# Exploring Fractions and Decimals Unit Plan – Year 3 and Year 4

11 x Lessons

This Mathematics unit covers a range of concepts relating to fractions and decimals.

It consists of 11 lessons of approximately 60 minutes duration.

The sequence of lessons and suggested time frames should be regarded as a guide only; teachers should pace lessons in accordance with the individual learning needs of their class.

An assessment task for monitoring student understanding of the unit objectives is included and will require an additional lesson.

## Overview

### Objectives

- To recognize common unit fractions such as halves, thirds, quarters, fifths and eighths.
- To represent common unit fractions and their multiples to create a whole.
- To identify equivalent fractions for one half, one third, one quarter and one fifth.
- To locate and represent some common equivalent fractions on a number line.
- To count by common unit fractions and mixed numerals.
- To convert between improper fractions and mixed numerals.
- To apply knowledge and understanding of fractions to a real-world context.
- To explore tenths as fractions and in decimal notation.
- To explore hundredths as fractions and in decimal notation.

### Preparing for Learning

Prior to commencing the unit, develop a fractions and decimals display in the classroom. Display *posters* and *word wall vocabulary* that the students will engage with throughout the unit to stimulate their learning. For examples of such resources, browse the *Fractions, Decimals and Percentages category* on the Teach Starter website.

There are many concepts to address within the topic of fractions and decimals. The lessons in this unit cover a range of these concepts, many of which have varying degrees of complexity. Teachers are encouraged to select lessons from the unit that best suit the learning needs of their students, or to adapt lessons accordingly.

Some of the resources which accompany this unit plan will need to be prepared prior to teaching. For this reason, it is advised that teachers browse through all lessons before commencing the unit.

## Lessons

## Resources

#### Common Core State Standards alignment

Grade 3 > Standards for Mathematical Practice > Number & Operations - Fractions > Develop understanding of fractions as numbers > **CCSS.MATH.CONTENT.3.NF.A.1**

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

Grade 3 > Standards for Mathematical Practice > Number & Operations - Fractions > Develop understanding of fractions as numbers > **CCSS.MATH.CONTENT.3.NF.A.2**

Understand a fraction as a number on the number line; represent fractions on a number line diagram.

Grade 3 > Standards for Mathematical Practice > Number & Operations - Fractions > Develop understanding of fractions as numbers > **CCSS.MATH.CONTENT.3.NF.A.3**

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Grade 4 > Standards for Mathematical Practice > Number & Operations - Fractions > Extend understanding of fraction equivalence and ordering > **CCSS.MATH.CONTENT.4.NF.A.1**

Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Grade 4 > Standards for Mathematical Practice > Number & Operations - Fractions > Build fractions from unit fractions > CCSS.MATH.CONTENT.4.NF.B.3 > **CCSS.MATH.CONTENT.4.NF.B.3.B**

Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

Grade 4 > Standards for Mathematical Practice > Number & Operations - Fractions > Understand decimal notation for fractions, and compare decimal fractions > **CCSS.MATH.CONTENT.4.NF.C.6**

Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

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