April+6+Assignments

1. Applet used for developing fraction concepts __[] __ Students will be able to develop understanding of how fractions actually make up parts of a whole. This works well for learners who are being introduced to fractions because it uses a pie chart and improper fractions cannot be shown. It does help students understand that even though 1/3 seems like the smaller number it actually is larger than 1/8. Students will have a chance to fill in a pie chart using percentages or fractions. They have as many sections cut from the pie as they want and they have scrollers or can use the keypad to type in the numbers to determine what the pie chart looks like.

 2. Applet used for practicing fraction concepts __[|http://nlvm.usu.edu/en/nav/frames_asid_194_g_2_t_1.html] __ Students will learn to practice fraction concepts that they have already learned but still need to obtain fluency. They will be able to practice multiplying fractions as well as visualize what they are doing during the multiplication process. Scrollers are provided to determine how many columns and rows are in a square and how many are highlighted. This makes them understand area and multiplication of fractions. Students are able to switch back and forth from proper and improper fractions. This tool is great for fourth to sixth graders because of the visual and conceptual aspect of it. Although it is recommended that students are taught the skills before they use this applet.

 3. KUSD 4th grade Standards and Benchmarks for fractions

 - **//<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 13.3333px; text-align: start; text-decoration: none; vertical-align: baseline;">I can represent unit fractions one-half, one-third, one-fourth, and one eighth (using drawings, a ruler, pictures, concrete objects, a number line, or a hundreds grid). // ** <span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">- **<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">//<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: serif; font-size: 13.3333px; text-align: start; text-decoration: none; vertical-align: baseline;">I can write equivalent fractions for unit fractions (e.g., halves, fourths, and tenths). // ** <span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">- **<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">//<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: serif; font-size: 13.3333px; text-align: start; text-decoration: none; vertical-align: baseline;">I can compare and order fractions with common denominators and com-pare and order unit fractions (e.g., one-third, one-fifth, and one-seventh). // **

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"> 4. Concepts related to fractions that are represented in my 4th grade field experience and the Everyday Mathematics curriculum.

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"> -Students compared fractions playing a fraction matching game <span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">-Students made equivalent fractions using a fraction matching game

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"> 5. Session 9:

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"> Part A

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"> 1)

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"> - 3/4 x 1/3 = 3/12

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"> - 3/5 x 2/3 = 6/15

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"> - 1/4 x 8/9 = 8/36

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"> 2) The area model shows the product of two fractions because it visually shows each fraction separately with one in vertical formation and the other one horizontal. This allows the student to see the fractions as length and width, which when they are multiplied together produce the area. In the same way the two fractions are superimposed together and the part that is overlapping is what is the product of the fractions being multiplied together.

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"> 3) (2/3) / (3/4) = 8/9

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"> 4) When the area model is used to multiply then the quotient must be greater than the first fraction because division is the opposite of multiplication. Just as in the multiplication area model the product is smaller than the fractions, in the division area model the quotient is greater than the fractions.

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"> 5)
 * <span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">**<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Verdana','sans-serif'; font-size: 11.3333px; text-align: start; text-decoration: none; vertical-align: baseline;">• ** || <span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Verdana','sans-serif'; font-size: 11.3333px; text-align: start; text-decoration: none; vertical-align: baseline;">How many 3s are there in 6? = 2  ||
 * <span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">**<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Verdana','sans-serif'; font-size: 11.3333px; text-align: start; text-decoration: none; vertical-align: baseline;">• ** || <span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Verdana','sans-serif'; font-size: 11.3333px; text-align: start; text-decoration: none; vertical-align: baseline;">How many groups of 3 tens are there in 6 tens? = 2  ||
 * <span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">**<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Verdana','sans-serif'; font-size: 11.3333px; text-align: start; text-decoration: none; vertical-align: baseline;">• ** || <span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Verdana','sans-serif'; font-size: 11.3333px; text-align: start; text-decoration: none; vertical-align: baseline;">How many groups of 3 fives are there in 6 fives? = 2  ||
 * <span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">**<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Verdana','sans-serif'; font-size: 11.3333px; text-align: start; text-decoration: none; vertical-align: baseline;">• ** || <span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Verdana','sans-serif'; font-size: 11.3333px; text-align: start; text-decoration: none; vertical-align: baseline;">How many groups of 3 tenths are there in 6 tenths? = 2  ||
 * <span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">**<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Verdana','sans-serif'; font-size: 11.3333px; text-align: start; text-decoration: none; vertical-align: baseline;">• ** || <span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Verdana','sans-serif'; font-size: 11.3333px; text-align: start; text-decoration: none; vertical-align: baseline;">How many groups of 3 @s are there in 6 @s? = 2  ||
 * <span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">**<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Verdana','sans-serif'; font-size: 11.3333px; text-align: start; text-decoration: none; vertical-align: baseline;">• ** || <span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Verdana','sans-serif'; font-size: 11.3333px; text-align: start; text-decoration: none; vertical-align: baseline;">How many groups of 3 anythings are there in 6 anythings (as long as both anythings refer to the same unit)? = 2  ||

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">All of these question yield the same answer

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">6) ( <span style="background-color: transparent; color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">3/5) <span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"> / <span style="background-color: transparent; color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">(3/4)

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">= (12/20) / (15/20)

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">= 4/5

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">7) These two problems have the same difference in numbers, but they don't share the same units, which as we saw above doesn't make any difference.

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">Part B

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">1)

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">a. $400

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">b. $320

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">2) $52

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">3) No, the prices were not the same because 20% of the original price is different than 20% of the sale price. If they add 20% to the sale price it is still going to be cheaper than the original price.

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">4) 1/200 = .5% = 0.005

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">5) .2% = 0.002 = 1/500

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">6) 170% = 1.7 = 17/10

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">7) 0.004 = .4% = 1/250

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">8) 25% of 12,000 = .25 x 12,000 = 3,000

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;">9) 80% of bridge remains. 80% = 4/5. 80 x 4/5 = 320/5 = 64

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"> 10)

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"> a. 68/100 = 0.68 = 68%

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"> b. shade 38 squares

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: start; text-decoration: none; vertical-align: baseline;"> 11) 40% of 80 is 33% of 96.