# 6th Grade Common Core Math

## Tips, Mathematical Practices, and Ideas about Ratios, Rates, and Proportions

Topic 12- Ratios, Rates, and Proportions

January 21-27 (Jan 28 posttest/pretest)

 Lesson12-1 Understanding Ratios CCSS6.RP.1 Arizona StandardsM06-S1C1-01 12-2 Equal Ratios and Proportions 6.RP.3 M06-S1C1-01 12-3 Understanding Rates and Unit Rates 6.RP.2 M06-S1C1-01, M06-S1C1-03 12-4 Comparing Rates 6.RP.3.b M06-S1C1-01, M06-S1C1-04 12-5 Distance, Rate, and Time 6.EE.9 M06-S1C2-04, M06-S3C3-04 12-6 Problem Solving: Draw a Picture** (2 days) 6.RP.2 M06-S3C2-01

### Double Dose Recommendations:

• Pre-teach the following: Mean, Median, Mode, 3 days (#68-#70)
• 12-6  Problem Solving, 2 days

### Tip of the Week:

The following tips  come straight from the ADE:

 Standard ADE Explanation and Example(s) CCSS.Math.Content.6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” CCSS.Math.Content.6.RP.A.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid \$75 for 15 hamburgers, which is a rate of \$5 per hamburger.” CCSS.Math.Content.6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. CCSS.Math.Content.6.RP.A.3b  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

### Mathematical Practices:

Attend to Precision — Remind students that ratios can be written as a fraction (3/7), which is the same as 3 to 7, which is the same as 3:7. They all compare the portion of 3 to the whole of 7. Ask students about the math terms they can apply in different situations. — What math terms apply in this situation? or “What math language, definitions, properties can you use to explain ….?

## Tips, Mathematical Practices, and Ideas about Two-Dimensional Figures

### Topic 11: Properties of Two-Dimensional Figures

Note: The original dates you set for this unit was January 6-16 (Jan 17 posttest/pretest). However, most of you will be starting this unit soon since your pacing is determined by student understanding.

 11-1 Basic Geometric Ideas 6.G.3* 11-2 Measuring and Drawing Angles 6.G.1* M06-S4C4-01 11-3 Step-Up Lesson: Angle Pairs 7.G.5 M06-S4C1-02 11-4 Triangles 6.G.1* 11-5 Quadrilaterals 6.G.1* 11-6 Step-Up Lesson: Circles 7.G.4 11-7 Step-Up Lesson: Transformations and Congruence 8.G.2 M06-S4C2-01, M06-S4C2-02 11-8 Step-Up Lesson: Symmetry 8.G.1 11-9 Problem Solving: Make a Table and Look for a Pattern 6.EE.9 M06-S5C2-07

### Double Dose Recommendations:

• Vertex Edge, 4 days, (AZ12, AZ13)

### Tip of the Week:

• There is a lot of new vocabulary during this unit; therefore, making connections to vocabulary are extremely important. Click here to view some ideas for integrating technology with vocabulary. It can be used as a center activity in math. For some students, you may even ask the home room teacher if there is any time your student could substitute something (such as the morning wake up review) to spend extra time with vocabulary.
• Kim Sutton also has vocabulary ideas too.

### Mathematical Practices:

When students share their thinking  and reasoning about the solutions, they are justifying their solutions (DOK 3),  a foundational critical-reasoning skill. The ability to articulate a clear explanation for a process and critique the reasoning of others is the backbone of Math Practice #3Construct viable arguments and critique the reasoning of others.

Some question stems for MP.3 are:

• What strategy will you try to solve …? How did you decide to try that strategy?
• How did you decide what the problem was asking you to find? (What was unknown?)
• Did you try a strategy that did not work? Why didn’t it work? When would it work?
• How could you demonstrate a counter-example?

Have you thought about having the students solve a problem and capture their thought process on an iPad? Then have students pass the iPad to another group to listen and critique their explanation?

How do you incorporate Mathematical Practices daily?

## Tips, Mathematical Practices, and Ideas about Integers

### Topic 10: Integers

Note: The original dates you set for this unit was December 6-18 (Dec.19 posttest/pretest). However, most of you will be starting this unit soon since your pacing is determined by student understanding.

 10-1 Understanding Integers 6.NS.5 M06-S1C1-04, M06-S1C1-05 10-2 Comparing and Ordering Integers 6.NS.7.a M06-S1C1-04 10-3 Rational Numbers on a Number Line 6.NS.6.c M06-S1C1-03, M06-S1C1-04 10-4 Step-Up Lesson: Adding Integers 7.NS.1.b M06-S1C2-01 10-5 Step-Up Lesson: Subtracting Integers 7.NS.1.c M06-S1C2-01 10-6 Step-Up Lesson: Multiplying Integers 7.NS.2.a 10-7 Step-Up Lesson: Dividing Integers 7.NS.2.b 10-8 Absolute Value 6.NS.7.d M06-S1C1-05 10-9 Graphing Points on a Coordinate Plane 6.NS.6.c M06-S4C3-01 K104 Missing Coordinates** (See double dose)J31 Use Reasoning** M06-S4C3-02M06-S5C2-09 10-10 Problem Solving: Use Reasoning 6.G.3 M06-S5C2-09

### Double Dose Recommendations:

• Kim Sutton math routines
• Pre-teach the following:
• Missing Coordinates, 3 days (AZ7, K104)
• Use Reasoning, 1 day (J31)

### Tip of the Week:

• Start your unit by looking at the performance task. Have students create need-to-know lists for what they need to know in order to complete the task.

• After each lesson, refer back to the need-to-know list to see which pieces they’ve learned in order to reach the final goal of completing the performance task.

### Technology Integration Resources:

Below are some Learn Zillion videos to use for each of the lessons beyond SuccessNet:

If you have iPads in your class, Educreations has a graphing grid with the coordinates to use as background paper and students can create tutorials with this app.

### Mathematical Practices:

In enVision, the “Hands-On, Minds-On” quick lesson to introduce the concept also incorporates Math Practices. When I was in the classroom, I’d use my pretest data and formative assessments to determine which students need pre-teaching. Every day I’d pre-teach a small group, and I’d spend time using these lessons to develop the concept and connect prior knowledge. When I’d start my lesson, I could quickly introduce it using the Interactive Learning, beneficial to all students.