6th Grade Common Core Math

Tips and Support for Common Core Math Implementation

Tips, Mathematical Practices, and Ideas about Dividing Fractions and Mixed Numbers — Week 2

Topic 9- Dividing Fractions and Mixed Numbers

November 21-December 4 (Dec. 5 posttest/pretest)

Lesson

9-1 Understanding Division of Fractions

CCSS

6.NS.1

AZ Standards

M06-S1C2-04, M06-S1C2-05, M06-S5C1-01

9-2 Dividing a Whole Number by a Fraction 6.NS.1 M06-S1C2-04, M06-S1C2-05, M06-S5C1-01
9-3 Dividing Fractions 6.NS.1 M06-S1C2-04
9-4 Estimating Quotients 6.NS.1 M06-S1C2-04, M06-S1C3-02
9-5 Dividing Mixed Numbers 6.NS.1 M06-S1C2-04
9-6 Solving Equations 6.EE.7 M06-S1C2-04
9-7 Problem Solving: Look for a Pattern 6.NS.6 M06-S3C1-01

Double Dose Recommendations:

  • Kim Sutton math routines.
  • Pre-teach the following: Area, 5 days (#34-38)

Tip of the Week:

Creative Commons License Photo Credit: Adelle & Justin via Compfight

The Performance Assessment has students working with fractions in recipes. Here’s an online activity that complements the performance task:

Feeding Frenzy

In this activity, students will multiply and divide a recipe to feed groups of various sizes. Students will use unit rates or proportions and think critically about real world applications of a baking problem.

Technology Integration Resources:

Videos:

Mathematical Practices:

Model with Mathematics  The CCSS says this about Model with Mathematics, “In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community.”
With the holidays, could you ask the students to Model with Math by asking  questions about how much food your household needs to buy to host a holiday party?
How do students demonstrate their conceptual understanding of mathematics in your classroom? What performance tasks do you have students work on?
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Tips, Mathematical Practices, and Ideas about Dividing Fractions and Mixed Numbers

Topic 9- Dividing Fractions and Mixed Numbers

November 21-December 4 (Dec. 5 posttest/pretest)

Lesson

9-1 Understanding Division of Fractions

CCSS

6.NS.1

AZ Standards

M06-S1C2-04, M06-S1C2-05, M06-S5C1-01

9-2 Dividing a Whole Number by a Fraction 6.NS.1 M06-S1C2-04, M06-S1C2-05, M06-S5C1-01
9-3 Dividing Fractions 6.NS.1 M06-S1C2-04
9-4 Estimating Quotients 6.NS.1 M06-S1C2-04, M06-S1C3-02
9-5 Dividing Mixed Numbers 6.NS.1 M06-S1C2-04
9-6 Solving Equations 6.EE.7 M06-S1C2-04
9-7 Problem Solving: Look for a Pattern 6.NS.6 M06-S3C1-01

Double Dose Recommendations:

  • Kim Sutton math routines.
  • Pre-teach the following: Area, 5 days (#34-38)

Tip of the Week:

Think about incorporating these ideas/resources:

  • The Topic Opener/STEM Project on page 201 not only brings in math in the context of the real world, but it also requires informational text reading and researching. 
  • New York City Department of Education created a performance task, Share My Candy, for dividing fractions by fractions, which includes a rubric.

Technology Integration Resources:

Videos:

Online & interactive practice, that progressively gets more difficult from IXL:

  1. Divide fractions: Divide by fractions – with models
  2. Divide fractions: Reciprocals
  3. Divide fractions: Divide fractions
  4. Divide fractions: Estimate quotients when dividing mixed numbers
  5. Divide fractions: Divide fractions & mixed numbers
  6. Divide fractions: Divide fractions & mixed numbers: word problems

Mathematical Practices:

MP6- Attend to Precision

  • Communicate precisely to others
  • Use clear definitions in discussion with others and in their own reasoning
  • State the meaning of symbols they choose (equal sign)
  • Specific with units of measure, labeling, and quantities
  • Calculate accurately and efficiently

Question/Practice Stems

  • Why do you believe that to be true?
  • How did you reach your conclusion?
  • How does your answer connect to the question?
  • What math vocabulary did you use today?
  • How did you use it?
  • What does that symbol mean?
  • What would happen if your removed the symbol?
  • How would the problem change?
  • Does my work need labeling? If so, what? Why?

Are students applying the math practices daily?  How do you know?  What do the math practices sound like and look like in your classroom? 

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Tips, Mathematical Practices, and Ideas about Multiplying Fractions and Mixed Numbers

Topic 8- Multiplying Fractions and Mixed Numbers

November 12-November 19 (Nov. 20 posttest/pretest)

Lesson

8-1 Multiplying a Fraction and a Whole Number

CCSS

6.NS.1*

 AZ AIMS Standards

M06-S1C2-04, M06-S1C2-05,  M06-S5C1-01

8-2 Estimating Products 6.NS.1* M06-S1C2-04, M06-S1C3-01
8-3 Multiplying Fractions 6.NS.1* M06-S1C2-04, M06-S1C3-01
8-4 Multiplying Mixed Numbers 6.NS.1* M06-S1C2-04, M06-S1C3-02,  M06-S5C1-01
8-5 Problem Solving: Multiple-Step Problems 6.G.1 M06-S1C2-04, M06-S5C2-01, M06-S5C2-02

 Double Dose Recommendations:

  • Preteach Perimeter: 3 days (#31-33)
  • Kim Sutton Math Routines

Tip of the Week: PBL

How do we move up Bloom’s Taxonomy and go deeper with Depth of Knowledge (DOK)? What beginning PBL is available to help with DOK and Bloom’s? 

PBL Title & Link to Lesson

CCSS

 Description

The Parchitecture Project

 

 

Using Google Sketch Up, students design a student play-area for the new High Tech High K-8 school in Chula Vista. Students create design firms, conduct student surveys for input on their design, determine budget costs, and propose their ideas to a panel of adults and peers. Students have complete control of the design of the space with the stipulation that it must be safe and accessible to all students.
Prime Putt – Putt
  • 6.G.1
  • 7.G.1
  • 7.G.4
  • 7.G.6
  • 7.RP.2
Prime Putt – Putt golf is looking to refurbish their miniature golf course. Mrs. Math, the owner, has outlined the desired repairs. Students are to submit a scale drawing of existing golf holes along with a list of materials necessary to give Prime Putt – Putt the makeover it desperately needs.
Step Right Up for a Good Cause
  • 6.NS.1
  • 5.NF.1
  • 5.NF.1
  • 6.NS.4
  • 7.SP.5
  • 7.SP.7
A local charity needs your help!  You have been asked to plan a Family Fun Night in order to raise money for the charity.  You will develop games and find theoretical and experimental probability of each game.   You will plan a concession stand menu with combo choices, shop for game prizes and concession needs, and propose a layout for the event.  In the end, you will present a proposal to a panel of charity officials that includes the projected cost and profit for the event.
Let’s Party!

 

As caterers, students are bidding on a job to plan a birthday party for a 13-year old.  Given a budget of $250, they will submit a party proposal for 30 guests that includes a budget spreadsheet, written description of party and events, menu, map of room, and an oral presentation.

Mathematical Practices: Make sense of problems and persevere in solving them.

This tip comes from the ADE:

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?”.

What opportunities are you providing students to persevere with problem solving (and PBL)?

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Tips, Mathematical Practices, and Ideas about Multiplying, Fractions, and Mixed Numbers

Topic 8- Multiplying Fractions and Mixed Numbers

November 12-November 19 (Nov. 20 posttest/pretest)

Lesson

8-1 Multiplying a Fraction and a Whole Number

CCSS

6.NS.1*

 AZ AIMS Standards

M06-S1C2-04, M06-S1C2-05,  M06-S5C1-01

8-2 Estimating Products 6.NS.1* M06-S1C2-04, M06-S1C3-01
8-3 Multiplying Fractions 6.NS.1* M06-S1C2-04, M06-S1C3-01
8-4 Multiplying Mixed Numbers 6.NS.1* M06-S1C2-04, M06-S1C3-02,  M06-S5C1-01
8-5 Problem Solving: Multiple-Step Problems 6.G.1 M06-S1C2-04, M06-S5C2-01, M06-S5C2-02

 Double Dose Recommendations:

  • Preteach Perimeter: 3 days (#31-33)
  • Kim Sutton Math Routines

Tip of the Week:

Bloom’s/DOK- Are we providing opportunities for our students to analyze, evaluate, create, and construct during math?

  • Analyzeconstruct models, graphing information, comparing and contrasting values
  • Evaluate– Prepare a list of criteria for solving, make a booklet that includes mathematical rules for solving and potential tools list

Technology Integration Weekly Resources:

You could have students view the video, and ask them to then create their own video (or tell a partner if you do not have video equipment), to demonstrate with models and create their own “tutorial” with models.

By having them create their own tutorial, or presentation to a partner, they would then be using different multiple intelligences, and mathematical practices, to explain the “why” behind the mathematical computations.

How else can you take advantage of these videos as a learning opportunity for students?

Mathematical Practices: Model with Mathematics

Model with mathematics includes:

  • Understand this is a way to reason quantitatively and abstractly (able to decontextualize and contextualize)
  • Are able to simplify a complex problem and identify important quantities to look at relationships
  • Represent mathematics to describe a situation either with an equation or a diagram and interpret the results of a mathematical situation
  • Ask themselves, “How can I represent this mathematically?”

In model with mathematics, students will:

  • Apply prior knowledge to new problems and reflect
  • Use representations to solve real life problems
  • Apply formulas and equations where appropriate

Teachers will:

  • Pose problems connected to previous concepts
  • Provide a variety of real world contexts
  • Use intentional representations
  • Gives students opportunities to model with mathematics and describe the mathematical situation

Some questions to develop mathematical thinking could be:

  • What number model could you construct to represent the problem?
  • How would it help to create a diagram, graph, table …?
  • What are some ways to visually represent …?

DOK Math Example.001

What opportunities are you providing students to analyze, evaluate, and create during math?

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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

CCSS

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

Technology Integration Weekly Highlight

Tip of the Week

This tip comes from the ADE:

http://www.azed.gov/standards-practices/files/2011/06/2010mathgr6.pdf -- Part 1

 

http://www.azed.gov/standards-practices/files/2011/06/2010mathgr6.pdf

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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