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Fractions

Equal parts. Clear reasoning. Confident problem solving.

Know what achievement looks likeCBE Proficiency & Achievement Indicators
Read the achievement indicators here

Number · Demonstrate an understanding of multiplying and dividing fractions, concretely, pictorially and symbolically (N6).

The criteria at each level include those described at prior levels.

Level 1

  • Express a variety of numbers as equivalent fractions including the simplest form.
  • Identify the operation required to solve a given problem involving positive fractions.
  • Model, concretely or pictorially, addition and subtraction of fractions or mixed numbers, and record symbolically.

Level 2

  • Provide a context for multiplying or dividing two given positive fractions.
  • Model multiplication and division of simple fractions and mixed numbers using a concrete model or pictorial representation.

Level 3

  • Model multiplication and division of simple fractions and mixed numbers using a pictorial representation and record the process symbolically.
  • Solve problems involving multiplication and division of fractions and mixed numbers.

Level 4

  • Solve complex problems involving fractions and mixed numbers, applying order of operations when appropriate.
  • Apply estimation strategies as appropriate to solve and determine reasonableness of solutions.

From the linked CBE Math Assessment and Reporting Guide, January 2020, page 83. Website practice summaries are not proficiency marks.

Class Notes

Start where you need help

Fractions lessons

Go straight to a skill, or follow the connections. Each lesson brings together an explanation, a visual model, your class notes and practice.

Build the foundations

Name, compare and represent the same amount.

01Understand fractions02Equivalent fractions & simplest form03Compare & order fractions04Mixed numbers & improper fractions

Work with fractions

Choose an operation. Explain why it works.

05Add fractions & mixed numbers06Subtract fractions & regroup07Multiply fractions & mixed numbers08Divide fractions & mixed numbers

Connect & apply

Bring the strategies together in a problem.

09Order of operations with fractions10Fraction problems & mathematical decisions
Start with a picture

Same whole. More ways to name it.

Split every part in the same way. Explain why the amount stays fixed.

Choose a fraction

Predict before changing a value. Every whole in a bar diagram uses the same size. The models use non-negative amounts up to two wholes per input.

Explore equivalence in depth →
Choose the operation

The same fractions. Different questions.

+Combine amounts1/2 + 1/4 = 3/4−Find a difference1/2 − 1/4 = 1/4×Take part of an amount1/2 × 1/4 = 1/8÷Count groups of a size1/2 ÷ 1/4 = 2
Learn together · apply the ideas

Bring the unit to life.

A good question to start with.

Why is 1/2 + 1/4 different from 1/2 ÷ 1/4? Draw both situations before checking.

Compare the meanings

Addition combines half a whole and a quarter of the same whole, giving 3/4. Division counts how many quarter-sized groups fit into one half, giving 2 groups. The output units and the relationships differ.

Mix the skills. Keep the reasoning.

Fresh questions · useful feedback

Build fluency, one decision at a time.

Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.

0 of 8 questions completed

Use an exact fraction (7/12), mixed number (1 3/4), or terminating decimal. For comparisons use <, = or >. Follow any requested form; leave units out of the answer box.

This round saves on this device. It is practice, not a school mark.

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