# 6th Grade Common Core Math

## 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

#### 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
7-6 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).

### 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?

## 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

#### 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
7-6 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.

### 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
• 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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## Tips, Mathematical Practices, and Ideas about Decimals, Fractions, and Mixed Numbers

### Topic 6- Decimals, Fractions, and Mixed Numbers

October 23-28 (Oct. 29 posttest 6/pretest 7)

#### Lesson

6-1 Fractions and Division

6.NS.1*

#### AZ AIMS Standards

M06-S1C1-03

6-2 Fractions and Decimals 6.NS.1* M06-S1C1-01
6-3 Improper Fractions and Mixed Numbers 6.NS.1* M06-S1C1-01, M06-S1C1-04
6-4 Decimal Forms of Fractions and Mixed Numbers 6.NS.1* M06-S1C1-01, M06-S1C1-04
6-5 Problem Solving: Draw a Picture** 6.NS.3

** See in double dose time.

### Double Dose Recommendations:

• Cyclical Review from Quarter 1.
• Pre-teach continuing measurement, 2 days (#22-23). Look for science connections.
• 6-5 Problem Solving: Draw a Picture, 2 days

### Tip of the Week

This tip comes from the ADE:

### Mathematical Practices

This tip comes from the ADE:

Math Practice #4: Model with Mathematics

In grade 6, students model problem situations symbolically, graphically, tabularly, and contextually. Students form expressions, equations, or inequalities from real world contexts and connect symbolic and graphical representations. Students begin to explore covariance and represent two quantities simultaneously. Students use number lines to compare numbers and represent inequalities. They use measures of center and variability and data displays (i.e. box plots and histograms) to draw inferences about and make comparisons between data sets. Students need many opportunities to connect and explain the connections between the different representations. They should be able to use all of these representations as appropriate to a problem context.

If you asked students to represent a fraction in three different ways, how would that help them think about the mathematical practice of modeling with mathematics?

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## Tips, Mathematical Practices, and Ideas about Number and Fractions Concept

### Topic 5- Number and Fraction Concepts

October 14-21 (Oct. 22 posttest 5/pretest 6)

#### Lesson

5-1 Factors, Multiples, and Divisibility

6.NS.4*

#### AZ AIMS Standards

M06-S2C3-02

5-2 Prime Factorization 6.NS.4* M06-S1C1-02
5-3 Greatest Common Factor 6.NS.4* M06-S1C1-02
5-4 Understanding Fractions 6.NS.1* M06-S1C1-03
5-5 Equivalent Fractions 6.NS.1* M06-S1C1-01, M06-S1C1-04
5-6 Fractions in Simplest Form 6.NS.1* M06-S1C1-01
5-7 Problem Solving: Make and Test Conjectures 6.NS.4* M06-S5C2-08

### Technology Integration Weekly Highlight

Have you used Galileo to identify the at risk students and students who need enrichment? (Cheri forwarded the directions to us via email with visuals). Here’s those directions again:

1. Go to the Dashboard.
2. See “Class Risk Level Summary” and “View Benchmark Results for Student Risk Levels.”
3. On Dashboard, it will show the risk level and students.
4. You can see the “Quiz Builder” to view areas of suggested reteaching or enrichment.

### Tip of the Week

• The Math Project for Topic 5 brings in real world examples and researching potentially active volcanoes in the USA. Based on their research, determine what fraction each is of the total number of active or potentially active volcanoes in the USA. Then have student determine which states have the most active or potentially active volcanoes. They can also rank them from greatest to least, and write their data in a table.
• I also liked the project mentioned in the ASCD article titled, “You Can’t Do That with a Worksheet.”

### Double Dose Recommendations

• Kim Sutton Math Routines (Number Line Workbook, Place Value, Math Drills to Thrill);
• Pre‐teach the following: Converting customary measures of length/weight/capacity, 5 days (#16‐#20) Look for science connections.

### Mathematical Practices

This tip comes from the ADE about making sense of problems and persevering in solving them (6.MP.7): Look for and make use of structure.

Students routinely seek patterns or structures to model and solve problems. For instance, students recognize patterns that exist in ratio tables recognizing both the additive and multiplicative properties. Students apply properties to generate equivalent expressions (i.e. 6 + 2x = 2 (3 + x) by distributive property) and solve equations (i.e. 2c + 3 = 15, 2c = 12 by subtraction property of equality; c=6 by division property of equality). Students compose and decompose two- and three-dimensional figures to solve real world problems involving area and volume.

Some questions that help students focus on structure are:

• What observations do you make about…?
• Do you recognize a rule or see an equation?
• Do you believe your rule will always work?
• How do you know your rule/equation will always work?
• What pattern or structure do you notice?
• Can sorting or grouping be used to solve?
• What are some other problems that are similar to this one?
• What ideas that we’ve learned before were useful in solving this problem?
• In what ways does this problem connect to other mathematical concepts?

What other questions could you ask to help students look for and make use of structure?