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?

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)?