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.

It’s easy… Multiply the numerators 5x2 =10 Multiply the denominators 6x3=18 Now you must reduce 10/18. divide 10 and 18

by 2 and you get 5/9

Do we need to invert? Or is that with

division?

Draw a representation and write a short story (scenario) to go with it.

5/6 + 2/3

5/6 x 2/3

…Solve the problem?

…Draw a picture/representation?

…Write a word problem?

What learning did that take from us?

Stolen Opportunity!

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.

Halves, fourths, and eighths

Thirds and sixths

Fractions of a set

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).

How do you know this is ¼?

How could you PROVE it?

How do you know these fourths are equal?

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”

COMMON MISCONCEPTION

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

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?

At your table…◦ Create 4

DIFFERENET representations of 1/8 of a sandwich.

Using fourths to find eighths

Chart: Fractions That are EqualLook 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 introduced?

Chart: Fractions That are EqualLook 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?

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?

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

Why?

¼ is greater than ½

??????

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

21

41

61

121

Bring some student examples of SAB 14

Students must find common denominators to add fractions.

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

1/2

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.