# 6th Grade Common Core Math

## Tips, Mathematical Practices, and Ideas about Equations and Graphs

### Topic 15- Equations and Graphs

Original dates: February 19-27 (Feb. 28 posttest/pretest)

 15-1 Equations with More Than One Operation 6.EE.7 M06-S3C3-02 15-2 Patterns and Equations 6.EE.9 M06-S3C1-01, M06-S3C3-01, M06-S3C3-02 15-3 More Patterns and Equations 6.EE.9 M06-S3C3-01, M06-S3C3-02 15-4 Graphing Equations 6.EE.9 M06-S3C2-01, M06-S4C3-01 15-5 Graphing Equations with More Than One Operation 6.EE.9 M06-S3C3-02, M06-S4C3-01 15-6 Understanding Inequalities 6.EE.8 M06-S1C1-04 15-7 Problem Solving: Act It Out and Use Reasoning 6.EE.5 M06-S3C2-01, M06-S5C2-02

### Double Dose Recommendations:

Pre-teach the following: Outcomes and Experiments (#86-91)

### Tip of the Day:

Teaching Channel: Daily Assessment with Tiered Exit Cards

### Mathematical Practices: #8 Look for and express regularity in repeated reasoning

In grade 6, students use repeated reasoning to understand algorithms and make generalizations about patterns. During multiple opportunities to solve and model problems, they may notice that a/b ÷ c/d = ad/bc and construct other examples and models that confirm their generalization. Students connect place value and their prior work with operations to understand algorithms to fluently divide multi-digit numbers and perform all operations with multi-digit decimals. Students informally begin to make connections between covariance, rates, and representations showing the relationships between quantities.

With looking for and expressing regularity in repeated reasoning, students will:

• Look for methods and shortcuts in patterns in repeated calculations
• Evaluate the reasonableness of intermediate results and solutions

Teachers will:

• Provide tasks and problems with patterns (such as multiplying fractions and mixed numbers)

Some question probes could be:

• What is happening in this situation?
• Is there a mathematical rule for?
• What predictions or generalizations can this pattern support?

What resources or tips would you share about solving for equations and graphs?

## Tips, Mathematical Practices, and Ideas Review

### Review Topics 1-4 and Preview Topic 5

October 2-4: Review Topics 1-4, Preview Topic 5

These pacing documents are meant to be a support to you in planning and delivering instruction this year, but are not intended to take the place of classroom level assessments and decisions based on those assessments. Pre-tests and formative assessments should be the driving forces behind the ultimate pacing decisions in your classroom with the understanding that all concepts represented in these pacing documents must be taught to students over the course of the year.

### Technology Integration Weekly Highlight

Here’s some game-based learning for equations:

• Gummii – An innovative site (private alpha)/app for different areas of Math (fractions, addition, subtraction). Gummi immerses students into a educational 3D world (similar to Minecraft) where they solve mathematical equations tailored to differentiated instruction.
• One Step Equation Games

### Weekly Tip

• Remember the Math Projects and Performance Based Practice/Assessments.
• Speaking/Listening opportunities should  be included in our math lessons. This is a great way to also incorporate mathematical practices.

### Double Dose

Continue 5th grade cyclical review based on IE;   Kim Sutton Math Routines (Number Line Workbook, Place Value, Math Drills to Thrill).

### Mathematical Practices

This is an ASCD article titled, “You Can’t Do That with a Worksheet” and talks about how math has to look different with the Common Core and the Math Practices. This article gives an example of a problem in a 5th grade classroom that uses all 8 practices. It’s worth reading.

What were the big take-aways you got from the ASCD article, You Can’t Do That with a Worksheet?

Did your students try any of the game-based learning sites? If so, how educational were they? How interesting were they?

Photo Credit: _Untitled-1 via Compfight

## Topic 4- Solving Equations

September 23-30 (Oct. 1 Post test 4/Pretest 5)

#### Lesson

4-1 Properties of Equality

6.EE.4

#### AZ AIMS Standards

4-2 Solving Addition and Subtraction Equations 6.EE.7
4-3 Problem Solving: Draw a Picture and Write an Equation 6.EE.7 M06-S3C2-01, M06-S5C2-03
4-4 Solving Multiplication and Division Equations 6.EE.7 M06-S1C1-06, M06-S1C2-02, M06-S1C2-03
K95 Powers and Roots M06-S1C1-06
4-5 Problem Solving: Draw a Picture and Write an Equation 6.EE.7 M06-S3C2-01, M06-S5C2-03, M06-S5C2-05

## Technology Integration Weekly Highlight

Have you allowed students to “show their thinking” with problem solving on an iPad app such as Educreations? This app records their voice and everything written on the screen. They can even take a photo of their paper (or book) and talk through how they solved the problem. If the teacher creates a free account, then is syncs with the  teacher account to be viewed on any device. Click here for a tutorial.

## Tip of the Week

This tip comes from the ADE for 6.EE.7:

Students create and solve equations that are based on real world situations. It may be beneficial for students to draw pictures that illustrate the equation in problem situations. Solving equations using reasoning and prior knowledge should be required of students to allow them to develop effective strategies.

Example:

• Meagan spent \$56.58 on three pairs of jeans. If each pair of jeans costs the same amount, write an algebraic equation that represents this situation and solve to determine how much one pair of jeans cost.

Sample Solution: Students might say: “I created the bar model to show the cost of the three pairs of jeans. Each bar labeled J is the same size because each pair of jeans costs the same amount of money. The bar model represents the equation 3J = \$56.58. To solve the problem, I need to divide the total cost of 56.58 between the three pairs of jeans. I know that it will be more than \$10 each because 10 x 3 is only 30 but less than \$20 each because 20 x 3 is 60. If I start with \$15 each, I am up to \$45. I have \$11.58 left. I then give each pair of jeans \$3. That’s \$9 more dollars. I only have \$2.58 left. I continue until all the money is divided. I ended up giving each pair of jeans another \$0.86. Each pair of jeans costs \$18.86 (15+3+0.86). I double check that the jeans cost \$18.86 each because \$18.86 x 3 is \$56.58.”

• Julio gets paid \$20 for babysitting. He spends \$1.99 on a package of trading cards and \$6.50 on lunch. Write and solve an equation to show how much money Julio has left.

(Solution: 20 = 1.99 + 6.50 + x, x = \$11.51)

## Double Dose Recommendations

Continue 5th grade cyclical review based on IE;   Kim Sutton Math Routines (Number Line Workbook, Place Value, Math Drills to Thrill).

## Math Practices

This tip comes from the ADE about making sense of problems and persevering in solving them (6.MP.1):

In grade 6, students solve problems involving ratios and rates and discuss how they solved them. Students solve real world problems through the application of algebraic and geometric concepts. Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may check their thinking by asking themselves, “What is the most efficient way to solve the problem?”, “Does this make sense?”, and “Can I solve the problem in a different way?”.

How do you make students’ thinking visible in the classroom especially with solving equations?