Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100. 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. 4.NF.2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Anchor Standard/Mathematical Practice(s)

MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. MP.7. Look for and make use of structure. MP.8. Look for and express regularity in repeated reasoning.

Information Technology Standard

Use technology tools and skills to reinforce classroom concepts and activities.

Revised Bloom's Level of thinking

Remembering Understanding Analyzing

Learning Target/Task Analysis

4.NF.1 This standard refers to visual fraction models. This includes area models, linear models (number lines) or it could be a collection/set models. This standard extends the work in third grade by using additional denominators (5, 10, 12, and 100). Students can use visual models or applets to generate equivalent fractions.

Example: All the area models show 1/2. The second model shows 2/4 but also shows that 1/2 and 2/4 are equivalent fractions because their areas are equivalent. When a horizontal line is drawn through the center of the model, the number of equal parts doubles and size of the parts is halved. Students will begin to notice connections between the models and fractions in the way both the parts and wholes are counted and begin to generate a rule for writing equivalent fractions.

4.NF.2 This standard calls students to compare fractions by creating visual fraction models or finding common denominators or numerators. Students’ experiences should focus on visual fraction models rather than algorithms. When tested, models may or may not be included. Students should learn to draw fraction models to help them compare and use reasoning skills based on fraction benchmarks. Students must also recognize that they must consider the size of the whole when comparing fractions (ie,1/2 and 1/8 of two medium pizzas is very different from1/2 of one medium and 1/8 of one large). Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

= 3/4 = 1/2

=1/3

Example: Use patterns blocks. 1. If a red trapezoid is one whole, which block shows 1/3? 2. If the blue rhombus is 1/3, which block shows one whole? 3. If the red trapezoid is one whole, which block shows 2/3?

Mary used a 12 x 12 grid to represent 1 and Janet used a 10 x 10 grid to represent 1. Each girl shaded grid squares to show 1/4. How many grid squares did Mary shade? How many grid squares did Janet shade? Why did they need to shade different numbers of grid squares? Possible solution: Mary shaded 36 grid squares; Janet shaded 25 grid squares. The total number of little squares is different in the two grids, so 1/4 of each total number is different.

Example: There are two cakes on the counter that are the same size. The first cake has ½ of it left. The second cake has 5/12 left. Which cake has more left?

Common Misconceptions: (4.NF.1-2) Students think that when generating equivalent fractions they need to multiply or divide either the numerator or denominator, such as, changing 1/2 to sixths. They would multiply the denominator by 3 to get 1/6, instead of multiplying the numerator by 3 also. Their focus is only on the multiple of the denominator, not the whole fraction. It’s important that students use a fraction in the form of one such as 3/3 so that the numerator and denominator do not contain the original numerator or denominator.

I can...

I can understand the value of a fraction. I can understand how a fraction model represents a fraction. I can understand how two fractions are equivalent. I can understand how two different looking fracton models are equal to the same value. I can recognize that two fractions with the same denominator and different numerators have a different value. I can use the symbols >, <, = to compare the value of fractions with same denominator and different numerators. I can recognize that two fractions with different denominators and same numerators represent different values. I can use the symbols >, <, or = to compare the value of fractios with different denominator and same numerators. I can determine whether a fraction is greater than, less than, or equal to a benchmark fraction. ( 1/4, 1/2, 3/4, 1/10) I can recognize that I can only compare 2 fractions when both fractions refer to the same whole. (using pattern blocks-hexagon = 1, so trapezoid = 1/2)

Fraction Tiles/Pizza, Tangram shapes, Grid Paper, Choice Boards, ELL/EC students: vocabulary list ahead of time, Post words with visuals on word wall and in vocabulary notebooks, Use Frayer Models and foldables, Dominoes, Have students work in partners to divide the class into a given number of ways. Use egg cartons & counters to represent fractions. DPI Classroom Strategies p. 22

Letter R--Have students work in groups to make fraction/decimal dominoes. One end has a picture; the other has the fraction and/or decimal notation. On the other side they could write the number/fraction out in word or expanded form and they could also write a story problem.

DPI Classroom Strategies pg 25—Letter AA Play Buckets & Bowls ---Label containers Near Zero, About ½ and Close to 1. Pass out index cards with decimal numbers. Students would work with partners to convert the decimal to a fraction and place your card in the correct bucket.

Read The Hershey’s Milk Chocolate Bar Fraction Book by Pallotta to introduce fractions during reading. Have students create a picture book of fractions to aid them in teaching younger siblings about fractions.

## Common Core Standards

Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.4.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.

4.NF.2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

## Anchor Standard/Mathematical Practice(s)

MP.2. Reason abstractly and quantitatively.MP.4. Model with mathematics.

MP.7. Look for and make use of structure.

MP.8. Look for and express regularity in repeated reasoning.

## Information Technology Standard

Usetechnologytools and skills to reinforce classroom concepts and activities.## Revised Bloom's Level of thinking

RememberingUnderstanding

Analyzing

## Learning Target/Task Analysis

4.NF.1This standard refers to visual fraction models. This includes area models, linear models (number lines) or it could be a collection/set models.

This standard extends the

workin third grade by using additional denominators (5, 10, 12, and 100).Students can use visual models or applets to generate equivalent fractions.

Example:

All the area models show 1/2. The second model shows 2/4 but also shows that 1/2 and 2/4 are

equivalent fractions because their areas are equivalent. When a horizontal line is drawn through

the center of the model, the number of equal parts doubles and size of the parts is halved.

Students will begin to notice connections between the models and fractions in the way both the

parts and wholes are counted and begin to generate a rule for writing equivalent fractions.

1/2 = 1/2 x 2/2 = 2/4 =

1/2 x 3/3 = 3/6 = 1/2 x 4/4 = 4/8 =

Technology Connection

4.NF.2

This standard calls students to compare fractions by creating visual fraction models or finding common denominators or numerators. Students’ experiences should focus on visual fraction models rather than algorithms. When tested, models may or may not be included. Students should learn to draw fraction models to help them compare and use reasoning skills based on fraction benchmarks. Students must also recognize that they must consider the size of

the whole when comparing fractions (ie,1/2 and 1/8 of two medium pizzas is very different from1/2 of one medium and 1/8 of one large). Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

= 3/4

= 1/2

=1/3

Example:

Use patterns blocks.

1. If a red trapezoid is one whole, which block shows 1/3?

2. If the blue rhombus is 1/3, which block shows one whole?

3. If the red trapezoid is one whole, which block shows 2/3?

Mary used a 12 x 12 grid to represent 1 and Janet used a 10 x 10 grid to represent 1. Each girl shaded grid

squares to show 1/4. How many grid squares did Mary shade? How many grid squares did Janet shade? Why did

they need to shade different numbers of grid squares?

Possible solution: Mary shaded 36 grid squares; Janet shaded 25 grid squares. The total number of little

squares is different in the two grids, so 1/4 of each total number is different.

Example:

There are two cakes on the counter that are the same size. The first cake has ½ of it left. The second cake has 5/12

left. Which cake has more left?

Common Misconceptions: (4.NF.1-2)

Students think that when generating equivalent fractions they need to multiply or divide either the numerator or denominator, such as, changing 1/2 to sixths. They would multiply the denominator by 3 to get 1/6, instead of multiplying the numerator by 3 also. Their focus is only on the multiple of the denominator, not the whole fraction. It’s important that students use a fraction in the form of one such as 3/3 so that the numerator and denominator do not contain the original numerator or denominator.

## I can...

I can understand the value of a fraction.I can understand how a fraction model represents a fraction.

I can understand how two fractions are equivalent.

I can understand how two different looking fracton models are equal to the same value.

I can recognize that two fractions with the same denominator and different numerators have a different value.

I can use the symbols >, <, = to compare the value of fractions with same denominator and different numerators.

I can recognize that two fractions with different denominators and same numerators represent different values.

I can use the symbols >, <, or = to compare the value of fractios with different denominator and same numerators.

I can determine whether a fraction is greater than, less than, or equal to a benchmark fraction. ( 1/4, 1/2, 3/4, 1/10)

I can recognize that I can only compare 2 fractions when both fractions refer to the same whole. (using pattern blocks-hexagon = 1, so trapezoid = 1/2)

## Essential Vocabulary

## equivalent fraction, numerator, denominator, common denominator, compare, denominator, benchmark fraction, symbols

## Sample Assessments

Fraction QuizzesUnderstanding Fractions Quiz

## Differentiation

## Intervention:

Fraction Tiles/Pizza, Tangram shapes, Grid Paper, Choice Boards, ELL/EC students: vocabulary list ahead of time, Post words with visuals on word wall and in vocabulary notebooks, Use Frayer Models and foldables, Dominoes, Have students work in partners to divide the class into a given number of ways. Use egg cartons & counters to represent fractions.DPI Classroom Strategies p. 22

Letter R--Have students work in groups to make fraction/decimal dominoes. One end has a picture; the other has the fraction and/or decimal notation. On the other side they could write the number/fraction out in word or expanded form and they could also write a story problem.

DPI Classroom Strategies pg 25—Letter AA Play Buckets & Bowls ---Label containers Near Zero, About ½ and Close to 1. Pass out index cards with decimal numbers. Students would work with partners to convert the decimal to a fraction and place your card in the correct bucket.

## Enrichment:

http://daretodifferentiate.wikispaces.com/Choice+BoardsLearning Logs

Read The Hershey’s Milk Chocolate Bar Fraction Book by Pallotta to introduce fractions during reading.

Have students create a picture book of fractions to aid them in teaching younger siblings about fractions.

Have students write in their journal how they could share lunch with two or friends (Or) write how knowing fractions helps you play a musical instrument.

Illuminations Fraction Models

Illuminations Equivalent Fractions

Fraction Lessons

## Instructional Resources

## Farmer Fred

Delightfully Different Fractions## Notes and Additional Information