# Essentials. Week by. Week. Calculate!

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1 Week by Week MATHEMATICS Essentials Grade WEEK 7 Calculate! Find two numbers whose product would be between 0 and 50. Can you find more solutions? Find two numbers whose product would be between,500 and,600. Can you find more solutions? (.05) Looking Out For Math Draw or cut out all possible different rectangles with a perimeter of 6 inches. Label. Find and record the area of each rectangle. Which rectangle has the greatest area? If you were building a dog pen, which rectangular shape would be best? Why? - = Thinking Mathematically Peter s math scores this semester are 9, 8, 8, 76, 9, 78, 8, and 9. Compute the median and range of his scores. What does he need to do to increase his median score? Can he lower the range? Why? (.0) Exploring Data List your place of birth by city, county, state, and country. Add your name to the class Venn diagram to show where you were born. Look at the data on the diagram. Were any students born outside the United States? How many students were born in your town? Fraction Action Count by thirds from 8 to. 8, 8,,... What whole number is equal to 8? Clue: = (.0,.0) (.0) (.0a) 70

2 Division Duel PLACE DIVISION FLASH CARDS FACE DOWN HERE Each player draws one flash card from the top of the deck. Both players answer the division problems. The winner is the player whose answer is the larger number (the winner must be able to say his or her number fact correctly.) The winner of each round places a marker on his or her number grid. The champion is the first player to win rounds. (.0) 7

3 Keeping Skills Sharp. D = x B = 0. L x 8 = = 6. How many obtuse angles in this figure? cm = m 8. How many dimes in \$.65? 9. The concession stand at the ballpark sells hot dogs for \$.00 each. Their cost per hot dog is \$0.5. If they sold 0 hot dogs what was the profit? 0. The grocer places a case of canned tomatoes in a three-shelf display. He put 7 cans on each shelf and had cans left over. How many cans in the case? - = Solve this! Listen to the song, The Twelve Days of Christmas. How many gifts in all did my true love give to me? First day: My true love gave to me a partridge in a pear tree. (.05) Second day: My true love gave to me two turtle doves and a partridge in a pear tree. Third day... 7

4 Calculate! x 0 = 0 0 x = 0 8 x = To the Teacher 85 x = 505 Looking Out for Math x 5 area 5 perimeter 6 x 6 area perimeter 6 x 7 area 7 perimeter 6 x area 6 perimeter 6 A square pen will give the largest area. Remember, squares are rectangles! Grade WEEK 7 80 x = x 58 = 580 Division Duel Game You will be able to adjust the difficulty by using easier or more difficult flash cards, according to which facts the students need to memorize. Fraction Action Answers: 8, 8 /, 8 /, 9, 9 /, 9 /, 0, 0 /, 0 /,, /, /, 8 / = 9 Problem of the Week Answer: 6 gifts. Have students set up a table in order to find a pattern that simplifies this task. st day: nd day: rd day: th day: Mental Math Directions to Students: Number your paper from to 8. Write your answers as the questions are called out. Each question will be repeated only once.. Write one thousand forty two in numerals. 5 =. Nearest ten cents: x 6. The value of 5 dimes, quarter, and nickels 7. Number of pints in 5 quarts 8. Number of sides on stop signs Keeping Skills Sharp m \$

5 Week by Week MATHEMATICS Essentials Grade WEEK 8 Calculate! Calculate these problems: x = n, x = n, x = n. Predict the solution to x. Check out your prediction. Following this pattern, predict x = n. Why can t you check this prediction on a regular -function calculator? (.05) Looking Out For Math Print your name. How many letters in your name have a line of symmetry? What letters would have more than one line of symmetry? - = (5.0) Thinking Mathematically Using a calendar, find figures like these: 9 What is the relationship of the center number to the outer numbers on each row of the figure? to the sum of all 5 numbers in the figure? Does this happen for any number on any calendar? Make a chart to find out. Center Sum of Why do you think this happens? Exploring Data Number ? 5 Numbers Collect information regarding the types of vehicles in the school parking lot each day for a week. Display the data using both bar and circle graphs. Is one type easier to read than the other? Why? (.0) Fraction Action Does the fraction describe the diagram? Why? If not, how would you fix it? a) 6 Why? b) Why? c) Why? (.05) (.0) 7

6 COAST COAST F RE F RE E E COAST COAST F RE E F RE E Directions: Choose numbers from the Possible Products Lighthouse sheet and place them in the COAST grid. Select carefully the first time because erased numbers will not be counted. Your teacher will call out two factors. You should cover the product of the factors if it is on your grid. Your teacher will tell how to win (5 in a row, four corners, letters of the alphabet, or cover the whole board). 75 (.0)

7 Possible Products Lighthouse

8 Number Facts for Coast Game 6 x 0 0 x 8 x x x x 5 x x 6 7 x x 8 x 9 x 5 x 6 x x 7 x x 5 x 8 x 9 x 6 x 0 x 5 x 7 x 6 x x 8 5 x 5 x 9 7 x 6 x 5 8 x 7 x 5 9 x 6 x 7 9 x 5 6 x 8 7 x 7 5 x 0 6 x 9 7 x 8 0 x 6 9 x 7 8 x 8 7 x 0 9 x 8 0 x 8 9 x 9 0 x 0 6 x 6 0 x Note: These factors are in a similar order as the products appear on the Possible Products Lighthouse. They need to be called randomly when playing COAST. 77

9 Keeping Skills Sharp. 7,777 =. 8,080 - H = x Z - = 8. 0 x 8 = 5. 9 x = 5 6. At :00 the hands of the clock are perpendicular. Give another time for which the hands of the clock are perpendicular. 7. Number of vertices on a cube? 8. Nearest thousand? 6, Joey got a new puppy. The puppy weighed pounds. This was half the weight of his bowling ball. How much does his bowling ball weigh? 0. If Sam bought a turkey sandwich for \$.95 and a drink for \$0.95, how much change would he receive from a \$0.00 bill? - = Solve this! 7 The post office has rectangular stamps for sale. How many different ways could the four stamps be arranged so that you buy them all attached? Here is one example How many different ways could five stamps be arranged so that you could buy them all attached? If each stamp is a rectangle.5 cm high and cm long, find the perimeter of each arrangement. (.0) 78

10 To the Teacher Grade WEEK 8 Calculate! x = x = x = so x = and x = 5 A regular -function calculator cannot display this 9-digit number. The display holds only 8 digits. Thinking Mathematically The sum of the outer numbers on each row will be double the center number. The sum of all 5 numbers will be five times the center number. The pattern is: n-7 n- n n n 7 Students should try several examples from different calendars. Fraction Action Solutions: a) There are only 5 groups so the stars are divided into fifths, not sixths b) correct c) The parts are not equal (the groups do not contain the same number of symbols). Problem of the Week Solution: stamps -5 ways 5 stamps - ways (These solutions relate to tetrominoes and pentominoes made with and 5 squares) Game of the Week Coast is a large group or whole class bingo game. Each student will need a gameboard. There are four games to each sheet. Make a transparency of the lighthouse. Students put products on their boards from your lighthouse transparency. There is a factor sheet to help keep track of the calls. Mental Math Directions to Students: Number your paper from to 8. Write your answers as the questions are called out. Each question will be repeated only once.. more than Nearest hundred: x minutes before 5:00 7. Which is longer -- feet or yard? 8. Number of ears plus tails on 9 mice. Keeping Skills Sharp : , lbs. 0. \$.0 79

11 Week by Week MATHEMATICS Essentials Grade WEEK 9 Calculate! Suppose division key on your calculator does not work. How would you solve this problem on the calculator without the division key? 6 divided by 5. - = Thinking Mathematically Write a story that could be solved by using this equation. of 5 is 5 Exploring Data (.05) (.0) Select a famous North Carolinian. Display on a time line five accomplishments or significant events in the life of this individual. Looking Out For Math Suppose all of the furniture were removed from your classroom. If th graders stand shoulder to shoulder in comfortably close rows, how many can stand together in your classroom? First make an estimate. Then figure out how you can investigate this. How many students would be able to stand on a football field? Fraction Action (.05) The Wright Brothers flew in Kitty Hawk, North Carolina. Interview 0 different people. Find out how many have been on an airplane. What fraction of the people interviewed have flown. What fraction have not flown? Compare your fractions to those of your classmates. Put all your data together. What fraction of all the people interviewed have ever flown? Develop a personal time line depicting significant activities and events in each student s life. (.0) (.0) 80

12 Deci-Moves Number of Players: players Materials: You need colored markers (cm cubes are good) for each player and a coin (.0c) Directions:. Each player chooses one side of the board and places her or his cubes on the triangles on that side.. Take turns tossing the coin.. If the coin comes up heads, move one of your markers to a space having a number larger than the number your cube is on.. If the coin comes up tails, move one of your cubes to a space having a number smaller than the number your cube is on. 5. You can move up or down, left or right, or diagonally, one space only: 6. If your cube can move to a space occupied by your opponent's cube, his or her cube moves back to a beginning triangle. Only one cube may be on a space at one time. 7. If you are able to move one of your cubes, you must do so, no matter what the direction. If the only move you can make is away from a triangle on your opponent's side, you must make that move. 8. If you have no move within the rules, you lose your turn. 9. The winner is the first player to get all of her or his cubes to the triangles on the other side of the board. 8

13 Keeping Skills Sharp. J 8 09 = =. 5 x 00 =. A x 7 = = 6. The time is :5 p.m. What time will it be in 5 minutes? 7. kilometer = meters 8. What is the value of the in 7,896? 9. Suppose a drummer plays the drums for beats and then plays a triangle for beats. If he continues this pattern, what instrument will he be playing on the 5th beat? 0. Mary and Jamie went to a swim meet. Mary swam 0 feet farther than Jamie. Altogether they swam 5 feet. How far did each person swim? - = Solve this! How many different ways can you use these 5 digits (use each number only once) and any operation to make? 0 (.0e) 8

14 To the Teacher Grade WEEK 9 Thinking Mathematically You may need to model with concrete objects what this type of equation means since students are working with a fractional part of a group Fraction Action Use this activity to help children see how mathematics, and specifically fractions, can help them make sense of real life data. Problem of the Week There are many solutions. Some possibilities are: x x x 0 = x x x - 0 = 0 x = x 0 = Mental Math Directions to Students: Number your paper from to 8. Write your answers as the questions are called out. Each question will be repeated only once.. In 98,000, what digit is in the thousands place? How many tens: x 6. The value of pennies, nickels, and dimes 7. Number of inches in feet 8. Number of minutes in hour Keeping Skills Sharp :50 7., , drums 0. Mary ; Jamie 8

15 Week by Week MATHEMATICS Essentials Grade WEEK 0 Calculate! How many different numbers can be multiplied by 7 to reach any target number between 00 and 00. What are they? (.05) Looking Out For Math Build this toothpick design. Remove five toothpicks and leave only three squares that are congruent. Remove four toothpicks and leave only four squares that are congruent. - = Thinking Mathematically Create a toothpick puzzle for others. (.0) How is the population of our state determined? of your town? Why is it important to know our state s (and town s) population? Fraction Action What sort of information does a census record? (.0) Research the history of the census. Exploring Data The labels for this graph were accidentally erased from the computer. Brainstorm: What could this graph represent? How should it be labeled? What could the title be? Is there more than one possible answer? Write the mixed number that names the shaded wholes and parts of each shape below: a) b) c) (.0) (.0) 8

16 Tangram Challenges Names: Complete these charts. Be certain both partners agree with the answers placed in the charts. If the entire tangram =, then... D E B A C Fraction Decimal Piece Name Name A B C D E Bonus: Suppose the value of the entire tangram is \$.00. What would be the value of the middle-sized triangle? _ How did you know this? If part D costs 0, then... If part A costs \$, then... Piece Cost Cost A B C D E Piece Fraction Decimal A B C D E 85 0 \$ If part B is equal to, then... or or.0 (.0a,.0)

17 Keeping Skills Sharp. 5 X 7 = ,00-5,987 = T. 7 x R = 56. = 5. What is the product of and 5? 6. Write >, <, or = 5 ft. yards 7. Whatis the area of this figure? 8. What is 00 more than 8,956? 0 m m m 6 m 9. It takes Nancy 5 minutes to walk a mile. How many miles would she walk in one and a half hours? 0. Larry reads an average of 0 pages an hour. How many hours will it take him to read a book with 60 pages? - = Solve this! Sharon has fewer than 0 coins. When she puts them in piles of 5, she has left over. When she put them in piles of, she also has left over. How many coins does Sharon have? (Show how you find your solution). Sylvia has fewer than 0 coins but more than 0. If she puts them in piles of 6, she has left over. If she puts them in piles of 5, she has left over. How many coins does Sylvia have? (Show your thinking). (.05) 86

18 To the Teacher Grade WEEK 0 Calculate! There are solutions: Students might first think of 70 as 7 x 0 and work from there. 8 x 7 = 6 9 x 7 = 0 x 7 = 70 x 7 = 97 Exploring Data There are many possible answers. Be sure students ideas make sense. Discuss when a bar graph might be used rather than a line plot or circle graph. Fraction Action a) / (Put halves together to make the third whole.) b) / c) / ( / / make the fourth whole.) Mental Math Directions to Students: Number your paper from to 8. Write your answers as the questions are called out. Each question will be repeated only once.. 0 less than Nearest hundred: 5, x 7 6. minutes after :5 7. Number of centimeters in decimeters 8. Mary has \$.00 and spent quarters. How much does she have left? Keeping Skills Sharp.. 6, < 7. 5 sq. m 8. 9, miles 0. 8 hours 87

NAME: 5 th Grade MATH SUMMER PACKET ANSWERS Please attach ALL work DATE: 1.) 26.) 51.) 76.) 2.) 27.) 52.) 77.) 3.) 28.) 53.) 78.) 4.) 29.) 54.) 79.) 5.) 30.) 55.) 80.) 6.) 31.) 56.) 81.) 7.) 32.) 57.)

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