1 Jason made made of the free throws and Kevin of the free throws. What fraction of the free throws did they make altogether? Area Model 1 You Try: Riley and Jasper were working on their science fair project. Riley completed and Jasper completed. How much have they In order to add these fractional parts, we must create the same-sized pieces, so add dashed lines to Jason s, and to Kevin s to make pieces that are the same size. completed altogether? Jason s free throws + Kevin s free throws 2 3 5 5 = 10 15 1 5 3 3 = 3 15 Combine the shaded pieces and you have 13 shaded out of 15. Altogether, Jason and Kevin made the free throws in the game. Finding a Common Denominator Write equation Multiply the denominators to find a common denominator 3x5=15 of Multiply each fraction by a fractional one to get equivalent fractions with the common denominator of 15. Add the fractions by adding the numerators and keeping the denominators the same. They made throws altogether. of the free 5.NF.1 5.NF.1 Page 1 of 12 MCC@WCCUSD (WCCUSD) 12/21/15
2 Find the product. 2 You Try: Find the product. 3 4 10 18 = 6 9 15 14 = Multiply Multiply the numerators and then denominators Multiply First then Divide by Common Factors This is useful if you want an equivalent fraction with smaller numbers (called simplest form ). Multiply the numerators and then the denominators. Divide by, because 2 is a common factor for 30 and 72. Divide by, because 3 is a common factor for 15 and 36. There are no more common factors, so it is in simplest form. Decompose to Prime Numbers First, then Multiply This is another way to get the answer in simplest form. Prime factor the numerators & denominators of both fractions Find fractional ones and multiply. 5.NF.4 5.NF.4 Page 2 of 12 MCC@WCCUSD (WCCUSD) 12/21/15
3 Hannah ate 3 2 of the bag of popcorn and Mia ate 1 of the bag of popcorn. How 6 much of the bag did they eat altogether? This is an addition problem because it s asking how much they ate altogether. 3 You Try: Choose all correct answers. Kenneth drank 4 1 of a liter of water. Zachary drank 8 3 of a liter of water. Which of the following methods correctly show how to find how much water they drank altogether? Bar Model Draw a bar representing two thirds. Add a piece representing addition of one sixth. A) 1 3 + 4 8 1 + 3 = 4 + 8 is equivalent to, so we B) can draw another bar under the first that shows the bar in sixths, then add up the sixths. There are altogether. They ate of the bag altogether. Use a Common Denominator C) Write equation Multiply the denominators to find a common denominator 3x6=18 Multiply each fraction by a fractional one to get equivalent fractions with the common denominator of 18. D) Add the fractions They ate of a bag of popcorn altogether. is equivalent to 5.NF.2 5.NF.2 Page 3 of 12 MCC@WCCUSD (WCCUSD) 12/21/15
4 Madison wants to make 5 pounds of trail mix for a class field trip. One pound takes 2/5 pound of nuts. How many pound of nuts does she need to make 5 pounds of trail mix? Bar Model: 4 You try: Alonzo was making 6 award ribbons. Each ribbon takes of a yard. How many yards does he need to make the award ribbons? If you count up the fifths, there are 10 of them and Number Line: If you jump 5 times, you end up at which equals 2. The calculations: OR Therefore, she will need 2 pounds of nuts for the trail mix. 5.NF.6 5.NF.6 Page 4 of 12 MCC@WCCUSD (WCCUSD) 12/21/15
5 If 3 friends share 7 feet of ribbon evenly, how long will each piece be? 7 feet of ribbon is being shared evenly with 3 friends, so we need to divide 7 by 3. Decomposition 5 You Try: Choose all correct answers. 4 friends share an 11-foot length of jump rope evenly. Which of these methods correctly show how to find how long each piece will be? Write as a fractional division problem A) Decompose the numerator into an addition expression with ones Group into 3 s because we are dividing by 3 Simplify the groups Rewrite using fractional ones Rewrite fractional ones as whole number 1 s B) Simplify Bar Model Draw a bar to represent. = 1 + 1 + 1 3 Draw a bar underneath to show groups of three thirds that equal 1 whole Write as an addition expression C) D) 11???? 1 = 2 ft. 3 Simplify by adding the whole numbers and the remaining one third 5.NF.3 11 11 11 11? 5.NF.3 Page 5 of 12 MCC@WCCUSD (WCCUSD) 12/21/15
6 Mateo spent Saturday and hours playing soccer on hours playing on Sunday. How much longer did he play on Saturday? How much longer is a subtraction problem. 6 You Try: Choose all correct answers. Tyson the Turtle is inches long. His brother Tyler is inches long. Which of the following methods correctly show how to find how much longer Tyson is compared to Tyler? Change to Improper Fractions then Subtract Write as a subtraction problem A) To change the mixed numbers to improper fractions, multiply the whole numbers by the number in the denominator and add the numerators. Multiply by fractional one to get common denominator Subtract improper fractions Decompose the numerator to form equivalent forms of ONE to get the mixed number. B) + + + Open Number Line: Jump on a number line to find the distance between the mixed numbers. Jumps can be any size. Draw a number line with the smallest number at the left end and the largest number at the right end +3 + I ll jump 3 because I can add 3 to in my head to get C) to on the number line. Then I ll jump to get to. Add jumps to find total hours. 5.NF.1 5.NF.1 Page 6 of 12 MCC@WCCUSD (WCCUSD) 12/21/15
7 Without actually multiplying, explain why is less than 7. 7 You try: Without actually multiplying, explain why is greater than 6. 1 x 7 = 7. = less than 7. Because 5/8 is less than 1, the product of must be less than 7. 5.NF.5 5.NF.5 Page 7 of 12 MCC@WCCUSD (WCCUSD) 12/21/15
8 Mariana had 2 1 lb. of grapes to share with 3 friends. How much did each person get? This is a division problem: 1 2 4 = Bar Model First draw a bar equivalent to one whole divided into two halves. Starting with one whole will help us find the size of each part each of the friends will get. 8 You Try: Thomas had 3 1 of a pizza to share with one of his friends. How much of the pizza did each person get????????? Draw another bar underneath and divide it into two halves. Then divide each of the halves into 4 pieces because is being shared with 4 people. To figure out the size of each piece in the 2 nd bar, count up the total number pieces in the whole bar. Since there are 8 total pieces and each of the pieces is 1 of 8, each piece is of the whole. Each person will get lb. of grapes. Area Model This shows the ½ is divided into 4 parts and the whole is 8 parts. Therefore ½ pound of grapes, divided into 4 equal parts is 1/8 of a pound per part. 1/2 Each person will get lb. of grapes. 5.NF.7 End of Study Guide 5.NF.7 Page 8 of 12 MCC@WCCUSD (WCCUSD) 12/21/15
1 You Try Solutions: You Try: Riley and Jasper were working on their science fair project. Riley completed and Jasper completed. How much have they completed altogether? 2 You Try: Find the product. 6 9 15 14 = Decompose to Prime Numbers First then Multiply 6 15 = 9 14 Area Model 3 2 3 5 = 3 3 2 7 3 2 3 5 = 3 3 2 7 = 5 7 Prime factor the numerators and denominators of both fractions Find fractional ones Simplify Multiply First then Divide by Common Factors 4 12 + 3 12 = 7 12 Therefore ( ), they have completed 7/12 of the science fair project. 6 9 15 14 = = 90 126 2 2 = 45 63 9 9 Multiply Divide by Divide by because they are even. = 5 7 Finding Common Denominator 1 3 + 1 4 = 1 3 4 4 + 1 4 3 3 = 4 12 + 3 12 = 7 12 Multiply Multiply numerators and denominators Therefore ( ), they have completed 7/12 of the science fair project. 5.NF.4 5.NF.1 Page 9 of 12 MCC@WCCUSD (WCCUSD) 12/21/15
3 You Try: Choose all correct answers. Kenneth drank 4 1 of a liter of water. Zachary drank 8 3 of a liter of water. Which of the 4 You try: Alonzo was making 6 award ribbons. Each ribbon takes 2/3 of a yard. How many yards does he need to make the award ribbons? following methods correctly show how to find how much water they drank altogether? Bar Model: A) 1 4 + 3 8 = 1+ 3 4 +8 Wrong, because the denominators should not be added. B) Number Line C) The Calculations: D) Wrong, you must multiply by and this just multiplied the denominator by 2. OR Therefore, Alonzo needs 12/3 yards, which is equivalent to 4 yards of ribbon. 5.NF.2 5.NF.6 Page 10 of 12 MCC@WCCUSD (WCCUSD) 12/21/15
5 A) You Try: Choose all correct answers. 4 friends share an 11-foot length of jump rope evenly. Which of these methods correctly show how to find how long each piece will be? 6 You Try: Choose all correct answers. Tyson the Turtle is Tyler is inches long. His brother inches long. Which of the following methods correctly show how to find how much longer Tyson is compared to Tyler? A) v B) B) v + + + C) 11???? D) Wrong because this illustrates 11 11 11 11? 5.NF.3 C) Wrong, because after you subtract the like terms (5-3 and ), you must put the two parts of the answer together by adding, NOT subtracting. 5.NF.1 Page 11 of 12 MCC@WCCUSD (WCCUSD) 12/21/15
7 You Try: Without actually multiplying, explain why is greater than 6. Because is greater than 1, the product of must be greater than 6. 5.NF.5 8 You Try: Thomas had a pizza to share with one of his friends. How much of the pizza did each person get? Bar Model Each person will get of the pizza. Area Model Each person will get of the pizza. 5.NF.7 Page 12 of 12 MCC@WCCUSD (WCCUSD) 12/21/15