by Tracy Watanabe
Topic 14 Understanding Percent
February 717 (Feb. 18 posttest/pretest)
141 Understanding Percent 
6.RP.3 
M06S1C104 
142 Fractions, Decimals, and Percents 
6.RP.3 
M06S1C101 
143 Percents Greater Than 100 and LessThan 1 
6.RP.3.c 
M06S1C101, M06S1C104 
144 Estimating Percent 
6.RP.3 
M06S1C101, M06S1C301 
145 Finding the Percent of a Number 
6.RP.3.c 
M06S1C302, M06S3C303, M06S5C205 
146 Applying Percents: Finding the Whole 
6.RP.3.c 
M06S3C301 
147 Problem Solving: Reasonableness 
6.RP.3.c 
M06S5C201 
 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.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
Double Dose Recommendations
Preteach the following:
 Measures of central tendency, 2 days (#76, #78)
 Applying mode, median, mean, 3 days, (#8385)
Technology Integration
Click here to see the full post by Mr. Avery. If you notice, Mr. Avery asks two guiding questions at the bottom of the post. Have you considered having groups of students respond to the post (or perhaps the whole class compose a response to send them)?
Tip of the Week #1
How would you apply percentages to the real world? Here an idea that would take one class hour, and would engage kids: Trashketball Review for ratios, fractions, decimals, and percentages.
Tip of the Week #2
What would this standard look like? This tip comes from the ADE, with examples and explanations of this standard:
Mathematical Practices: #7 Look for and make use of structure
In grade 6, students routinely seek patterns or structures to model and solve problems. For instance, students recognize patterns that exist in ratio tables recognizing both the additive and multiplicative properties. Students apply properties to generate equivalent expressions (i.e. 6 + 2x = 2 (3 + x) by distributive property) and solve equations (i.e. 2c + 3 = 15, 2c = 12 by subtraction property of equality; c=6 by division property of equality). Students compose and decompose two and threedimensional figures to solve real world problems involving area and volume.
What are some specific questions you can ask about math practices during this unit?
Percent Ratios & Proportional Relationships
by Tracy Watanabe
Standards
Topic 13 focuses mainly on Ratios and Proportional Relationships (RP) 3, 3a, and 3b:
 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.3a Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
 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?
Double Dose Recommendation:
Preteach the following:
 Reading Frequency tables and histograms, 2 days (#712)
 Stem and Leaf Plots, 3 days (#7335)
Tip of the Week:
One highlight of my walkthrough at FPES a few weeks ago was seeing an awesome cumulative review game in several classes. Math Instructional Coach, Kathleen Donlan, engaged classes in this powerful collaborative group math game. She originally got the idea from a math competition she went to years ago, and has tailored the game to fit the classes with the standards they’ve learned so far.
Click here to download Kathleen’s game (used with permission).
Technology Integration Resources:
Math Practices
The Teaching Channel created a great video about including math practices and explicitly in daily instruction.
How do you include the math practices daily?
If you have used Kathleen Donlan’s review game, what insight can you share with others?
Ratios & Proportional Relationships
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 7 — Adding and Subtracting Fractions and Mixed Numbers
Oct. 30Nov. 7 (Nov. 8 posttest/pretest)
Lesson
71 Adding and Subtracting: Like Denominators 
CCSS
6.NS.1* 
AZ AIMS Standards
M06S1C207 
72 Least Common Multiple 
6.NS.4 
M06S1C102 
73 Adding and Subtracting: UnlikeDenominators 
6.NS.1* 
M06S1C207 
74 Estimating Sums and Differences of Mixed Numbers 
6.NS.1* 
M06S1C301 
75 Adding Mixed Numbers 
6.NS.1* 

76 Subtracting Mixed Numbers 
6.NS.1* 

77 Problem Solving: Make a Table 
6.RP.1 

Double Dose Recommendations — Preteach the following:
 Relating measures, 2 days (#24‐#25). Look for science connections.
 Elapsed time, 3 days (#26‐28)
Tip of the Week:
 Assessing/Higher Level Learning: Are we having our students complete the Performance Based Assessments at the end of each Topic?
 Enrichment: In your teacher’s manual you will find ideas for enrichment under “Advanced/Gifted” on page 160D. There are two different ideas listed here.
Technology Integration Weekly Highlight:
 Math in the Real World Project: The math project on page 161 in the Teacher’s Guide, connects to the real world by researching how many miles the top hiking trails are in the USA (the Appalachian Trail, the Pacific Crest Trail, and the Continental Divide Trail); then have the students pick one of the three trails and show the portion of the total trail in one state as a fraction. Then make a table that lists the state and the portion of the trail as a fraction.
 Students would use the computer for their research, and they could also use it for their reflection on the learning that took place in the above project. This would also be a great way to bring in the mathematical practice of attend to precision.
 Students could use Educreations on the iPad to narrate and show their thinking.
 On the netbooks or thin clients, students could create their table in Google Docs, then narrate their reflection by connecting Voice Comments (in Kaizena) to their document. Click here for instructions (see slide #14).
 Click here for more resources/videos for 6.NS.1.
 Click here for more resources/videos for 6.NS.4.
 Click here for more resources/videos for 6.RP.1.
Mathematical Practices:
The following comes from the ADE: 6.MP.6. Attend to precision. In grade 6, students continue to refine their mathematical communication skills by using clear and precise language in their discussions with others and in their own reasoning. Students use appropriate terminology when referring to rates, ratios, geometric figures, data displays, and components of expressions, equations or inequalities.
Some questions that can be asked for attending to precision includes:
 What mathematical terms apply in this situation?
 How did you know your solution was reasonable?
 What mathematical language…, definitions…, properties can you use to explain…?
 Explain how you might show that your solution answers the problem.
How do you use, and challenge students to use mathematics vocabulary precisely and consistently?
Adding and Subtracting Fractions Number System Ratios & Proportional Relationships