Topic 7 — Adding and Subtracting Fractions and Mixed Numbers
Oct. 30-Nov. 7 (Nov. 8 posttest/pretest)
Lesson7-1 Adding and Subtracting: Like Denominators |
CCSS |
AZ AIMS StandardsM06-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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