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1 Multiplication, Division & Fractions Unit Four Unit Four Answer Keys Session Blacklines A.., Unit Four Pre-Assessment Responses will vary. example example a b Sketches will vary. Example: a, Sketches will vary. Example: I split a circle into parts and colored in of them. Then I colored in more. There are in all. b, Sketches will vary. Example: If you make in one egg carton and then in another, and add them together, you can see that you get in all. a Yes. b Explanations will vary. Example: You can see that these fractions are all the same size when the whole is the same size. a more than a whole sandwich b Explanations will vary. example If you have, you need to make a whole sandwich. is more than, so if someone gave you, you would have more than a whole sandwich. example If you move this will fill up the missing and then a little more. over, it a Estimates will vary. b Strategies will vary. c They will have 7 bags of apples. Session Bridges Student Book, page 99, Which Estimate Makes the Most Sense? a 7, Explanations will vary. Example: 7 because 7 is. is only and is, so 7 is the closest. b, Explanations will vary. Example: 9 is and 7 9 is. is closer to 7, so is the best. c, Explanations will vary. Example: = and =. is closer to than is. d, Explanations will vary. Example: is. If you add another it s and another is. is closest to 7, so I picked. a & b (challenge) Problems and solutions will vary. Bridges in Mathematics, Grade

2 Unit Four Multiplication, Division & Fractions Session (cont.) Home Connection, pages and, Estimation Interviews Responses will vary. Example: miles because we know is. Responses will vary. Example: About \$7 because. = \$. = \$. = \$ + + = \$7 Responses will vary. Example: About 7 hours because 7 =. Responses will vary. Example: To find out if you have enough money to buy some things. To find out which item is a better deal to purchase. To estimate how much change you should get back. To estimate how much money you ll save if something is on sale. Session Bridges Student Book, pages and, Multiplication Menus a,,,, 7,, b, Strategies will vary. Example: = ; = + = a,,, 7,, 7, b, Strategies will vary. example = ; = + = b example = ; = a, 7,, 7,,, b, Strategies will vary. Example: = 7; = a & b Responses will vary. Bridges Student Book, page, Timely Problems (challenge), Responses will vary based on the length of your school day. Responses will vary. One million seconds is a little more than and a half days. Session Home Connection, pages and, More Multiplication Menus a,,,, 7,, b, Strategies will vary. Example : = ; = = Example : would be, but is two s less than that, and =. a,,, 9,, 9, b, Strategies will vary. Example: = ; = + = 9; + 9 = a,,, 9,, 9, b Responses will vary. Session Bridges Student Book, pages 7 and, Water Conservation a gallons b gallons c gallons saved in a day, 7 gallons in a week a gallons b 9 gallons c gallons saved in a week, gallons in a month Bridges Student Book, page 9, Water Conservation Challenge (challenge) Strategies will vary. gallons. Strategies will vary. gallons or gal, cups. Bridges in Mathematics, Grade

3 Multiplication, Division & Fractions Unit Four Session 7 Home Connection, pages 9, Multiplication & Division Practice example Menu for = 7 = 7 9 = 7 7 Menu for = = 7 = 9 = Menu for = = 9 = 7 7 Menu for = = = = Menu for 7 7 = 7 7 = 7 = 7 = 7 7 = 7 = Menu for = = = = = = 7 a 9 cookies b dozen plus more cookies, Strategies will vary. Example: R = = = = 7 7 a feet b sections c \$ (challenge) Riddle The number is 7. Strategies will vary. Example:,,,,,, 7,, 9,,,,,,,, 7,, 9,,,,,, 7 + = + = 7 + = It has to be a multiple of 7 plus more, so it could be, 7, or. I know it s an odd number because when you divide it by, you get a remainder of. So I think it has to be 7 and then I divided it by the other numbers to see if the remainders came out right and they did. 7 = R 7 = R 7 = R 7 = R (challenge) Riddle The number is. Strategies will vary. Example: I know it has to be even because there s no remainder when you divide by. And it has to be a multiple of 7 plus. The multiples of 7 between and are 7,,,,,, = + = + = + = + = 9 + = 9 + = is more than and,, and 9 are odd, so it has to be,, or. = = R = R When you divide it by, the remainder has to be so it must be. I tried dividing by the other numbers to make sure and it works. = R = 9 R = 7 R 7 = R Session 9 Home Connection, pages and, The Tangerine Problem Estimates and explanations will vary. Example: Between and because = and =, Methods will vary. Example: Multiplication Menu = = = = = Other useful combinations: = - - Bridges in Mathematics, Grade

4 Unit Four Multiplication, Division & Fractions Session 9 (cont.) Home Connection, pages and, The Tangerine Problem (cont.) Ali is correct. Responses and explanations will vary. Example: Yes, I agree with Ali because if you make one side of the rectangle in Problem half as long and you keep the same area,, the other side will have to be twice as long. Responses will vary. Example: If you put tangerines into bags of, you ll get bags with tangerines in each bag. \$. = \$. If you divide up the tangerines into bags, you ll have bags with tangerines in each bag. \$. = \$. Max s plan is better for Max and Holly because they ll make more money. Holly s plan is better for the people who buy the tangerines because they ll get tangerines instead of for the same price. They might be able to sell more bags if they give people more for their money. Session Bridges Student Book, pages and, Sunflower Seeds Responses may vary somewhat. Example: Multiplication Menu = = = = T he Problem: Estimate: = 7 7 Figuring Box + + Session Bridges Student Book, page, Comparing, Adding & Subtracting Pieces a < b > c = d = e < f = a f Responses will vary. Equivalent fractions are correct answers for all problems below. a b c d or or e f g h or i Equivalent fractions are correct answers for all problems below. a b c d e f g h i + 7 Home Connection, pages and, Lady Liberty,,,,,, Responses will vary based on the problems students select. Bridges in Mathematics, Grade

5 Multiplication, Division & Fractions Unit Four Session (cont.) Home Connection, pages and, Lady Liberty (cont.) a Estimates will vary, and some may be able to compute the exact answer mentally. b Explanations of estimates will vary. c, Methods will vary. Example: (challenge) = = = 7 = steps 7 steps steps steps steps = = = =steps = = = steps steps steps 7 7 steps = steps = steps steps steps steps = = = =steps steps steps steps Session Bridges Student Book, pages 7 and, Different Ways to Make One Responses will vary. Students can show their thinking with labeled sketches, numbers, or words. The chart below shows all the different possibilities. steps Bridges in Mathematics, Grade 7

6 Unit Four Multiplication, Division & Fractions Session (cont.) Bridges Student Book, pages 7 and, Different Ways to Make One (cont.) Responses will vary. Example: The third is hard to put with the others to make. The halves, fourths, and eighths all fit together easily, but nothing fits with the except for more thirds. I think it s because,, and are all multiples of, but isn t. If we could use sixths and twelfths, it would work easier. (challenge) Strategies will vary. will be four times as long as the strip shown, since is equal to. Session Bridges Student Book, pages 9 and, Quilt Block Fractions Keys for the quilt blocks are shown here. Quilt blocks themselves are not replicated here. = = = = = = (challenge) 9 = = = = = = = = Home Connection 7, pages and, Fraction & Division Story Problems a b or He got the same amount of pizza each day. Observations will vary. Examples: is the same as. + = I split the pizzas into pieces each, but I could have just split them into fourths, because a fourth of is like an eighth of. a Story problems will vary. Example: We got 7 balloons to decorate the room for a big party. We divided the balloons evenly among tables. How many balloons were there on each table? b Story problems will vary. Example: kids made 7 brownies and shared them evenly among themselves. How many brownies did each kid get? c Story problems will vary. Example: I got new shirts for \$7. including tax. They each cost the same amount. How much did I have to pay for each shirt? d Story problems will vary. Example: Bridges in Mathematics, Grade

7 Multiplication, Division & Fractions Unit Four Session (cont.) Home Connection 7, pages and, Fraction & Division Story Problems (cont.) d Story problems will vary. Example: kids were going to the game. If each car could hold kids, how many cars did they need to get there? 7 (challenge), Strategies will vary: Example: If she gave half the cards to Erin and to her brother, she gave away of her cards. If she has, that s of her cards. Since she still has of the cards, her brother must have gotten the same amount,, and Erin must have gotten twice that amount,. Session to Erin to brother + + = Bridges Student Book, pages and, Fractions on a Geoboard D = B = A = C = E = Observations will vary. Session or or Bridges Student Book, pages and, Design Your Own Quilt Blocks Responses will vary. Home Connection, pages 7 9, The Mini- Quilt Project Designs will vary. Titles will vary. Observations will vary. 9 square centimeters, Strategies will vary. Example: Each big square is sq. cm, and there are of them. So would be the whole area. = + = + = 9. Responses will vary based on students designs. (challenge) Responses will vary widely. Session 7 Bridges Student Book, page, Comparing Fractions (challenge) /, /, /, /, 7 /, /, /, Students will need to insert the fraction they made up in its proper place in the sequence. a > b < c > d > e > Session Bridges Student Book, page 7, Equivalent Fractions,,,, 9,,,, 7,,,,,,, 9, 9,,,,,, (If some students write, clarify with them that a single - egg carton is the whole in this problem.),,, Bridges Student Book, page, Eggsploration Challenge Sheet (challenge), 9,, are all correct names for the fraction. Lines on the carton will depend on which fraction students have selected. Bridges in Mathematics, Grade 9

8 Unit Four Multiplication, Division & Fractions Session (cont.) Bridges Student Book, page, Eggsploration Challenge Sheet (challenge) (cont.), 9,, are all correct names for the fraction. a a,,, b, c,, d 9, e, 7,, a b b Eggs in Minutes in Inches in a carton an hour a foot Eggs in Minutes in Inches in a carton an hour a foot c c Eggs in Minutes in Inches in a carton an hour a foot d Responses will vary. Example: They all have parts. You can show halves, thirds, fourths, sixths, and twelfths on all of them. You can divide them all by,,,, and. Home Connection 9, pages, Egg Carton Fractions & More Students lines will vary depending on the fractions they write. Correct fraction names for all models are shown at the top of the next column. Students need only write for each one. (challenge) Responses will vary. Example: I think he divided the carton into thirds. Then he saw that of the thirds are filled and half of the last third is filled. a (challenge) The carton must contain eggs total. The orientation does not matter. Example: Bridges in Mathematics, Grade

9 Multiplication, Division & Fractions Unit Four Session (cont.) Home Connection 9, pages, Egg Carton Fractions & More (cont.) b The carton must contain eggs total. The orientation does not matter. Example: (challenge) Solutions may vary. Example: 7 9 Session Home Connection, pages and, More Fraction Story Problems months, Strategies will vary. example = Her hair needs to grow inches to get back to the length she wanted it to be. Month Month Session 9 Bridges Student Book, page 9, Combining Egg Carton Fractions For all problems, sums may be expressed as equivalent forms of the fraction. Month Month Month example + = + = + = If you add groups of /, it comes out to /, so it ll take months for her hair to grow back to where she wants it. a & b miles Jamal s House miles miles 9 c Responses will vary. Example: + is, so the whole distance must be. Since + + is, I put Jamal s house about a third of the way along the line from Loon Lake to Crescent City. Bridges in Mathematics, Grade

10 Unit Four Multiplication, Division & Fractions Session (cont.) Home Connection, pages and, More Fraction Story Problems (cont.) (challenge) \$7., Strategies will vary. Example: \$ = \$ because \$ = \$, and of \$ is \$. \$ = \$ because \$ = \$ and of \$ is \$. = \$. because \$ = \$ and of \$ is half of \$ and that s \$.. \$ = \$ because \$ = \$ and of \$ is \$, so of \$ must be \$. \$ + \$ + \$. + \$ = \$7. Session Home Connection, pages 7 9, Unit Four Review The orientation of the dots will vary. Example: Students need write only two names for each fraction. All possibilities are shown here. a 9, b,,,,, a b Responses will vary. Example: of a carton only has eggs, but has, so >. a 7, Sketches will vary. Example: b (or or ), Sketches will vary. Example: a, Sketches will vary. Example: b / (or /, /, /), Sketches will vary. Example: a,,,,,, b, Strategies will vary. Example: = = = 7 a Estimates will vary. b Solutions and strategies will depend on the student and problem selected. Answers for each problem are shown below. = = = 7 = Bridges in Mathematics, Grade

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