Fractions. Chapter NUMBER. Big Idea. Learning Goals. Essential Question. Important Words

Transcription

1 NUMBER Fractions Chapter Big Idea Understanding improper fractions and mixed numbers can help me solve problems. Learning Goals I can relate improper fractions to mixed numbers. Essential Question How can fractions help me understand the world around me? Important Words denominator improper fraction mixed number numerator

2 Merry Mixing Draw, build, and write to represent mixed numbers and to find equivalent numbers. Compare and order numbers that are given as pictures, constructions, and numbers. Example: Order the following numbers from smallest to largest:,,,. Samina s strategy: I drew a number line from to and marked it with twelve sections. Thirds are four sections each. For I counted eight sections because that is four twice. Quarters are three sections. For I counted three sections. For I counted nine sections. Nancy s strategy: I drew each fraction in a circle and then ordered them from smallest to biggest. Odessa s strategy: I built each fraction using fraction strips and then ordered them from smallest to largest. Patience s strategy: = I wrote each fraction as an equivalent = fraction out of twelve and then ordered them from smallest to largest. = The order is:,,,. = 0 CHAPTER : Fractions

3 Merry Mixing (continued). Study the pictures below. Write a mixed number for each picture. A mixed number is a number with a fraction part and a whole number part. c. d.. Use pattern blocks to build each fraction. c. d.. Draw a picture to represent each fraction. c. d. 0. Write two mixed numbers equivalent to each of the following. c. d. CHAPTER : Fractions 0

4 Merry Mixing (continued). Write a statement using the less than symbol (<), equal to symbol (=), or greater than symbol (>) to compare the two numbers.??, c.? d.?. Order each set of numbers from the least to the greatest using the strategy of your choice.,,,,,, c.,,, d.,,,. Describe the strategies you used to compare mixed numbers.. How do you use mixed numbers in real life? I can relate improper fractions to mixed numbers. 0 CHAPTER : Fractions

5 Nice Numbers Write, draw, or build mixed numbers. Solve problems from contexts including food, time, sports, and crafts. Example: Joseph went to a birthday party and saw these pizzas. How many pizzas are there? There is one whole pizz There is one half of a pizz That makes pizzas. How much of a pizza have the guests eaten so far? If there were two pizzas to begin with, there is one half of a pizza missing. That means they ate a pizz. Tanner worked in the yard for hours on Saturday and hours on Sunday. Build a model or draw a picture to show each time. On which day did Tanner work longer? How can you tell?. A football quarterback played quarters last season. One of the wide receivers played quarters last season. How many games did the quarterback play? Record this amount as a mixed number. How many games did the wide receiver play? Record this amount as a mixed number. c. Who played more games last season?. Susie made twenty muffins using several -muffin trays. Draw to show how many full trays of muffins she made. Record the number of trays of muffins Susie made as a mixed number. CHAPTER : Fractions 0

6 Nice Numbers (continued). Mr. Sagan read to his class for of an hour each day. Build a model or draw a picture to show for how many full hours he read in days. Record the number of hours for which Mr. Sagan read as a mixed number.. Leah filled her glass with milk three times, and then only drank half of the third glass. Write the number of glasses of milk that she drank as a mixed number. Write the number of glasses of milk that Leah drank as a mixed number with a different denominator. The denominator is the number of parts in a fraction, the bottom number.. Nigel, the cat, eats of a can of cat food for breakfast and of a can again at supper. How much cat food will Nigel eat in one day? How much cat food will Nigel eat in one week? Record this amount as a mixed number.. The time it took Penny to drive from Hinton to Edmonton is shown below Express how long it took Penny to drive home as a time in minutes. Use a mixed number to express in hours how long it took Penny to drive home. c. Use as a decimal to express in hours how long it took Penny to drive home. 0 CHAPTER : Fractions

7 Nice Numbers (continued). Victor is making beaded belts as gifts for his friends. Each of the belts uses 0 beads. How many belts can Victor make with a package of 00 beads? Record this amount as a mixed number.. Wesley collected sand dollars on the beach. In one week he collected dozen sand dollars. How many sand dollars did Wesley collect? 0. Zavier, Yuvraj, and Zain run together on the cross country team. At one practice, the boys ran for 0 minutes. In that time, Zavier ran laps, Yuvraj ran laps, and Zain ran laps. Put the boys in order according to the distance they ran, from least to greatest.. Use the clues below to solve the riddle. I am a mixed number between and. I am larger than but smaller than. I have an even denominator. What could the mystery fraction be? Could there be more than one answer?. Write your own fraction riddle about a mixed number. Exchange riddles with a classmate and try to solve each others riddles.. How did drawing or building to show mixed numbers help you solve these problems? I can relate improper fractions to mixed numbers. CHAPTER : Fractions 0

8 Properly Improper Draw, build, and write to represent improper fractions and to find equivalent numbers. Compare and order fractions that are given as pictures, constructions, and numbers. Example: Show using the strategy of your choice. Jinee s strategy: I drew circles with each one in four pieces. Then I coloured in sections to represent. Rachel s strategy: I built this number using interlocking cubes. I used cubes and arranged them into groups of four. Sadie s strategy: I showed on a number line. I made tic-marks and then labeled them with quarters. Then I put a dot at. < > 0 0. Study the pictures below. Write an improper fraction for each picture. An improper fraction is a fraction that has a top number that is bigger than the bottom number. c. d. 0 CHAPTER : Fractions

9 Properly Improper (continued). Use pattern blocks to build each fraction. c. d.. Draw a picture to represent each fraction. c. d.. Write two improper fractions equivalent to each of the following. c. d. CHAPTER : Fractions

10 Properly Improper (continued). Write a statement using the less than symbol (<), equal to symbol (=), or greater than symbol (>) to compare the two numbers.?? c.? d. 0? 0. Order each set of numbers from smallest to largest using the strategy of your choice.,,,,,, c.,, 0,. How do you know what the denominator will be when you are given a picture of a fraction?. Some people call improper fractions top-heavy fractions. Explain why this name makes sense. I can relate improper fractions to mixed numbers. CHAPTER : Fractions

11 Fraction Fun Write, draw, or build the improper fractions to solve problems. Problems come from contexts including music, measurements, food, time, sports, and crafts. Example: Two different recipes use cups or cups of chocolate chips. Which recipe uses more chocolate? Vanessa s strategy: I made an equivalent fraction with a denominator of for each fraction. = by multiplying both the denominator and numerator by. = by multiplying both the denominator and numerator by. Taryn s strategy: I drew each fraction using rectangles. Whitney s strategy: I built each fraction using fraction circles. Yara s strategy: I divided each fraction. = more than two = less than two CHAPTER : Fractions

12 Fraction Fun (continued). Mrs. Winter bought a half-dozen cinnamon buns, eight onion buns, one dozen whole wheat buns, and a half-dozen dinner buns. Draw to find the number of buns she bought. Write the number of dozen of buns she bought as an improper fraction with a denominator of. c. Explain what the denominator and numerator represent in this fraction. d. Write this fraction with a different denominator. The numerator is the top number in a fraction. It is the number of parts of the whole.. David has completed laps of a 0-lap run. Blake has completed laps. Who has run further? How can you tell?. Moe spent of an hour cleaning the inside of his dad s car. He spent a total of hours cleaning the entire car. Build a model or draw a picture to show how long Moe spent cleaning the inside of the car. Build a model or draw a picture to show how long Moe spent cleaning the entire car. c. Write, as an improper fraction of an hour, the amount of time Moe spent cleaning the outside of the car. d. Write, in minutes, the amount of time Moe spent cleaning the outside of the car. e. Write, in decimals of an hour, the amount of time Moe spent cleaning the outside of the car. CHAPTER : Fractions

13 Fraction Fun (continued). Joel had to read a story that was pages long. He read pages before dinner. How many pages did he need to read after supper? Record this amount as an improper fraction.. Ahmed counted 0 slices of bread in half a loaf. How many slices are in a whole loaf? What fraction of a loaf is one sandwich? c. How many loaves did Ahmed use to make sandwiches? Record this amount as an improper fraction.. Uriah is sewing a pair of shorts. The pattern calls for yards of fabric. Uriah has yards of fabric. Does Uriah have enough fabric to make the shorts?. Elias cut. metres of string into 0-centimetre lengths for a craft at his birthday party. Write the length of string Elias started with as an improper fraction with a denominator of 0. Explain what the denominator and numerator represent in this fraction. c. What does the fraction you wrote in part represent? d. Elias decided to cut the string into cm lengths instead of 0 cm lengths. Explain what denominator might make more sense in this situation. CHAPTER : Fractions

14 Fraction Fun (continued). Cael plays hockey. The number of periods he played in a tournament is shown by the diagram below. Game Game Game Game Draw or build to show this number in another way. Express the total number of games Cael played as an improper fraction. c. Explain what the numerator and the denominator represent in this fraction.. Fletcher, Gabriel, Hamza, and Ian competed in a Trumpet-a-thon. Fletcher played for hours, Gabriel played for hours, Hamza played for 0 hours, and Ian played for hours. Put the boys in order from least to greatest according to the time they played. 0. Use the clues below to solve the riddle. I am an improper fraction. I am larger than but smaller than. I have an even denominator. What could the mystery fraction be? Could there be more than one answer?. Write your own improper fraction riddle about an improper fraction. Exchange riddles with a classmate and try to solve each other s riddle.. What strategies did you use to solve problems with improper fractions? I can relate improper fractions to mixed numbers. CHAPTER : Fractions

15 Real Relations Draw, build, and write to represent improper fractions and mixed numbers. Compare and order numbers that are given as pictures, constructions, improper fractions, and mixed numbers. Example: Which should you choose, of a pie or of a pie? Cyndy s strategy: I converted to a mixed number by dividing. = R = is one quarter less than. is one third less than. is bigger than because it is a whole divided into fewer pieces. pie is bigger. I should choose the pie. Zainab s strategy: I drew the fractions. I can see that. Addison s strategy: I built the fractions using fraction circles. I can see that.. Use ten frames to build each number. c. d. 0 CHAPTER : Fractions

16 Real Relations (continued). Study the pictures below. Write a mixed number and an improper fraction for each picture. c. d.. Draw a picture to represent each number. c. d.. Write a mixed number equivalent to each of the following improper fractions. c. d. CHAPTER : Fractions

17 Real Relations (continued). Write an improper fraction equivalent to each of the following mixed numbers. c. d.. Write a statement using the less than symbol (<), equal to symbol (=), or greater than symbol (>) to compare the two numbers.?? c.? d.?. Order each set of numbers from smallest to largest using the strategy of your choice.,,,,,, c.,,,. Explain the strategies you used to write improper fractions as mixed numbers.. Explain the strategies you used to write mixed numbers as improper fractions. 0. When might you use mixed numbers instead of improper fractions?. When might you use improper fractions instead of mixed numbers? I can relate improper fractions to mixed numbers. CHAPTER : Fractions

18 Clear Comparisons Write, draw, or build improper fractions and mixed numbers to solve problems. Explain what the numerators and denominators mean in each situation. Example: Andrei is years and two months old. Write his age as a mixed number and as an improper fraction. I know that there are months in one year, so that will be my denominator. He is whole years and out of months. Andrei is years old. years is x months = months. Andrei is + = months old. Andrei is years old. What do the numerator and denominator mean in this improper fraction? The numerator is. is Andrei s age in months. The denominator is. Twelve is the number of months in one year.. How old are you? Write your age as a mixed number. Write your age as an improper fraction. c. Explain what the numerator represents in each number. d. Explain what the denominator represents.. Raiden collected eggs. Draw to show the number of dozens of eggs. Write the number of eggs as an improper fraction with a denominator of a dozen. c. Explain what the numerator means. d. Write the number of eggs as a mixed number with a denominator of a dozen. e. Explain what the denominator means. 0 CHAPTER : Fractions

19 Clear Comparisons (continued). Your mom is making cookies and needs cups of flour. She only has a cup measuring cup. Build a model or draw a picture to show how many half cups of flour she needs for this recipe. Express cups as an improper fraction. c. Explain what the numerator and denominator represent in the fraction. d. How are the number of half cups and the improper fraction related?. Sawyer s swimming lessons take an hour and a half. Write this number as a mixed number with a denominator of, and explain what the whole number, numerator and denominator mean. Write this number as an improper fraction with a denominator of, and explain what the numerator and denominator mean. c. Write this number as an improper fraction with a denominator of 0, and explain what the numerator and denominator mean. d. Explain which representation Sawyer should use to tell his parents how long his swimming lessons are.. Jackson is knitting a scarf and has completed the squares shown below. Write the number of squares of the scarf that Jackson has knit as an improper fraction. Write the number of squares of the scarf that Jackson has knit as a mixed number. c. Explain the strategy you used to write the number in each form.. Kai and Lorenzo each play in the school band. Kai practised for hours over the weekend. Lorenzo practised for hours. Compare the length of time each boy practised. CHAPTER : Fractions

20 Clear Comparisons (continued). Malik has $0 to buy fabric to make a flag. The fabric costs $ for each metre. How many metres, expressed as a mixed number, can Malik buy? How many metres, expressed as an improper fraction, can Malik buy? c. Explain what each number tells you in this situation.. Nicolas has competed in five pie-eating contests. His results are shown in the table below. Contest Number of pies eaten Stampede Capital Ex Westerner Days Highland Games 0 Blueberry Festival Order the contests from the one in which Nicolas ate the fewest pies to the one in which he ate the most pies. Describe the strategies you used to order the numbers.. Write your own problem involving mixed numbers and improper fractions. Exchange problems with a classmate and try to solve each other s problem. 0. Explain which strategy you find most useful when comparing fractions in different forms. I can relate improper fractions to mixed numbers. CHAPTER : Fractions