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Learning Sequences

Target students' misconceptions and help them develop a deeper understanding of important concepts.

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Expressions & Equations

Students build their understanding of expressions and equations by exploring relationships between variables, numbers and operations.

Fractions

Students explore big ideas about fractions using number lines and area models to represent relationships and operations with fractions.

Ratios & Proportions

Students use manipulatives, tables, graphs, and double number lines to explore the relationship between ratios, proportions, slope and scaling.

Statistics & Probability

Students discover how data, statistics, and probability can be used to describe, make predictions and inform decisions about their world.

Fractions

1. What is a Fraction?

This lesson helps students understand and visualize a fraction as a number that can be represented as a point on a number line.

3.NF.1
3.NF.2a
3.NF.2b
3.NF.3

3.3
3.7.A

GRADE LEVEL 3,4

Fractions

2. Equivalent Fractions

This lesson helps students understand that two fractions are equivalent (or equal) if they are located at the same point on the number line.

3.NF.3d
3.NF.3a
3.NF.3b
3.NF.3c

3.3
3.7.A
4.3.A

GRADE LEVEL 3,4

Fractions

3. Fractions and Unit Squares

This lesson uses a dynamic geoboard to extend the concept of fraction to unit squares, where the unit fraction (1/b) is a portion of the area of a unit square.

3.G.2
3.NF.1
4.NF.3b

3.3
3.6.E
4.3

GRADE LEVEL 3,4

Fractions

4. Creating Equivalent Fractions

In this lesson, students explore how to create equivalent fractions by multiplying the numerator and denominator of a fraction by a common factor.

3.NF.3a
3.NF.3b
4.NF.1

4.3.C
4.3.G

GRADE LEVEL 3,4,5

Fractions

5. Adding and Subtracting Fractions with Like Denominators

This lesson uses interactive number lines to investigate addition and subtraction of fractions that refer to the same whole (i.e. have the same denominator).

4.NF.3a
4.NF.3b
4.NF.3c
5.NF.1

3.3.D
4.3
5.3.K

GRADE LEVEL 4,5,6

Fractions

6. Mixed Numbers

This lesson uses interactive number lines to help students investigate mixed numbers as a way to write improper fractions.

4.NF.4a
5.NF.1

5.3.K
6.2.C

Fractions

7. Adding Fractions with Unlike Denominators

This lesson uses unit squares to help students investigate addition and subtraction of fractions with unlike denominators.

5.NF.1

5.3.H
5.3.K

GRADE LEVEL 4,5,6

Fractions

8. Fractions as Division

This lesson connects the concept of obtaining fractions through division; the whole number a divided by the whole number b.

4.NF.3b
5.NF.3

4.3
6.3.E

GRADE LEVEL 3,4,5,6

Fractions

9. Multiplying Fractions by a Whole Number

This lesson can be used to develop multiplication of a fraction by a whole number.

4.NF.4a
4.NF.4b
5.NF.4a

3.7.A
4.3.A
5.3.I
6.3.E

GRADE LEVEL 3,5,6

Fractions

10. Fraction Multiplication

This lesson uses interactive unit squares to explore the concept of fraction multiplication.

5.NF.4b

3.3
6.3.E

GRADE LEVEL 5,6

Fractions

11. Dividing a Fraction by a Whole Number

This lesson uses a unit square to explore division of fractions by whole numbers.

5.NF.7a

5.3.L
5.3.J
6.3.A
6.3.E

Fractions

12. Dividing a Whole Number by a Fraction

In this lesson, unit squares are used to investigate division of whole numbers by a fraction.

5.NF.7b

5.3.J
5.3.L

GRADE LEVEL 5,6

Fractions

13. Dividing a Fraction by a Fraction

This lesson can be used to develop an understanding of dividing a fraction (a/b) by the fraction (c/d).

5.NF.7a
5.NF.7b

6.3.A
6.3.E

GRADE LEVEL 4,5,6

Fractions

14. Units Other Than a Unit Square

This lesson helps students to understand the importance of the unit by approaching fractions using area models.

4.NF.3b

4.3
6.2.D

GRADE LEVEL 3,4,5,6

Fractions

15. Comparing Units

This lesson helps students to understand that the size of a fraction will vary with the scale used to define a unit fraction.

3.6.E
6.2.C

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