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

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)

Tip of the Week:

  • Assessing/Higher Level Learning:  Are we having our students complete the Performance Based Assessments at the end of each Topic?
  • Enrichment: In your teacher’s manual you will find ideas for enrichment under “Advanced/Gifted” on page 160D. There are two different ideas listed here.

Technology Integration Weekly Highlight:

  • Math in the Real World Project: The math project on page 161 in the Teacher’s Guide, connects to the real world by researching how many miles the top hiking trails are in the USA (the Appalachian Trail, the Pacific Crest Trail, and the Continental Divide Trail); then have the students pick one of the three trails and show the portion of the total trail in one state as a fraction. Then make a table that lists the state and the portion of the trail as a fraction.
  • Students would use the computer for their research, and they could also use it for their reflection on the learning that took place in the above project. This would also be a great way to bring in the mathematical practice of attend to precision.
    • Students could use Educreations on the iPad to narrate and show their thinking.
    • On the netbooks or thin clients, students could create their table in Google Docs, then narrate their reflection by connecting Voice Comments (in Kaizena) to their document. Click here for instructions (see slide #14).
  • Click here for more resources/videos for 6.NS.1.
  • Click here for more resources/videos for 6.NS.4.
  • Click here for more resources/videos for 6.RP.1.

Mathematical Practices:

The following comes from the ADE: 6.MP.6. Attend to precision. In grade 6, students continue to refine their mathematical communication skills by using clear and precise language in their discussions with others and in their own reasoning. Students use appropriate terminology when referring to rates, ratios, geometric figures, data displays, and components of expressions, equations or inequalities.

Some questions that can be asked for attending to precision includes:

  • What mathematical terms apply in this situation?
  • How did you know your solution was reasonable?
  • What mathematical language…, definitions…, properties can you use to explain…?
  • Explain how you might show that your solution answers the problem.

How do you use, and challenge students to use mathematics vocabulary precisely and consistently?

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

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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