Number Sense and Numeration: representing and ordering numbers to 100 000; representing money amounts to $1000; developing the concept of place value to hundredths; comparing and ordering fractional amounts with like denominators; adding and subtracting decimal amounts to hundredths; multiplying two-digit whole numbers by two-digit whole numbers; dividing three-digit whole numbers by one-digit whole numbers; relating simple fractions to decimals
Measurement: measuring time intervals to the nearest second; determining elapsed time; measuring temperature; converting from metres to centimetres and from kilometres to metres; relating the 12-hour clock to the 24-hour clock; developing and applying area and perimeter relationships for a rectangle; relating capacity and volume; developing and applying the volume relationship for a right rectangular prism
Geometry and Spatial Sense: distinguishing among polygons and among prisms; identifying acute, right, obtuse, and straight angles; measuring angles to 90° with a protractor; constructing triangles; constructing nets of prisms and pyramids; locating objects using the cardinal directions; performing and describing translations
Patterning and Algebra: representing a pattern using a table of values; predicting terms in a pattern; determining the missing numbers in equations involving addition, subtraction, multiplication, or division and one- or two-digit numbers; investigating variables as unknown quantities; demonstrating equality using multiplication or division in equations with unknown quantities on both sides
Data Management and Probability: collecting and organizing discrete and continuous data; displaying data using broken-line graphs; sampling data from a population; understanding mean; comparing two related sets of data; representing probability using fractions
Throughout Grade 5, students will:
develop, select, and apply problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding;
• 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;
• 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);
• select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
• 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);
• 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;
• 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.
Number Sense and Numeration
• read, represent, compare, and order whole numbers to 100 000, decimal numbers to hundredths, proper and improper fractions, and mixed numbers;
• demonstrate an understanding of magnitude by counting forward and backwards by 0.01;
• 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;
• demonstrate an understanding of proportional reasoning by investigating whole-number rates.
Measurement
• estimate, measure, and record perimeter, area, temperature change, and elapsed time, using a variety of strategies;
• determine the relationships among units and measurable attributes, including the area of a rectangle and the volume of a rectangular prism
Geometry and Spatial Sense
• identify and classify two-dimensional shapes by side and angle properties, and compare and sort three-dimensional figures;
• identify and construct nets of prisms and pyramids;
• identify and describe the location of an object, using the cardinal directions, and translate two-dimensional shapes.
Patterning and Algebra
determine, through investigation using a table of values, relationships in growing and shrinking patterns, and investigate repeating patterns involving translations;
• demonstrate, through investigation, an understanding of the use of variables in equations
Data Management and Probability
collect and organize discrete or continuous primary data and secondary data and display the data using charts and graphs, including broken-line graphs;
• read, describe, and interpret primary data and secondary data presented in charts and graphs, including broken-line graphs;
• represent as a fraction the probability that a specific outcome will occur in a simple probability experiment, using systematic lists and area models.
Lesson reviews
Chapter 1: Patterns in Mathematics
Chapter 4: Addition and Subtraction
Chapter 5: Measuring Length and Time
Chapter 6: Multiplication and Division
Chapter 9: Multiplying Greater Numbers
Chapter 10: Dividing Greater Numbers
Chapter 11: 3-D Geometry and 3-D Measurements
Chapter 12: Fractions and Decimals
Chapter 14: Patterns and Motion in Geometry