gr8_percents

= Percents =

//It is expected that students will://
 * **Prescribed Learning Outcomes**

A3 Demonstrate an understanding of percents greater than or equal to 0%. [CN, PS, R, V] || --Optional extension: If the blue rhombus is given a value of one, what is the new value of the shape? Represent this with grids. --Have students exchange their shapes with a partner and calculate the value of their partner's shape. They should compare their findings and discuss.
 * **Planning for Assessment** || **Assessment Strategies** ||
 * Provide students with pattern blocks (real or virtual-- use only yellow hexagons, red trapezoids, blue rhombi, and green triangles). Ask them to create a shape using 3-5 pieces, one of which is a yellow hexagon. Given that the yellow hexagon has value of one, have the students calculate the value of the shape they have created. Record this value as both a fraction and a percent. Have students represent this value using small 100-square grids.

Have students make a small booklet in which they explain how to change the following: For each conversion they should provide an example, a written explanation, and drawings and/or grid representations. The written explanation should include how the two items formed are the same and how they are different. Give students a variety of fractions, decimals, and percents (e.g., 7/8, 0.45, 125%, 2 4/5, 1.05, 0.9%) and have them place these on a number line, explaining their reasons for choosing specific places.
 * a percent to a decimal
 * a percent to a fraction
 * a decimal to a percent
 * a decimal to a fraction
 * a fraction to a decimal
 * a fraction to a percent

Have students solve the following problems:
 * A hardware store is planning a "sale" for father's day. It wants to offer 20 percent off the price of all power tools but still have customers pay just as much for the tools as if they were not on sale. Explain how this can be done using specific examples and grid representations.


 * Preet purchased three items at a local sports store. Preet complained to his friend that since he had been charged 5%GST and 7%PST on each item, he had paid a total of 36% tax. Pretend you are Preet's friend and explain, using examples and/or representations, why this is not the case.


 * Mallory claims that 0.5% of the students in his mathematics class were born in South America. Marcy disagrees with Mallory and says she thinks that he has made some kind of error. Who is most likely correct? Explain your reasoning.


 * Describe several ways in which 25% of 80 can be calculated.

Note: Students often rely on a rule or formula for calculating percentages. Developing number sense in this area requires students to think in different ways regarding percentages. Students should be encouraged to make connections to benchmark fractions and decimals and use these in their thinking. For instance, calculating 25% of 80 can be done in a number of ways such as these: Note: These are all forms of the same fundamental concept.
 * changing 25% to 0.25 and then multiplying by 80
 * changing 25% to 1/4 and multiplying by 80
 * changing 25% to 1/4 and then dividing 80 by 4 to get 1/4 of 80
 * calculating 1% of 80 as 0.8 and then multiplying by 25
 * calculating 10% of 80 as 8, taking that amount again for another 10% (8 more), and taking half of the 10% amount to get 5% (4 more), finally adding 8 + 8 + 4 to get the amount equal to 25% || Verify that students have a have a clear understanding that:
 * decimals are fractions simply written in a different form
 * percentages are another way of representing hundredths, and so are a third way of writing fractions.

Students need to understand that the base 10 system extends infinitely in two directions, with each "place" representing a multiplication or division by a factor of 10 from an adjacent "place", left or right, respectively.

Asses students abilities to describe several ways in which a% of b can be calculated. For example 25% of 80. ||