Mathematics, Grade 5

Unit 1: Number

Whole numbers to 100 000; equivalent fractions from halves to twelfths, and decimals to hundredths; percents introduced; multi-digit multiplication and division; fraction addition and subtraction; and equivalent ratios and rates.

• Reading and representing numbers to 100 000
• Comparing and ordering numbers to 100 000

• Representing equivalent fractions, halves to twelfths
• Comparing and ordering fractions, halves to twelfths

• Reading, representing, comparing, and ordering decimals to hundredths
• Rounding decimals to the nearest tenth

• Equivalences between fractions and decimals
• Equivalences between decimals and whole-number percents

• Using properties of operations to solve multi-operation problems
• Recalling multiplication and division facts to 12 x 12
• Mental math: multiplying by 0.1 and 0.01, estimating with decimals

• Adding and subtracting whole numbers to 100 000 and decimals to hundredths
• Adding and subtracting fractions with like denominators

• Multiplying two-digit numbers (area model and algorithm)
• Dividing three-digit numbers by two-digit numbers (area model and algorithm)

• Multiplying and dividing whole numbers by unit fractions
• Representing and creating equivalent ratios and rates

Unit 2: Algebra

Repeating, growing, and shrinking patterns; algebraic expressions, equations, and inequalities; and code involving conditional statements and control structures.

• Identifying and describing repeating, growing, and shrinking patterns
• Creating and translating growing and shrinking patterns (tables and graphs)
• Determining pattern rules for repeating, growing, and shrinking patterns
• Creating patterns to show relationships among whole numbers and decimals

• Translating among words, algebraic expressions, and visual representations
• Evaluating algebraic expressions with whole numbers
• Solving equations with whole numbers up to 100
• Solving and graphing one-operation inequalities up to 50

• Writing and running code with conditional statements and control structures
• Reading and altering code with conditional statements and control structures

Unit 3: Data

Sampling techniques, relative-frequency tables, stacked-bar graphs, and infographics; mean, median, and mode; analysing data and misleading graphs; and probability using fractions, theoretical, and experimental comparisons.

• Explaining why sampling techniques give a representative sample
• Collecting data with sampling and organizing it in relative-frequency tables

• Selecting and justifying a graph type, including stacked-bar graphs
• Creating an infographic using relative-frequency tables and stacked-bar graphs

• Determining mean and median and identifying mode(s)
• Analysing data in stacked-bar and misleading graphs

• Using fractions and a probability line to make predictions
• Comparing theoretical and experimental probability

Unit 4: Spatial Sense

Triangle properties and construction; congruent shapes; views of objects; the Cartesian plane and translations; reflections and rotations; metric measurement and conversions; angles and protractors; and area and perimeter, including parallelogram and triangle formulas.

• Identifying triangle properties and constructing triangles
• Identifying and constructing congruent shapes

• Drawing and matching top, front, and side views of objects

• Plotting and reading coordinates in the first quadrant
• Describing translations that move a point between coordinates

• Performing and predicting translations, reflections, and rotations up to 180°

• Estimating and measuring with metric units
• Converting larger metric units to smaller ones

• Comparing angles by matching and with non-standard units
• Using a protractor to measure and construct angles up to 180°

• Developing and using the area formula for a parallelogram
• Developing and using the area formula for a triangle
• Showing that equal-area shapes can have different perimeters

Unit 5: Financial Literacy

Ways money is transferred; estimating and calculating transaction costs including sales tax; basic budgets; credit and debt; unit rates and best value; and taxes in Canada.

• Describing ways money can be transferred
• Estimating and calculating transaction costs, including sales tax

• Designing sample basic budgets
• Explaining credit and debt

• Calculating unit rates and identifying the best value
• Describing taxes collected by governments in Canada