# 6th Grade Common Core Math

## 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 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

## Continuing with Topic 3- Operations with Decimals

September 6-19 (Sep. 20 Posttest Topic 3/Pretest Topic 4)

#### Lesson

3-1 Estimating Sums and Differences

6.NS.3

#### AZ AIMS Standards

M06-S1C3-02

3-2 Adding and Subtracting 6.NS.3 M06-S1C2-07
3-3 Estimating Products and Quotients 6.NS.3 M06-S1C2-03, M06-S1C3-02
3-4 Multiplying Decimals 6.NS.3 M06-S1C2-02, M06-S5C1-01
3-5 Dividing Whole Numbers 6.NS.2 M06-S1C2-03
3-6 Dividing by a Whole Number 6.NS.3 M06-S1C2-03
3-7 Dividing Decimals 6.NS.3 M06-S1C2-03, M06-S1C3-02, M06-S5C1-01
3-8 Evaluating Expressions 6.EE.2.c M06-S1C2-07, M06-S3C3-04
3-9 Solutions for Equations and Inequalities 6.EE.5 M06-S1C2-07, M06-S3C3-01
3-10 Problem Solving: Multiple-StepProblems 6.NS.3 M06-S5C2-01, M06-S5C2-02

## Technology Integration Weekly Highlight

Have you seen these two sites with math videos created by teachers?

Students could view the movie as reteaching or preteaching (which is part of the flipped classroom model).

## Tip of the Week: Differentiation and Real-World Connections

How are you differentiating instruction and making real-world connections with math?

Two underutilized places in enVisions that has ideas are the Project in the Topic Opener and the Performance Task.

#### Project Ideas:

• enVisions has a math project idea in the Topic Opener, on page 61 about Roller Coasters, and averaging the length (in feet) and the height (in feet) of five roller coasters.
• You can do that with many things. For example, research September high and low temperatures in Apache Junction and compare them to today’s temperature. Make a table, and compare the mean.
• Another idea is to research, create a table, then calculate the mean of the magnitude of the top five earthquakes in the world today.

The performance task gives students an opportunity to apply their learning in the context of real-world application.

## 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

One of the math practices students should be using this week is Construct viable arguments and critique reasoning of others. How might this look in the classroom? How do we teach students to respectfully critique their peers? Students might need a sentence frame when they first start. “I agree with __________ because…” “I respectfully disagree with this part of _____________ solution because…” Modeling our expectations is key!

How are you differentiating instruction and making real-world connections with math?

## Topic 3- Operations with Decimals

September 6-19 (Sep. 20 Posttest Topic 3/Pretest Topic 4)

#### Lesson

3-1 Estimating Sums and Differences

6.NS.3

#### AZ AIMS Standards

M06-S1C3-02

3-2 Adding and Subtracting 6.NS.3 M06-S1C2-07
3-3 Estimating Products and Quotients 6.NS.3 M06-S1C2-03, M06-S1C3-02
3-4 Multiplying Decimals 6.NS.3 M06-S1C2-02, M06-S5C1-01
3-5 Dividing Whole Numbers 6.NS.2 M06-S1C2-03
3-6 Dividing by a Whole Number 6.NS.3 M06-S1C2-03
3-7 Dividing Decimals 6.NS.3 M06-S1C2-03, M06-S1C3-02, M06-S5C1-01
3-8 Evaluating Expressions 6.EE.2.c M06-S1C2-07, M06-S3C3-04
3-9 Solutions for Equations and Inequalities 6.EE.5 M06-S1C2-07, M06-S3C3-01
3-10 Problem Solving: Multiple-StepProblems 6.NS.3 M06-S5C2-01, M06-S5C2-02

## Technology Integration Weekly Highlight

Mr. Avery’s 6th graders write a post and create a movie about decimals.

## Tip of the Week

The use of estimation strategies supports student understanding of operating on decimals.

Example:

First, students estimate the sum and then find the exact sum of 14.4 and 8.75. An estimate of the sum might be 14 + 9 or 23. Students may also state if their estimate is low or high. They would expect their answer to be greater than 23. They can use their estimates to self-correct.

Answers of 10.19 or 101.9 indicate that students are not considering the concept of place value when adding (adding tenths to tenths or hundredths to hundredths) whereas answers like 22.125 or 22.79 indicate that students are having difficulty understanding how the fourtenths and seventy-five hundredths fit together to make one whole and 25 hundredths.

Students use the understanding they developed in 5th grade related to the patterns involved when multiplying and dividing by powers of ten to develop fluency with operations with multi-digit decimals.

## 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

Make “Why?”; “How do you know?”; and “Can you explain?” classroom mantras.

If the answer is correct, ask those questions — “Why?” “How do you know?” “Can you explain?”

If the answer is wrong, you can address it the same way you would if it was right, and they often figure out where they went wrong. Don’t tell them, “No” or “Wrong”, allow them a chance to talk through it.

Why does asking “Why?” support the mathematical practices of

reason abstractly and quantitatively (MP.2) and

construct viable arguments and critique the reasoning of others (MP.3)?