6th Grade Common Core Math

Tips and Support for Common Core Math Implementation

Tips, Mathematical Practices, and Ideas about Adding and Subtracting Fractions and Mixed Numbers

on October 24, 2013

Topic 7 — Adding and Subtracting Fractions and Mixed Numbers

Oct. 30-Nov. 7 (Nov. 8 posttest/pretest)

Lesson

7-1 Adding and Subtracting: Like Denominators

CCSS

6.NS.1*

AZ AIMS Standards

M06-S1C2-07

7-2 Least Common Multiple 6.NS.4 M06-S1C1-02
7-3 Adding and Subtracting: UnlikeDenominators 6.NS.1* M06-S1C2-07
7-4 Estimating Sums and Differences of Mixed Numbers 6.NS.1* M06-S1C3-01
7-5 Adding Mixed Numbers 6.NS.1*
7-6 Subtracting Mixed Numbers 6.NS.1*
7-7 Problem Solving: Make a Table 6.RP.1

Double Dose Recommendations — Preteach the following:

  • Relating measures, 2 days (#24‐#25). Look for science connections.
  • Elapsed time, 3 days (#26‐28)

Technology Integration Weekly Highlight:

Here are some websites with fractions for students to interact and engage with:

  • Comparing Fractions — If you have students who need more experience with understanding fractions, this might be a place to build background. Have them use manipulatives while playing this game.
  • Equivalent Fractions Game — If you have students who need more experience with understanding fractions, this might be a place to build background. Have them use manipulatives while playing this game.
  • Equivalent Fractions Target Shoot — If you have students who need more experience with understanding fractions, this might be a place to build background. Have them use manipulatives while playing this game.
  • LCM — This is an online worksheet. It gives immediate feedback to student about accuracy.
  • LCM of three numbers —  This is an online worksheet. It gives immediate feedback to student about accuracy.
  • Adding Mixed Numbers  —  This is an online worksheet. It gives immediate feedback to student about accuracy.
  • Click here for more resources for 6.NS.1.
  • Click here for more resources for 6.NS.4.
  • Click here for more resources for 6.RP.1.

Tip of the Week: Examples and Explanations

This tip comes from the ADE about finding the GCF and LCM: 6.NS.4

  • What is the greatest common factor (GCF) of 24 and 36? How can you use factor lists or the prime factorizations to find the GCF?

Solution: 22 • 3 = 12. Students should be able to explain that both 24 and 36 have 2 factors of 2 and one factor of 3, thus 2 x 2 x 3 is the greatest common factor.)

  • What is the least common multiple (LCM) of 12 and 8? How can you use multiple lists or the prime factorizations to find the LCM?

Solution: 23 • 3 = 24. Students should be able to explain that the least common multiple is the smallest number that is a multiple of 12 and a multiple of 8. To be a multiple of 12, a number must have 2 factors of 2 and one factor of 3 (2 x 2 x 3). To be a multiple of 8, a number must have 3 factors of 2 (2 x 2 x 2). Thus the least common multiple of 12 and 8 must have 3 factors of 2 and one factor of 3 ( 2 x 2 x 2 x 3).

  • Rewrite 84 + 28 by using the distributive property. Have you divided by the largest common factor? How do you know?
  • Given various pairs of addends using whole numbers from 1-100, students should be able to identify if the two numbers have a common factor. If they do, they identify the common factor and use the distributive property to rewrite the expression. They prove that they are correct by simplifying both expressions.
    • 27 + 36 = 9 (3 + 4)

63 = 9 x 7

63 = 63

    • 31 + 80

There are no common factors. I know that because 31 is a prime number, it only has 2 factors, 1 and 31. I know that 31 is not a factor of 80 because 2 x 31 is 62 and 3 x 31 is 93.

Mathematical Practices:

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

Students routinely seek patterns or structures to model and solve problems. When students can rewrite 84 + 28 by using the distributive property, then answer if they divided by the largest common factor, then they are looking for and making use of structure.

Students will:

  • look for, develop, and generalize relationships and patterns
  • apply conjectures about patterns and properties to new situations

Teachers will:

  • provide time for applying and discussing properties
  • ask questions about the application of patterns
  • highlight different approaches for solving problems

What higher level questions will you ask during Topic 7 to help students look for and make use of structure?

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One Response to “Tips, Mathematical Practices, and Ideas about Adding and Subtracting Fractions and Mixed Numbers”

  1. […] 7: Adding and Subtracting Fractions and Mixed Numbers Checking for Understanding ideas/activities, and Math in the Real World Project/Performance […]

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