1. Expectations from the Number and Operations Standard Principles and Standards for School Mathematics National Council of Teachers of Mathematics 2000

2. Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Grades 6-8 Develop meaning for percents greater than 100 and less than 1. Understand and use ratios and proportions to represent relationships

3. Compute fluently and make reasonable estimates. Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios. 4’ 12’

4. Ratio-relationship between 2 quantities. 3 games for 50 cents 3/50 3 to 503:50

5. Proportion-equal ratios Joe will often tape 6 minutes of audio tape to obtain enough footage for a 30-second music clip. At that rate, how many minutes of tape will it take to shoot a 45-second music clip? 6 tape =N tape 30min = 45min cross multiply: 30 x N = 6 x 45 30 x N = 270 N=9

6. Percent-per 100 a special ratio N/100 25/100=.25=25% Prerequisite skills Decimals fractions multiplication equations/variables-find missing numbers

7. Percent Shortcuts A% of B = B% of A Ex: 28% of 50 = 50% of 28 (KA)% of B = K(A% of B) Ex: 20% of 35 is twice 10% of 35 (2x10)% of 35 = 2(10% of 35) Source: Glatzer, Arithmetic Teacher, Feb. 1994

8. Percent Shortcuts (A+C)% of B = (A% of B) + (C% of B) Ex: 15% of 60 = (10% of 60) + (5% of 60) Source: Glatzer, Arithmetic Teacher, Feb. 1994

9. Tangrams and Percent Find the area of each of the seven tangram pieces using a ruler or grid paper. Record your results. What is the total area of all seven tangram pieces? Find what percent of the whole area each piece is. Record your results.

10. Jacob: Fourth Month of Seventh Grade

11. Jacob: Fourth Month of Seventh Grade (con’t)

12. Bradley: Fourth Month of Seventh Grade

14. Allan: Fourth Month of Seventh Grade

16. Jessica: Fourth Month of Seventh Grade