February 15th, 2013
– By @PearceThera in Math Learning
Each month we will be featuring one of our FREE Teacher Tools for interactive whiteboards. Ready for use in elementary classrooms with any type of interactive whiteboard, these highquality virtual manipulative tools help teachers connect students with great ways to make sense of math. Use these tools to create an environment for students to explain, discuss, and defend their mathematical thinking.
This month we are featuring “Decomposing Fractions Using Time or Money” for Grade 3.
Students investigate building equivalent fractions using time and money. The teacher uses questioning to assist students with making the connection between denominators and divisible units. The clock is used as a model for halves, thirds, fourths, sixths and twelfths. Money is used as a model for halves, fifths, tenths, and twentieths. Students convert the units of each model into whole numbers (minutes or cents) as well as fractions.
Sample Lesson 
Objective: 
Students choose time or money as models for decomposing fractions. 

Background: 
Students should be able to compare and order fractions whether or not the fractions have like denominators. They should also be familiar with how to represent fractions using either time or money models and understand the use of improper fractions. Don’t be afraid to allow students to make mistakes in this lesson. Use these as teachable moments and help students think critically about the models and math. Allow the model to illustrate why their choice works or doesn’t work. 

Instruction: 
1. To begin, discuss how each model can be expressed as a fraction. You can draw or copy the models of clocks and money on the board. Starting with the clock, ask students to find the fraction linked to each model. Spend a significant time discussing and using physical manipulatives if necessary. This step could be a class lesson by itself. For Example:
2. Bring up the DreamBox interactive white board lesson. Let students know, “We need to build a model of the fraction 3/20. Should we use money or time to build that model? Discuss which model you would choose with your partner and why you chose it.” After students have discussed their responses, ask a student explain his or her choice and select time or money on the interactive whiteboard tool. Possible responses: 3. The teacher points to the prompt, Use coins to build 3/20 of a dollar. She asks the class, “How would you build 3/20 using coins? Which coins would you use and why? Discuss and then plan to share your response and record it on the board.” See pictures (a) and (b). Possible responses: 4. Once the student enters a response and clicks “done,” the teacher points to the next prompt: “Type the missing value in the equation.” See picture (c). Ask for a volunteer to calculate the total amount of change over the whole dollar and explain the equivalent fraction and click done. Possible responses: 5. 5. Below is an example of a prompt that involves an improper fraction. Use questioning and discussion for these as you did above; however, you may add conversations that discuss how to represent the whole (hour or dollar), how students know the fraction is improper and how much is left after representing the whole. Don’t be afraid to allow students to make mistakes. Use these as teachable moments and guide the students to correct choices using questions. Use the models and context as a way for students to construct their arguments, illustrating why their choice works or doesn’t work. 
Common Core State Standard 
Grade  CCSS ID  Domain  Cluster  Standard 
3  3.NF.3  Number & Operations—Fractions 
Develop understanding of fractions as numbers. 
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. 
3  3.SMP.2  Standards for Mathematical Practice 
Reason abstractly and quantitatively. 

3  3.SMP.5  Standards for Mathematical Practice 
Use appropriate tools strategically. 