.B Number

• 5.B1 Number Sense

  • Whole Numbers

    • 5.B1.1 read, represent, compose, and decompose whole numbers up to and including 100 000, using appropriate tools and strategies, and describe various ways they are used in everyday life

      • Expanded form up to 100 000 (5-A.1)
      • Place value up to 100 000 (5-A.3)
      • Word names for numbers up to 100 000 (5-A.7)
      • Spell word names for numbers up to 100 000 (5-A.9)

    • 5.B1.2 compare and order whole numbers up to and including 100 000, in various contexts

      • Compare numbers up to 100 000 (5-A.12)
      • Order numbers up to 100 000 (5-A.14)

  • Fractions, Decimals and Percents

    • 5.B1.3 represent equivalent fractions from halves to twelfths, including improper fractions and mixed numbers, using appropriate tools, in various contexts

      • Find equivalent fractions using area models (5-O.1)
      • Graph equivalent fractions on number lines (5-O.2)
      • Equivalent fractions (5-O.3)
      • Write fractions in lowest terms (5-O.5)
      • Convert between improper fractions and mixed numbers (5-O.6)

    • 5.B1.4 compare and order fractions from halves to twelfths, including improper fractions and mixed numbers, in various contexts

      • Graph and compare fractions on number lines (5-P.1)
      • Benchmark fractions (5-P.2)
      • Compare fractions using benchmarks (5-P.3)
      • Compare fractions (5-P.4)
      • Compare fractions and mixed numbers (5-P.5)
      • Order fractions with like denominators (5-P.6)
      • Order fractions with like numerators (5-P.7)
      • Order fractions with unlike denominators (5-P.8)
      • Order fractions review (5-P.9)

    • 5.B1.5 read, represent, compare, and order decimal numbers up to hundredths, in various contexts

      • What decimal number is illustrated? (5-G.1)
      • Understanding decimals expressed in words: up to hundredths (5-G.3)
      • Expanded form of decimals up to hundredths (5-G.5)
      • Decimal number lines (5-G.8)
      • Compare decimals using grids (5-G.9)
      • Compare decimals on number lines (5-G.10)
      • Compare decimal numbers up to hundredths (5-G.11)
      • Put decimals in order: up to hundredths (5-G.12)

    • 5.B1.6 round decimal numbers to the nearest tenth, in various contexts

      • Round decimals to the nearest whole number or tenth (5-G.7)

    • 5.B1.7 describe relationships and show equivalences among fractions, decimal numbers up to hundredths, and whole number percents, using appropriate tools and drawings, in various contexts

      • Model decimals and fractions (5-G.2)
      • Convert fractions to decimals: up to hundredths (5-G.13)
      • Convert decimals to fractions: up to hundredths (5-G.14)
      • Convert decimals between standard and expanded form using fractions: up to hundredths (5-G.15)
      • Compare decimals and fractions on number lines (5-G.16)
      • Compare decimals and fractions: up to hundredths (5-G.17)
      • Convert fractions to percents using grid models (5-Y.3)
      • Represent percents with grid models, decimals and fractions (5-Y.4)
      • Convert between percents and fractions (5-Y.5)
      • Convert between percents and decimals (5-Y.6)
      • Convert between percents, fractions and decimals (5-Y.7)
      • Compare percents to each other and to fractions and decimals (5-Y.8)
      • Compare percents and fractions: word problems (5-Y.9)

• 5.B2 Operations

  • Properties and Relationships

    • 5.B2.1 use the properties of operations, and the relationships between operations, to solve problems involving whole numbers and decimal numbers, including those requiring more than one operation, and check calculations

      • Complete addition and subtraction sentences (5-B.5)
      • Properties of addition (5-B.8)
      • Add using properties (5-B.9)
      • Properties of multiplication (5-C.8)
      • Multiply using properties (5-C.9)
      • Multi-step word problems: multiplicative comparison (5-D.22)
      • Relate multiplication and division (5-D.23)
      • Complete the decimal addition or subtraction sentence: up to hundredths (5-I.7)
      • Evaluate numerical expressions (5-V.4)
      • Identify mistakes involving the order of operations (5-V.5)
      • Evaluate numerical expressions with parentheses in different places (5-V.6)
      • Multi-step word problems (5-W.3)
      • Multi-step word problems: identify reasonable answers (5-W.4)

  • Math Facts

    • 5.B2.2 recall and demonstrate multiplication facts from 0 × 0 to 12 × 12, and related division facts

      • Multiplication facts to 10 (5-C.1)
      • Multiplication facts to 12 (5-C.2)
      • Division facts to 10 (5-D.1)
      • Division facts to 12 (5-D.3)

  • Mental Math

    • 5.B2.3 use mental math strategies to multiply whole numbers by 0.1 and 0.01 and estimate sums and differences of decimal numbers up to hundredths, and explain the strategies used

      • Estimate sums and differences of decimals using rounding: up to hundredths (5-I.9)
      • Estimate sums and differences of decimals using benchmarks (5-I.10)
      • Multiply a whole number by 0.1 or 0.01 (5-K.3)

  • Addition and Subtraction

    • 5.B2.4 represent and solve problems involving the addition and subtraction of whole numbers that add up to no more than 100 000, and of decimal numbers up to hundredths, using appropriate tools, strategies, and algorithms

      • Add and subtract whole numbers up to 100 000 (5-B.1)
      • Add and subtract whole numbers up to 100 000: word problems (5-B.3)
      • Add decimal numbers up to hundredths (5-I.2)
      • Subtract decimal numbers up to hundredths (5-I.3)
      • Add and subtract decimal numbers up to hundredths (5-I.4)
      • Add and subtract decimals up to hundredths: word problems (5-I.5)
      • Add and subtract money amounts (5-M.1)
      • Add and subtract money: word problems (5-M.2)
      • Price lists with addition and subtraction (5-M.3)

    • 5.B2.5 add and subtract fractions with like denominators, in various contexts

      • Decompose fractions multiple ways (5-Q.1)
      • Add fractions with like denominators using area models (5-Q.2)
      • Add fractions with like denominators using strip models (5-Q.3)
      • Add fractions with like denominators using number lines (5-Q.4)
      • Add fractions with like denominators (5-Q.5)
      • Subtract fractions with like denominators using area models (5-Q.6)
      • Subtract fractions with like denominators using strip models (5-Q.7)
      • Subtract fractions with like denominators using number lines (5-Q.8)
      • Subtract fractions with like denominators (5-Q.9)
      • Add and subtract fractions with like denominators using number lines (5-Q.10)
      • Add and subtract fractions with like denominators (5-Q.11)
      • Add and subtract fractions with like denominators: word problems (5-Q.12)
      • Add three or more fractions with like denominators (5-Q.13)
      • Add three or more fractions with like denominators: word problems (5-Q.14)
      • Add and subtract mixed numbers with like denominators (5-Q.18)
      • Add and subtract mixed numbers with like denominators: word problems (5-Q.19)

  • Multiplication and Division

    • 5.B2.6 represent and solve problems involving the multiplication of two-digit whole numbers by two-digit whole numbers using the area model and using algorithms, and make connections between the two methods

      • Multiply 2-digit numbers by 2-digit numbers using area models I (5-C.13)
      • Multiply 2-digit numbers by 2-digit numbers using area models II (5-C.14)
      • Multiply 2-digit numbers by 2-digit numbers: complete the missing steps (5-C.15)
      • Multiply 2-digit numbers by 2-digit numbers (5-C.16)
      • Multiply 2-digit numbers by 2-digit numbers: word problems (5-C.17)

    • 5.B2.7 represent and solve problems involving the division of three-digit whole numbers by two-digit whole numbers using the area model and using algorithms, and make connections between the two methods, while expressing any remainder appropriately

      • Divide by 2-digit numbers using models (5-D.14)
      • Divide by 2-digit numbers using partial products (5-D.15)
      • Divide 2-digit and 3-digit numbers by 2-digit numbers (5-D.16)
      • Divide 2-digit and 3-digit numbers by 2-digit numbers: word problems (5-D.17)

    • 5.B2.8 multiply and divide one-digit whole numbers by unit fractions, using appropriate tools and drawings

      • Multiply unit fractions by whole numbers using number lines (5-S.1)
      • Multiply unit fractions by whole numbers: choose the model (5-S.2)
      • Multiply unit fractions and whole numbers: sorting (5-S.4)
      • Multiply unit fractions by whole numbers (5-S.5)
      • Multiply unit fractions by whole numbers: word problems (5-S.6)
      • Divide whole numbers by unit fractions using models (5-T.1)
      • Divide whole numbers by unit fractions using area models (5-T.2)
      • Divide whole numbers by unit fractions (5-T.3)

    • 5.B2.9 represent and create equivalent ratios and rates, using a variety of tools and models, in various contexts

      • Identify equivalent ratios (5-X.5)
      • Write an equivalent ratio (5-X.6)
      • Ratio tables (5-X.7)
      • Equivalent rates (5-X.9)

5.C Algebra

• 5.C1 Patterns and Relationships

  • Patterns

    • 5.C1.1 identify and describe repeating, growing, and shrinking patterns, including patterns found in real-life contexts

    • 5.C1.2 create and translate growing and shrinking patterns using various representations, including tables of values and graphs

      • Make a repeating pattern (5-Z.3)
      • Use a rule to complete a table and a graph (5-AA.5)

    • 5.C1.3 determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in repeating, growing, and shrinking patterns

      • Find the next shape in a repeating pattern (5-Z.1)
      • Complete a repeating pattern (5-Z.2)
      • Find the next row in a growing pattern of shapes (5-Z.4)
      • Complete an increasing number sequence (5-Z.8)
      • Complete a geometric number sequence (5-Z.9)
      • Number sequences: word problems (5-Z.10)
      • Number sequences: mixed review (5-Z.11)

    • 5.C1.4 create and describe patterns to illustrate relationships among whole numbers and decimal tenths and hundredths

      • Addition patterns over increasing place values (5-B.11)
      • Subtraction patterns over increasing place values (5-B.12)
      • Multiplication patterns over increasing place values (5-C.5)
      • Division patterns over increasing place values (5-D.8)
      • Decimal division patterns over increasing place values (5-L.2)
      • Identify mistakes in number patterns (5-Z.7)

• 5.C2 Equations and Inequalities

  • Variables and Expressions

    • 5.C2.1 translate among words, algebraic expressions, and visual representations that describe equivalent relationships

      • Write variable expressions (5-BB.1)
      • Write variable expressions: word problems (5-BB.2)

    • 5.C2.2 evaluate algebraic expressions that involve whole numbers

      • Evaluate variable expressions (5-BB.3)

  • Equalities and Inequalities

    • 5.C2.3 solve equations that involve whole numbers up to 100 in various contexts, and verify solutions

      • Does x satisfy an equation? (5-CC.1)
      • Which value makes the equation true? (5-CC.2)
      • Model and solve equations using algebra tiles (5-CC.4)
      • Write and solve equations that represent diagrams (5-CC.5)
      • Solve addition and subtraction equations with whole numbers (5-CC.6)
      • Solve multiplication and division equations with whole numbers (5-CC.7)
      • Solve equations with whole numbers (5-CC.8)
      • Write a one-step equation: word problems (5-CC.9)
      • Which word problem matches the one-step equation? (5-CC.10)

  • Equalities and Inequalities

    • 5.C2.4 solve inequalities that involve one operation and whole numbers up to 50, and verify and graph the solutions

      • Solutions to inequalities (5-DD.1)
      • Graph inequalities on number lines (5-DD.2)
      • Write inequalities from number lines (5-DD.3)
      • Solve one-step inequalities (5-DD.4)
      • Graph solutions to one-step inequalities (5-DD.5)

• 5.C3 Coding

  • Coding Skills

    • 5.C3.1 solve problems and create computational representations of mathematical situations by writing and executing code, including code that involves conditional statements and other control structures

    • 5.C3.2 read and alter existing code, including code that involves conditional statements and other control structures, and describe how changes to the code affect the outcomes

5.D Data

• 5.D1 Data Literacy

  • Data Collection and Organization

    • 5.D1.1 explain the importance of various sampling techniques for collecting a sample of data that is representative of a population

      • Identify biased samples (5-GG.12)

    • 5.D1.2 collect data, using appropriate sampling techniques as needed, to answer questions of interest about a population, and organize the data in relative-frequency tables

      • Create relative frequency tables (5-FF.16)

  • Data Visualization

    • 5.D1.3 select from among a variety of graphs, including stacked-bar graphs, the type of graph best suited to represent various sets of data; display the data in the graphs with proper sources, titles, and labels, and appropriate scales; and justify their choice of graphs

      • Choose the best type of graph (5-FF.20)

    • 5.D1.4 create an infographic about a data set, representing the data in appropriate ways, including in relative-frequency tables and stacked-bar graphs, and incorporating any other relevant information that helps to tell a story about the data

      • Complete bar graphs (5-FF.6)
      • Complete double bar graphs (5-FF.8)
      • Create relative frequency tables (5-FF.16)

  • Data Analysis

    • 5.D1.5 determine the mean and the median and identify the mode(s), if any, for various data sets involving whole numbers and decimal numbers, and explain what each of these measures indicates about the data

      • Find the mean (5-GG.6)
      • Mean: find the missing number (5-GG.7)
      • Interpret charts and graphs to find the mean (5-GG.8)
      • Calculate mean, median and mode (5-GG.9)
      • Mean, median and mode: find the missing number (5-GG.10)
      • Interpret charts to find mean, median and mode (5-GG.11)

    • 5.D1.6 analyse different sets of data presented in various ways, including in stacked-bar graphs and in misleading graphs, by asking and answering questions about the data, challenging preconceived notions, and drawing conclusions, then make convincing arguments and informed decisions

      • Interpret bar graphs (5-FF.4)
      • Interpret bar graphs: multi-step problems (5-FF.5)
      • Interpret double bar graphs (5-FF.7)
      • Interpret frequency charts: one-step problems (5-FF.13)
      • Interpret frequency charts: multi-step problems (5-FF.14)

• 5.D2 Probability

  • Probability

    • 5.D2.1 use fractions to express the probability of events happening, represent this probability on a probability line, and use it to make predictions and informed decisions

      • Understanding probability (5-GG.1)
      • Find the probability (5-GG.2)
      • Make predictions (5-GG.3)

    • 5.D2.2 determine and compare the theoretical and experimental probabilities of an event happening

      • Experimental probability (5-GG.4)

5.E Spatial Sense

• 5.E1 Geometric and Spatial Reasoning

  • Geometric Reasoning

    • 5.E1.1 identify geometric properties of triangles, and construct different types of triangles when given side or angle measurements

      • Acute, obtuse and right triangles (5-KK.1)
      • Scalene, isosceles and equilateral triangles (5-KK.2)
      • Classify triangles (5-KK.3)

    • 5.E1.2 identify and construct congruent triangles, rectangles, and parallelograms

      • Identify congruent figures (5-LL.6)

    • 5.E1.3 draw top, front, and side views of objects, and match drawings with objects

      • Three-dimensional figures viewed from different perspectives (5-MM.5)

  • Location and Movement

    • 5.E1.4 plot and read coordinates in the first quadrant of a Cartesian plane using various scales, and describe the translations that move a point from one coordinate to another

      • Objects on a coordinate plane (5-AA.2)
      • Graph points on a coordinate plane (5-AA.3)
      • Graph points from a table (5-AA.4)
      • Follow directions on a coordinate plane (5-AA.8)

    • 5.E1.5 describe and perform translations, reflections, and rotations up to 180° on a grid, and predict the results of these transformations

      • Reflection, rotation and translation (5-LL.3)
      • Combinations of reflections, rotations and translations (5-LL.4)
      • Transformations on the coordinate plane (5-LL.5)

• 5.E2 Measurement

  • The Metric System

    • 5.E2.1 use appropriate metric units to estimate and measure length, area, mass, and capacity

      • Which metric unit of length is appropriate? (5-II.1)
      • Which metric unit of mass is appropriate? (5-II.3)
      • Which metric unit of capacity is appropriate? (5-II.5)

    • 5.E2.2 solve problems that involve converting larger metric units into smaller ones, and describe the base ten relationships among metric units

      • Compare and convert metric units of length (5-II.2)
      • Compare and convert metric units of mass (5-II.4)
      • Compare and convert metric units of capacity (5-II.6)

  • Angles

    • 5.E2.3 compare angles and determine their relative size by matching them and by measuring them using appropriate non-standard units

      • Types of angles (5-JJ.6)
      • Angles of 90, 180, 270 and 360 degrees (5-JJ.7)

    • 5.E2.4 explain how protractors work, use them to measure and construct angles up to 180°, and use benchmark angles to estimate the size of other angles

      • Measure angles with a protractor (5-JJ.8)
      • Draw angles with a protractor (5-JJ.9)

  • Area

    • 5.E2.5 use the area relationships among rectangles, parallelograms, and triangles to develop the formulas for the area of a parallelogram and the area of a triangle, and solve related problems

      • Understanding area of a parallelogram (5-NN.5)
      • Area of parallelograms (5-NN.6)
      • Understanding area of a triangle (5-NN.7)
      • Area of triangles (5-NN.8)

    • 5.E2.6 show that two-dimensional shapes with the same area can have different perimeters, and solve related problems

      • Rectangles: relationship between perimeter and area (5-NN.12)

5.F Financial Literacy

• 5.F1 Money and Finances

  • Money Concepts

    • 5.F1.1 describe several ways money can be transferred among individuals, organizations, and businesses

      • Identify advantages and disadvantages of payment methods (5-OO.1)
      • Evaluate payment methods (5-OO.2)
      • Debit cards and credit cards (5-OO.3)

    • 5.F1.2 estimate and calculate the cost of transactions involving multiple items priced in dollars and cents, including sales tax, using various strategies

      • Price lists with addition and subtraction (5-M.3)
      • Debit cards and credit cards (5-OO.3)

  • Financial Management

    • 5.F1.3 design sample basic budgets to manage finances for various earning and spending scenarios

      • Balance a budget (5-OO.6)
      • Adjust a budget (5-OO.7)

    • 5.F1.4 explain the concepts of credit and debt, and describe how financial decisions may be impacted by each

      • Reading financial records (5-OO.4)
      • Keeping financial records (5-OO.5)

  • Consumer and Civic Awareness

    • 5.F1.5 calculate unit rates for various goods and services, and identify which rates offer the best value

      • Unit rates (5-X.8)

    • 5.F1.6 describe the types of taxes that are collected by the different levels of government in Canada, and explain how tax revenue is used to provide services in the community