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October 2, 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 Describe how Math Sprints: diagnose fluency gaps build fluency Create Math Sprints Identify strategies to teach ratio and proportion problems Fluency in 6-8 Transition Units (Gap Analysis) Teaching Ratios and Proportional Relationships Module Unit alignment Grade 6 Grade 7 A grocery store sign indicates that bananas are 6 for $1.50, and a sign by the oranges indicates that they are 5 for $3.00. Find the total cost of buying 2 bananas and 2 oranges. A $0.85 B $1.70 C $2.25 D $4.50 Jeremy has two 7-foot-long boards. He needs to cut pieces that are 15 inches long from the boards. What is the greatest number of 15-inch pieces he can cut from the two boards? A 15 B 10 C 11 D 12 A comparison of 8 black circles to 4 white circles can be written as the ratio of 8:4 and can be regrouped into 4 black circles to 2 white circles (4:2) and 2 black circles to 1 white circle (2:1). Students should be able to identify all these ratios and describe them using “For every…., there are …” A clothing store offers a 30% discount on all items in the store. Part A: If the original price of a sweater is $40, how much will it cost after the discount? A clothing store offers a 30% discount on all items in the store. Part B: A shopper bought three of the same shirt and paid $63 after the 30% discount. What was the original price of one of the shirts? A clothing store offers a 30% discount on all items in the store. Part C: Every store employee gets an additional 10% off the already discounted price. If an employee buys an item with an original price of $40, how much will the employee pay? The new floor in the school cafeteria is going to be constructed of square tiles that are either gray or white and in the pattern that appears below: Part A: What is the ratio of gray tiles to white tiles? Part B: What is the ratio of white tiles to the total number of tiles in the pattern? Answer: ____________________ The new floor in the school cafeteria is going to be constructed of square tiles that are either gray or white and in the pattern that appears below: Part C: If the total cost of the white tiles is $12, what is the unit cost per white tile? Answer: $____________________ Part A: 10 to 8, 5:4, or other equivalent ratio Part B: 8 to 18, 4:9, or other equivalent ratio Part C: $1.50 per white tile On a bicycle you can travel 20 miles in 4 hours. What are the unit rates in this situation, (the distance you can travel in 1 hour and the amount of time required to travel 1 mile)? Last summer, a family took a trip to a beach that was about 200 miles away from their home. The graph below shows the distance driven, in miles, and the time, in hours, taken for the trip. While on vacation, a group can rent bicycles and scooters by the week. They get a reduced rental rate if they rent 5 bicycles for every 2 scooters rented. The reduced rate per bicycle is $15.50 per week and the reduced rate per scooter is $160 per week. The sales tax on each rental is 12%. The group has $1600 available to spend on bicycle and scooter rentals. What is the greatest number of bicycles and the greatest number of scooters the group can rent if the ratio of bicycles to scooters is 5:2? While on vacation, a group can rent bicycles and scooters by the week. They get a reduced rental rate if they rent 5 bicycles for every 2 scooters rented. The reduced rate per bicycle is $15.50 per week and the reduced rate per scooter is $160 per week. The sales tax on each rental is 12%. The group has $1600 available to spend on bicycle and scooter rentals. What is the greatest number of bicycles and the greatest number of scooters the group can rent if the ratio of bicycles to scooters is 5:2? Number # Bikes 5 10 15 20 # Scooters 2 4 6 8 Value Bikes 77.5 155 232.50 310 Value Scooters $320 $640 $960 $1280 Value of both $397.5 $795 $1192.50 $1590 Cost with Tax $445.20 $890.40 $1335.60 $ 1780 David is making his own strawberry yogurt. In David’s mixture, the number of strawberries is proportional to the amount of milk, in cups. David uses 4 cups of milk for every 14 strawberries in his mixture. Which equation represents the relationship between s, the number of strawberries, and m, the number of cups of milk he uses? Jill walks 3 meters every 2 seconds. Let d be the number of meters Jill has walked after t seconds. d and t are in a proportional relationship. If 2 pounds of beans cost $5, how much will 15 pounds of beans cost? Based on the Sample Questions • What are the skills most students have to be successful • What are the skills students don’t have Part 1: Fluency Work (10 minutes) Part 2: Problem Solving (6 minutes) Part 3: Content Lesson and Debrief (34 min) Gr 6 R.P. Effective Teaching: Feedback Engagement & 7th Grade Exemplar and the intro to the Shifts CCLS Shifts and (8) Math Practices Progressions, Illustrative Mathematics and Math Discussions Contingent • • The praise is based on something you really did You earned it • • I state specifically what it is you’re being praised for “You included a diagram in every word problem!” • • I really mean it I’m not just saying it • • It’s matched to you- your level Matched to the person you are • Different all the time Specific Genuine Appropriate Varied Attributed to performance and effort The tone of the praise statement suggests that obviously the student has the ability to do well, and that it is the effort the student exerted that made the performance turn out so well • “You worked hard on math-facts and it paid off on the quiz.” • Thanks for coming! Links www.btboces2.org/mathpd ETS’ CBAL Test • Fractions: http://youtu.be/w7h64xjN-PM • Common Core in Mathematics: Overview • Common Core in Mathematics: Shift 1 – Focus www.Engageny.org www.btboces.org