Elementary Mathematics

4th Grade Unit 6: Fraction Cards and Decimal Squares


Unit at a Glance

Suggested Dates:
January 13- March 7

Estimated Duration: 30  Days

*Investigation 1: 8 lessons (Including 1.8A)

*Investigation 2: 7 lessons (Including 2.7A)

*Investigation 3A: 3 lessons (Multiplying Fractions)

3 Lessons:  More practice multiplying fractions -(5 days)

*Investigation 3:  7 Lessons

Use these additional Real World addition and subtracting fractions lessons as a supplement, if you are looking for something extra.


Smart Board, Promethean, and Power Point Files:

Fraction Smart Board Template

 
Decimal Smart Board Template

Smart Board Files:

Fractions Part 1



Tools for Teachers

 
Virtual Manipulative 10 x 10 Grid for Representing Percents from National Library of Virtual Manipulatives

Play Fraction Track Online

Extension Projects for Investigations

Build a fraction using an Area Model to match the fraction in symbolic form

Fraction Model
  Provides an area model for a fraction when you input the values.

Fractions Using Pattern Blocks
Challenge

Students drag and drop fractions onto their correct position on a
number line.

Identify and Write
the fraction shown on the number line.
  
Fraction Concentration
-Match fractions to their pictoral equivalents.

Create Equivalent Fractions
by dividing and shading squares or circles, then match each fraction to its location on the number line.

Explore
Different Representations or fractions including improper fractions, mixed numbers, decimals, and percentages. Additionally,there are length, area, region, and set models. Adjust numerators and denominators to see how they alter the representations and models. Use the table to keep track of interesting fractions.

Fraction Activities:

Creating Equivalent Fractions

Birthday Fractions

Pattern Block Fractions

Who Ate More?

Which is larger?

Snack Time

Using Benchmarks to Compare Fractions

Decomposing Fractions

Adding and Subtracting Fractions

Mixed Fraction Word Problems

Whole number x a fraction word problems

Decimal Activities:

Using Place Value

Adding Tenths and Hundredths

Expanded Fractions and Decimals

Equivalent Fractions with a Denominator of 100 Problems


STANDARDS FOR MATHEMATICAL PRACTICE

MP 1 Make sense of problems and persevere in solving them.

How can you support students to model the problem in several ways and make it relative?

MP 2 – Reason abstractly and quantitatively.

How can you support the students using flexibility to use different properties of operations to solve problems?

MP 4 – Model with mathematics.

How can you help students use representations and contexts judiciously and with purpose?



TEAM TIME!
DISCUSS THE FOLLOWING WITH YOUR GRADE LEVEL TEAM:

View the video for 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.  After watching the video discuss strategies that will help students better understand how fractions are equivalent.

Unit 6 page 151-152:  Provide students with two fractions for each type of comparison situation.  As students are solving the problems ask them to come up with a rule that helps them solve the problem.  Read “Strategies for Comparing Fractions” on page 151-152 Discuss the conjecture for each strategy. 

View the video for the standard 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.  Review how to teach comparing fractions using a number line and a visual representation.  

159- End of Unit Assessment





OPPORTUNITIES FOR DIFFERENTIATION...

Suggestions for students who are struggling…

Allow students to use fraction bars and Cuisenaire rods.

Students can find parts of a set using cubes or color tiles.

Create fraction bar books- fold construction paper to make a flip book of fractions

Students who have difficulty visualizing sets of a region may find it easier to start by finding one third of 24 objects and then counting out that number of squares on the rectangle. 

Pair a student who is having difficulty with one who quickly splits the regions into thirds and ask the student who has difficulty to check that the regions are equal.

Use this Decimal Designs activity that uses decimal grids to model conversions of fractions to decimals.

Use this decimal-fraction number line activity
and this
comparing decimals-double number line activity
that allow students to compare decimals to one another.

Suggestions for students who fully understand…

Students who quickly make thirds and sixths and can explain clearly how they know fraction represents a part of the rectangle can work with twelfths.  They can also divide a rectangle into a combination of thirds, sixths, and twelfths.

Students who are fluent in comparing two fractions at a time can play the game with a group of three or four so that more fractions are considered in each round.


*Remember to upload files to share with others, or locate files to use, on the wiki. Be sure to join discussion posts with other colleagues to ask questions, answer questions, and discuss math.
COMMON CORE STATE STANDARDS IN THIS UNIT

Link to the CCSS Unpacking Document- Updated Sept. '14

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.

4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
     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.

     c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

      d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

        a. Understand a fraction a/b as a multiple of 1/b.

        b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

        c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.

4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.

4.NF.6 Use decimal notation for fractions with denominators 10 or 100.

4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g.,by using a visual model.

Words you should hear students use in Mathematical Conversations...

Fractions, Line plot, Greater/less than, Numerator, Denominator, Equivalent, Decimal, Mixed numbers, Improper fractions, Simplify /reduce, common denominator, hundredth, tenth

While students are creating their fraction cards ask them how they know that their pictures are representing their fraction. 

Have students compare two fractions and explain their thinking.  

When students are playing Capture Fraction, Comparing Decimals and Fill in you should be listening to students’ conversations.  You should be hearing students explaining why the fractions and decimals are bigger.    

Have students read aloud decimals.

4th Grade Vocabulary List in English and Spanish

4th Grade Vocabulary List

Investigations Vocabulary

Investigations Unit Vocabulary

3-5 Literature List



Literature

Full House: An Invitation to Fractions

Fractions = Trouble

Apple Fractions

The Wishing Club: A Story About Fractions

TAKE NOTE FOR EACH INVESTIGATION
INVESTIGATION 1

Combinations that equal 1- discuss 0, ½, 1 benchmarks

ID benchmarks ½, ¼, 1/8, 1/3, 1/6, 1/12

Identify and compare fractions

Adding and subtracting fractions

INVESTIGATION 2

*Add line plots in for ordering fractions*

fractions benchmarks- 0, ½, 1

put all assessments on a number line

*Make fraction cards with a visual and laminate– parent volunteer?

INVESTIGATION 3

Multiplying whole numbers and fractions. Be sure to have students use a visual model to represent multiplication

3 x 6/8=

Decimal compare and order decimals (e.g., Least to Greatest .03, .3, .34)

convert fractions to decimals

TEN MINUTE MATH! 
Practicing Place Value

4.NBT.4 Have students articulate place value terms and rounding rules
Quick Survey

4.MD.4  Students should graph results and analyze those graphs. May need to give extra help to students by putting an example on the board