by Tracy Watanabe
Topic 12 Ratios, Rates, and Proportions
January 2127 (Jan 28 posttest/pretest)
Lesson121 Understanding Ratios 
CCSS6.RP.1 
Arizona StandardsM06S1C101 
122 Equal Ratios and Proportions 
6.RP.3 
M06S1C101 
123 Understanding Rates and Unit Rates 
6.RP.2 
M06S1C101, M06S1C103 
124 Comparing Rates 
6.RP.3.b 
M06S1C101, M06S1C104 
125 Distance, Rate, and Time 
6.EE.9 
M06S1C204, M06S3C304 
126 Problem Solving: Draw a Picture** (2 days) 
6.RP.2 
M06S3C201 
Double Dose Recommendations:
 Preteach the following: Mean, Median, Mode, 3 days (#68#70)
 126 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 realworld 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?


Technology Integration Resources:
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 ….?”
How do you communicate precisely, using math language, when discussion ratios, rates, and proportions?
Rates Ratios & Proportional Relationships
by Tracy Watanabe
Topic 11: Properties of TwoDimensional Figures
Note: The original dates you set for this unit was January 616 (Jan 17 posttest/pretest). However, most of you will be starting this unit soon since your pacing is determined by student understanding.
111 Basic Geometric Ideas 
6.G.3* 

112 Measuring and Drawing Angles 
6.G.1* 
M06S4C401 
113 StepUp Lesson: Angle Pairs 
7.G.5 
M06S4C102 
114 Triangles 
6.G.1* 

115 Quadrilaterals 
6.G.1* 

116 StepUp Lesson: Circles 
7.G.4 

117 StepUp Lesson: Transformations and Congruence 
8.G.2 
M06S4C201, M06S4C202 
118 StepUp Lesson: Symmetry 
8.G.1 

119 Problem Solving: Make a Table and Look for a Pattern 
6.EE.9 
M06S5C207 
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.
Technology Integration Resources:
Mathematical Practices:
When students share their thinking and reasoning about the solutions, they are justifying their solutions (DOK 3), a foundational criticalreasoning skill. The ability to articulate a clear explanation for a process and critique the reasoning of others is the backbone of Math Practice #3—Construct 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 counterexample?
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?
Geometry
by Tracy Watanabe
Topic 10: Integers
Note: The original dates you set for this unit was December 618 (Dec.19 posttest/pretest). However, most of you will be starting this unit soon since your pacing is determined by student understanding.
101 Understanding Integers 
6.NS.5 
M06S1C104, M06S1C105 
102 Comparing and Ordering Integers 
6.NS.7.a 
M06S1C104 
103 Rational Numbers on a Number Line 
6.NS.6.c 
M06S1C103, M06S1C104 
104 StepUp Lesson: Adding Integers 
7.NS.1.b 
M06S1C201 
105 StepUp Lesson: Subtracting Integers 
7.NS.1.c 
M06S1C201 
106 StepUp Lesson: Multiplying Integers 
7.NS.2.a 

107 StepUp Lesson: Dividing Integers 
7.NS.2.b 

108 Absolute Value 
6.NS.7.d 
M06S1C105 
109 Graphing Points on a Coordinate Plane 
6.NS.6.c 
M06S4C301 
K104 Missing Coordinates** (See double dose)J31 Use Reasoning** 

M06S4C302M06S5C209 
1010 Problem Solving: Use Reasoning 
6.G.3 
M06S5C209 
Double Dose Recommendations:
 Kim Sutton math routines
 Preteach 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 needtoknow lists for what they need to know in order to complete the task.
 After each lesson, refer back to the needtoknow 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 “HandsOn, MindsOn” 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 preteaching. Every day I’d preteach 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.
How do you differentiate for your students?
Integers