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December 18, 2012 “Teachers are thus free to provide students with whatever tools and knowledge their professional judgment and experience identify as most helpful for meeting the goals set out in the Standards.” ~ Introduction to the CCSS

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Describe the overview of 6-8 math curriculum Identify properties of the RDW modeling technique for application problems Describe and apply tape diagrams Evaluate foundational and challenging problems from gr. 6-8

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State Overview of scope and sequence and modules Tape Diagram Problems Grade Level Problems Assessment Problems (PARCC)

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Grades Modules Lessons

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PK-5 Common Core Inc 6-12 CCI with Support from EdutTron

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Tape diagrams are best used to model ratios when the two quantities have the same units.

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1. David and Jason have marbles in a ratio of 2:3. Together, they have a total of 35 marbles. How many marbles does each boy have?

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2. The ratio of boys to girls in the class is 5:7. There are 36 children in the class. How many more girls than boys are there in the class?

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Lisa, Megan and Mary were paid $120 for babysitting in a ratio of 2: 3: 5. How much less did Lisa make than Mary?

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The ratio of Patrick’s M & M’s to Evan’s is 2: 1 and the ratio of Evan’s M & M’s to Michael’s is 4: 5. Find the ratio of Patrick’s M & M’s to Michael’s.

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The ratio of Abby’s money to Daniel’s is 2: 9. Daniel has $45. If Daniel gives Abby $15, what will be the new ratio of Abby’s money to Daniel’s?

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Double number line diagrams are best used when the quantities have different units. Double number line diagrams can help make visible that there are many, even infinitely many, pairs of numbers in the same ratio—including those with rational number entries. As in tables, unit rates (R) appear in the pair (R, 1).

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It took Megan 2 hours to complete 3 pages of math homework. Assuming she works at a constant rate, if she works for 8 hours, how many pages of math homework will she complete? What is the average rate at which she works?

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Read (2x) Draw a model Write an equation or number sentence Write and answer statement Unit Object Context

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2 boxes of salt and a box of sugar cost $6.60. A box of salt is $1.20 less than a box of sugar. What is the cost of a box of sugar? Salt Sugar $1.20 $6.60 3 parts = $6.60- $1.20 3 parts = $5.40 1 part = $5.40 ÷ 3 = $1.80 $1.20+$1.80= $3.00

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The students in Mr. Hill’s class played games at recess. 6 boys played soccer 4 girls played soccer 2 boys jumped rope 8 girls jumped rope 1) Compare the number of boys who played soccer and jumped rope using the difference. Write your answer as a sentence as Mika did. 2) Compare the number of boys who played soccer and jumped rope using a ratio. Write your answer as a sentence as Chaska did. 3) Compare the number of girls who played soccer to the number of boys who played soccer using a ratio. Write your answer as a sentence as Chaska did. Mika Said: “Four more girls jumped rope than played soccer.” Chaska Said: “For every girl that played soccer, two girls jumped rope.” Mr Hill Said: “Mika compared girls by looking at the difference and Chaska compared the girls using a ratio”

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Compare these fractions: Which one is bigger than the other? Why?

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Using Grade level packets, explain the exemplar solution of problems.

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Thanks for coming! Links www.btboces2.org/mathpd www.btboces2.org/mathpd http://www.parcconline.org/samples/ma thematics/grade-6-slider-ruler http://www.parcconline.org/samples/ma thematics/grade-6-slider-ruler http://www.parcconline.org/samples/ma thematics/grade-7-mathematics http://www.parcconline.org/samples/ma thematics/grade-7-mathematics www.Engageny.org www.Engageny.org

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