Riverside USD Scope and Sequence: 4.N F.5 [4.2], 4.N F.6 [4.2] Oklahoma Academic Standards Mathematics: 4.D.1.2, 4.N.2.5,

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1 1 Lesson Plan Converting Fractions to Decimals - 3 Decimal Places Age group: 4 t h Grade, 5 t h Grade Texas - TEKS: G4.2.N O.G, G4.3.N O.B, G4.3.N O.G Riverside USD Scope and Sequence: 4.N F.5 [4.2], 4.N F.6 [4.2] Oklahoma Academic Standards Mathematics: 4.D.1.2, 4.N.2.5, 4.N.2.6 Virginia - Mathematics Standards of Learning (2009): 4.3 d, 5.2a Common Core: 4.N F.C.5, 4.N F.C.6 Mathematics Florida Standards (MAFS): 4.N F.3.5, 4.N F.3.6 Alaska: 4.N F.3 b, 4.N F.6 Minnesota: , , , , Fairfax County Public Schools Program of Studies: 4.3.d.1, 4.3.d.2, 4.3.d.3, 5.2.a.1, 5.2.a.2, 5.2.a.3, 5.2.a.4, 5.2.a.5 Nebraska Mathematics Standards: M A h, M A i South Carolina: 4.N SF.6, 4.N SF.7 Indiana: 4.C.5, 4.N S.6 Georgia Standards of Excellence: M GSE 4.N F.5, M GSE 4.N F.6 Virginia - Mathematics Standards of Learning (2016): 4.3.d, 5.2.a, 6.2.a Online resources: F rac t i o n t o De c i mal Opening Teacher present s Students pract ice Ext ension Closing

2 2 GOAL S: E xpe ri e nc e multiple representations of numbers P rac t i c e finding equivalent fractions Learn to convert fractions to decimals De vel o p critical thinking skills Ope ni ng 6 Have the students work in pairs. Display the following table: Ask the students to copy the table. They should make check marks when the number in the left column is a factor of 10, 100, or When the students have filled in their tables, share. Which numbers are factors of 10?

3 3 The numbers two and five are factors of 10. Which numbers are factors of 100? The numbers two, four, and five are factors of 100. Which numbers are factors of 1000? The numbers two, four, five, and eight are factors of Say: So two, four, and eight are factors of 1000, but six is not. All of these numbers are even. How is six different from two, four, and eight? Six has a factor of three. Two, four, and eight are all powers of two. Can we use the fact that six is a multiple of three to explain why six is not a factor of 1000? Three is not a factor of So no multiple of three can be a factor of T e ac he r prese nt s M at h game : F rac t i o n t o De c i mal 3 De c i mal P l ac e s 10 Present Matific s episode F rac t i o n t o De c i mal 3 De c i mal P l ac e s to the class, using the projector. The goal of the episode is to convert fractions to decimals. Example :

4 4 Say: Read the instruction. Students should read the instruction at the bottom of the screen. Say: There are three buttons in the episode, Expand by 2, Expand by 5, and Simplify. We can use these buttons to make equivalent fractions to the fraction we are given. Our goal is to have the denoator be 10, 100, or 1000, so that we can then easily convert to a decimal. Which button should we click on first in order to change our fraction s denoator to a power of 10? Click on the button that the students suggest. Does our fraction have a denoator of 10, 100, or 1000 yet? Students should respond based on the episode. Continue to ask the students for guidance as to what steps to take to arrive at a denoator that is a power of 10. Once the denoator is 10, 100, or 1000, ask the students how to write it as a decimal. Enter their decimal by clicking on the. If the answer is correct, the episode will proceed to the next fraction. If the answer is incorrect, the instruction will wiggle. The episode will present a total of six fractions to convert to decimals.

5 5 St ude nt s prac t i c e M at h game : F rac t i o n t o De c i mal 3 De c i mal P l ac e s 12 Have the students play F rac t i o n t o De c i mal 3 De c i mal P l ac e s on their personal devices. Circulate, answering questions as necessary. E xt e nsi o n: F rac t i o n t o De c i mal M at h Wo rkshe e t 15 Say: We know that Since seven is not a factor of 100, we cannot use the exact same process for. However, we can approximate. Seven is a factor of 98, which is close to 100. What numerator makes this statement true:? The missing numerator is 14. Say: Yes, so, which is close to. So is close to Let s get a better approximation. If I think of a number close to 1000 that is a multiple of seven, I get Now I can ask myself:? What number belongs in the numerator? The missing numerator is 143. Say: So, which is close to So is close to is a better approximation of than Now you are going to repeat these steps with other fractions to come up with decimal approximations for and. Distribute the following: A. Find an approximate decimal representation of. 1. Find a multiple of 3 that is close to Set up equivalent fractions, with the answer to #1 as the new

6 6 denoator: 3. Calculate the numerator from #2. 4. Since the denoator is close to 100, we can use this as an approximation for 5. Re-write the fraction from #4 as a decimal. 6. Repeat steps #1 through 5, except this time use a multiple close to B. Find an approximate decimal representation of. 1. Find a multiple of 6 that is close to Set up equivalent fractions, with the answer to #1 as the new denoator: 3. Calculate the numerator from #2. 4. Since the denoator is close to 100, we can use this as an approximation for 5. Re-write the fraction from #4 as a decimal. 6. Repeat steps #1 through 5, except this time use a multiple close to C. Find an approximate decimal representation of. 1. Find a multiple of 9 that is close to Set up equivalent fractions, with the answer to #1 as the newv denoator: 3. Calculate the numerator from #2. 4. Since the denoator is close to 100, we can use this as an approximation for 5. Re-write the fraction from #4 as a decimal. 6. Repeat steps #1 through 5, except this time use a multiple close to

7 If there is time, students can find decimal approximations for other fractions, such as and. Review solutions. Answers may vary, depending on what denoator students chose to be close to 100 or For example, when looking for a multiple of seven that is close to 1000, we might think of 994 or So then we have two different problems: and. The first problem becomes and the second problem becomes. So one approximation could be while another is You may wish to further the discussion by asking which approximation is more accurate, or Discuss any questions the students may have.

8 8 Cl o si ng 4 What steps can we take to convert to a decimal? We can make equivalent fractions. We want to write as a fraction with 1000 in the denoator. So we set for the numerator. The numerator is 125. So. and solve If we know that is 0.125, then how could we convert decimal? Responses may vary. Two possible responses: to a. We could solve for the numerator (375) and then re-write as a decimal (0.375). is 0.125, then is three times as big. So three times is So if we know that is, then what is as a decimal? is twice, so if is, then is double that, or.