Grade Four:Fractions and Decimals

Understanding Common Core Fraction Expectations In 4th Grade-

Villa Heights/Northeast Learning CommunityTuesday, January 14, 2014 3:30 pm -- 5:30 pm Tuesday, January 28, 2014 3:30 pm -- 5:30 pm

Thursday, February 20, 2014 3:30 pm -- 5:30 pm

Unit 6Fraction Cards and Decimal Squares

Today’s Goals Honor the challenge in this work and set the tone for teachers as

learners

Build conceptual knowledge of fractions, and acknowledge most of us come with procedural

Become proficient with the work in Investigation 1

Know how and where to highlight the standards for students.

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.

Let’s Start with some MATH!

What do the Common Core State Standards have to say about HOW students demonstrate their understanding of fractions?

On your standards, highlight the phrase “using (a) visual fraction model(s)” everywhere you see it.

Highlighting the Common Core

What makes work with fractions and decimals so difficult for students? (p. 139-140)

Halves, fourths, and eighths

Thirds and sixths

Fractions of a set

Investigation 1Fractions of an Area:

Halves, Fourths, and Eighths

In grade 4, expectations are limited to fractions with

….? denominators

At your table…◦ Create 4

DIFFERENET representations of ¼ of a sandwich. (On the left side of your poster).

One-fourth of a sandwich

How do you know this is ¼?

How could you PROVE it?

One-fourth of a Sandwich

How do you know these fourths are equal?

One-fourth of a Sandwich

2.G.3. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths.

RECOGNIZE THAT EQUAL SHARES OF IDENTICAL WHOLES NEED NOT HAVE THE SAME SHAPE.

“If they don’t look the same, they aren’t equal”

Why Bother? Common Misconception

COMMON MISCONCEPTION

If the blue is ¼, then what is the white?

One-fourth of a Sandwich

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

4.NF.3. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

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.

Where is the opportunity to be mindful about standards 4.NF.3 a and b?

Page 29

At your table…◦ Create 4

DIFFERENET representations of 1/8 of a sandwich.

One-eighth of a Sandwich

How did you find Eighths?

Using fourths to find eighths

Relationships are KEY!

Fractions that are Equal

Chart: Fractions That are Equal Look at the bottom of page 34: Discussion- How are

Thirds and Sixths Related? Read to the bottom of page 35.

What is the math focus for discussion?

How is the idea of equivalent fractions reintroduced?

Thirds and Sixths

Chart: Fractions That are Equal Look at the bottom of page 34: Discussion- How are

Thirds and Sixths Related? Read to the bottom of page 35.

If you skipped this discussion, what standard would students miss?

Thirds and Sixths

4.NF.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.

I have a crate of 24 oranges. ¼ go to Mr. Freed. The rest go to Ms. Lee.

What fraction of the oranges will Ms. Lee get?

How many oranges will Mr. Freed get? How many oranges will Ms. Lee get?

Fractional Parts of a Group

Look at the 3 possible student responses on page 39. Which student best illustrates this standard?

Why?

Read Standard 4.NF.3d

¼ is greater than ½

Give a situation where…

??????

Write fractions to show all of the parts of the rectangle = 1

How could students prove whether the following equation is true or false?

+ + + = 1

But I thought students didn’t have to add with unlike denominators! Read teacher note p. 56

Combinations to 1

21

41

61

121

Bring some student examples of SAB 14

Next Time

Students must find common denominators to add fractions.

Students in 4th grade only add and subtract with common denominators.

True or False

Students develop understanding of fraction equivalence and operations with fractions. They recognize that two different fractions can be equal (e.g., 15/9 = 5/3), and they develop methods for generating and recognizing equivalent fractions. Students extend previous understandings about how fractions are built from unit fractions, composing fractions from unit fractions, decomposing fractions into unit fractions, and using the meaning of fractions and the meaning of multiplication to multiply a fraction by a whole number.

Big Picture