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Facts to know Subtracting 3 from 9139 gives 9136 30 divided by 5 is 6 4 × 4 = 16 8 * 3 = 24 8 take away 7 is 1 2 multiplied by 7 is 14 55 + 9 = 64 44 − 3 = 41 36 - 3 = 33 20 / 4 = 5 10 x 3 = 30 6 times 9 equals 54 60 ÷ 12 = 5 8 - 6 = 2
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Quiz practice 1. Puzzle: A triangle has sides of 11, 12 and 5 feet. What is the perimeter? Answer: 28 feet. 2. Some students made a tally of favorite season. Summer: 38 Spring: 7 Winter: 33 Fall: 31 How many more votes did fall get than spring? The ones: 1 is less than 7, so borrow a ten: 11 - 7 = 4. The tens: 3 - 1 - ...
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Review A shape is made of two rectangles. One is 2 units by 3 units. The other is 4 units by 8 units. What is the area of the shape? 2 groups of 3 is 6. 4 groups of 8 is 32. Add: 6 + 32 = 38. Together they cover 38 square units. Tutor: A ruler costs 79 cents and an orange costs 94 cents. How much do they cost togethe...
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Homework A quarter is 25 cents, a dime is 10 cents, a nickel is 5 cents and a penny is 1 cent. Example 1: At the classroom, a ruler is 78 cents and a badge is 29 cents. Both items come to 107 cents. Example 2: At the pet shop, a postcard is 61 cents and a toy car is 16 cents. The total cost is 77 cents. Example 3: Exer...
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Practice page Problem 1: Ned read 6 pages. Theo read 34 pages. How many more pages does Theo have than Ned? Find the difference: 34 - 6 = 28. The difference is 28 pages. Problem 2: Each side of a hexagon with equal sides is 19 units. All the sides add up to 114 units. Problem 3: Isaac is holding 4 acorns. Natalia is ho...
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Math corner Dividing means sharing into equal groups. Example 1: 59 batteries are put into bags of 7. Only full bags count. How many are left over? 8 groups of 7 is 56. Find the difference: 59 - 56 = 3. Left over there are 3 batteries. Example 2: Serena shared 14 pins equally among 7 cousins. Every child gets 2 pins. E...
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Story time math 1) One paper strip is 96 centimeters. Another is 15 centimeters. They are joined. How long are they together? Together they measure 111 centimeters long. 2) A bike ride took 3 hours and 11 minutes. How many minutes is that? Multiply: 3 × 60 = 180. 180 + 11 = 191. In minutes, that is 191 minutes. 3) D...
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Practice sheet 1) Tom had a pencil 18 centimeters long and cut off 8 centimeters. How long is it now? 2) The pail had 19 toy robots in it. Andre put 742 more in it. How many toy robots does the pail hold now? 3) A bar graph of favorite sport shows 6 for basketball, 31 for swimming, 32 for tennis, 14 for running, 23 for...
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Practice set #1 Dr. Patel counted 4 limes. The next day, Dr. Patel sent 3 to Thea. The rest came to 1. #2 Problem: Quinn lays a ribbon that is 20 centimeters long next to a piece of yarn that is 77 centimeters long, end to end. How long are they together? Answer: Together they measure 97 centimeters long. #3 There were...
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Quick practice 90 / 9 = 10 35 + 20 = 55 76 plus 2 equals 78 3 - 2 = 1 12 × 8 = 96 55 + 63 = 118 15 divided by 3 equals 5 8 × 11 = 88 2 + 53 = 55 3 * 4 = 12 28 plus 36 equals 64 8 + 28 = 36 80 / 8 = 10 The sum of 75 and 419 is 494 94 + 11 = 105 9 times 5 equals 45 620 − 5 = 615 The difference between 761 and 8 is 753 41...
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Problem 1: Step 1 has 166, step 2 has 216, step 3 has 266, step 4 has 316, step 5 has 366. What comes next? Problem 2: Uncle Walker came to the toy store with 183 pencils. Uncle Walker was sent 75 more by Abdul. How many pencils does he have now? Problem 3: Faye picked 21 tiles. Chloe picked 63 tiles. How many more til...
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Math journal (1) A cooler held 59 socks. June picked 34 from the cooler. How many socks are in the cooler now? Taking away gives 59 - 34 = 25. In the end, the cooler held 25 socks. (2) A hall is set up with 4 rows and 8 chairs in each row. How many chairs are set up? Step 1: 4 * 8 = 32. The hall has 32 chairs. (3) Kofi...
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Word problems Problem 1: 3 tiles sat in the cart. 31 more were dropped in. This leaves 34 tiles. Problem 2: Raj buys an orange for 21 cents and a crayon box for 54 cents. Raj pays 75 cents. Problem 3: 298 - 249 = 49 Problem 4: The bowl had 86 pancakes in it. 44 were sold. Then 65 more arrived. The bowl now has ____...
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1 + 6 = 7; 240 + 18 = 258; 8 + 1 = 9; 81 and 76 more is 157; 26 - 5 = 21; 27 - 14 = 13; Subtracting 62 from 944 gives 882; Adding 48 and 9 gives 57; 94 + 22 = 116; 7 multiplied by 3 is 21
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Homework 5893 - 5678 = 215 20 + 526 = 546 A notebook costs 71 cents and a comb costs 48 cents. How much do they cost together? Together they cost 119 cents. Challenge: A class made a tally of ways to get to school. Walking: 19 Bus: 18 Bike: 38 How many students in all? Answer: 75 students. Hailey sorted rubber duc...
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Practice page 1. Challenge: Chioma has 20 napkins and puts 10 in each bag. How many bags are there? Answer: 2 bags. 2. Sarah has 7 pouches with 4 folders in each. How many folders are there in all? That comes to 28 folders. 3. Skyler owned 24 dominoes. That afternoon, they used up 20. How many dominoes does Skyler h...
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Math practice Problem 1: Word problem: Maisie owns 94 photos, and Dr. Nakamura owns 20 photos. How many photos do they have in all? Solution: Adding them up gives 114 photos. Problem 2: A field is 12 feet long and 15 feet wide. The distance around it is 54 feet. Problem 3: The lunch box had 71 balloons in it. 51 rol...
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Practice page (1) On Thursday, the toy shop gave out 5 tickets. On Friday, it gave out 5839. Over the two days the total came to 5844 tickets. (2) Try this: At first, 35 runners were in the race. Soon 5 more joined the race. How many runners are there now? Answer: Now there are 40 runners. (3) 16 kids were in the game....
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Math practice Morgan has 8 pieces of chalk and Dad has 97 pieces of chalk. Morgan is short by 89 pieces of chalk. Bo owned 3 crayons. On Saturday, he left 1 at school. How many crayons does Bo have now? Take 1 away from 3: 3 - 1 = 2. Bo still has 2 crayons. Bethany sorted horses into two piles: 556 white and 6 large. A...
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Mental math A fraction names equal parts of a whole. Half of something is one of two equal parts. Example 1: An orange was cut into 8 pieces. Albert gave away 1 pieces. How many pieces are left? Subtract 1 from 8 to get 7. The pieces left number 7 pieces left. Example 2: Try this: An orange was cut into 12 pieces. Maya...
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(1) There are 36 muffins, and Morgan gives away 3/4 of them. How many is 3/4 of 36? (2) Survey of favorite pet | Choice | Votes | | Fish | 35 | | Cats | 20 | | Rabbits | 4 | | Birds | 30 | | Dogs | 16 | How many more votes did cats get than dogs? (3) Morgan has 8 pails with 5 posters in each. How many posters are there...
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Number facts 51 - 34 = 17; 47 take away 14 leaves 33; The sum of 80 and 36 is 116; 9292 + 28 = 9320; 12 x 9 = 108; 496 + 3 = 499; 94 - 7 = 87; 74 - 6 = 68
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Math journal One hour has 60 minutes. To find how long something took, count the minutes from start to end. Example 1: A bike ride starts at 3:28 and lasts 30 minutes. It ends at 3:58. Example 2: David spent 48 minutes on a walk and 36 minutes on reading. The total time is 84 minutes. Example 3: Delia does 9 minutes of...
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Practice set One hour has 60 minutes. To find how long something took, count the minutes from start to end. Example 1: Tutor: From 4:23 to 5:18, Marisol was busy with a nap. How long did it take? Learner: Marisol spent 55 minutes. Example 2: 29 + 17 = 46 Example 3: Tutor: Baking took 27 minutes. Then piano practice too...
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Math journal #1 A school voted on their favorite color: purple 17, orange 16, red 22. How many more votes did red get than orange? The ones: 2 is less than 6, so borrow a ten: 12 - 6 = 6. The tens: 2 - 1 - 1 = 0. So 22 - 16 = 6. Red beat orange by 6 votes. #2 Seth found 2 quarters and 6 nickels under the couch. How muc...
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Math class notes 1) Chidi shared 77 bouncy balls equally among 7 cousins. How many does each get? 2) A table top is 3 units long and 5 units wide. What is the area? 3) A paper strip was 44 centimeters long. Ariana cut 16 centimeters off it. How long is it now? 4) Rosie collected 62 painted rocks. Peyton collected 19 pa...
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Story problems There are 5 carts. Each cart has 11 tomatoes. How many tomatoes are there in all? We multiply 5 by 11 and get 55. That makes 55 tomatoes. A pool is 3 feet long and 9 feet wide. What is the area? 3 × 9 = 27. Its area comes to 27 square feet. Question: Sara buys a pear for 35 cents and pays with 50 cents. ...
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Drill 400 take away 76 is 324 4 + 36 = 40 10 + 97 = 107 23 + 338 = 361 The product of 9 and 3 is 27 9 groups of 2 make 18 The difference between 602 and 9 is 593 62 + 6 = 68 Subtracting 7 from 44 gives 37 63 and 5 more is 68 9 - 2 = 7
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Math journal The difference between two numbers is how much bigger one is than the other. Example 1: Casey scored 44 points and Skyler scored 49 points. Casey would need 5 more. Example 2: Puzzle: Wendy read 36 pages. Ms. Hayes read 3 pages. How many more pages does Wendy have than Ms. Hayes? Answer: The difference is ...
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1. Nell counted 1 flash card on Monday. In the afternoon Nell counted 60 flash cards. How many flash cards is that in all? 1 + 60 = 61. In all, Nell counted 61 flash cards. 2. A shape is made of two rectangles. One is 6 units by 2 units. The other is 9 units by 8 units. The total area is 84 square units. 3. At first,...
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Math journal (1) My brother owned 11 crayons. My brother handed out 7 crayons. Later, my brother came home with 9 more. What is the number of crayons my brother has at the end? By the end, my brother had 13 crayons in total. (2) My brother picked 56 books. Ellie picked 1 book. The difference comes to 55 books. (3) 5...
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Think and solve Subtraction tells us what remains, or how far apart two amounts are. Example 1: 632 - 416 = 216 Example 2: Ariana has 68 geese. She gave 48 to Luca. How many geese does she have now? 68 - 48 = 20. Left over were 20 geese.
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Mental math 1) Puzzle: Benjamin scored 305 points and Cameron scored 594 points. How many more points does Cameron have than Benjamin? Answer: That is a difference of 289 points. 2) 47 + 76 = 123 3) 3 × 4 = 12 4) The numbers 182, 282, 382 follow a rule. The number after 382 is 482. 5) A rectangle drawn on grid pap...
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Morning work Viktor cut a quiche into 6 equal pieces and packed 1 of them. How many pieces are left? Subtract 1 from 6 to get 5. The pieces left number 5 pieces left. Count by 2s starting at 182: 182, 184, 186, 188, 190. What number comes next? 190 + 2 = 192. The number after 190 is 192. 16 rubber bands are split evenl...
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Problem of the day There are 3 pails. Each pail has 8 highlighters. The total is 24 highlighters. Anna cuts a piece of string into 8 pieces, each 18 centimeters long. The whole length was 144 centimeters. A pile of 51 cookies is packed into bags of 8. That makes 6 full bags with 3 left over. Cyrus filled a pail wit...
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Morning work A pool is 4 centimeters long and 6 centimeters wide. It covers 24 square centimeters. Row 1 has 79, row 2 has 94, row 3 has 109. What comes next? Following the pattern, row 4 has 124 chairs. Audrey collected 90 worksheets, and Obi collected 10 fewer than that. How many worksheets does Obi have? The number ...
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Math practice A table or chart shows counts. We can add them, compare them, or find the biggest. Example 1: Task: Some students voted on their favorite season: fall 12, winter 26, spring 18. How many more votes did winter get than fall? Result: 14 votes. Example 2: Exercise: A group of friends made a tally of favorite ...
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Quick practice 144 shared by 12 is 12 each 141 + 33 = 174 5 + 8 = 13 86 − 11 = 75 63 + 4349 = 4412 54 + 612 = 666 14 - 5 = 9 77 take away 8 leaves 69 7114 - 7 = 7107 6 fewer than 6 is 0 69 + 1 = 70 8 times 11 equals 88 62 + 852 = 914 518 + 35 = 553 24 shared by 3 is 8 each 3 + 56 = 59 92 + 9 = 101
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Math journal #1 The coach began the game at 9:04 and finished at 9:53. The game lasted 49 minutes. #2 Aaron has 72 daisies to share fairly with 9 bags. How many does each get? Answer: 8 daisies. #3 Look at the pattern: 109, 99, 89, 79, 69. Next comes 59. #4 The goal is 1137 sunflowers. Peyton has gathered 144. To r...
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Story problems #1 Each day, Tom writes 6 words. How many words in 2 days? #2 At the yard sale, a button is 54 cents and a pack of seeds is 59 cents. How much do they cost together? #3 22 chickens are put into bags of 3. Only full bags count. How many are left over? #4 At first, 57 frogs were by the pond. After a while,...
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Math class notes #1 Q: There were 6 frogs by the pond. Then 5 more hopped over. How many frogs are there now? A: 11 frogs. #2 The numbers 38, 138, 238 follow a rule. Next comes 338. #3 An orange was cut into 6 pieces. Iris ate 1 pieces. That leaves 5 pieces left. #4 A pencil case held 60 paper clips. Bea stacked 98...
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Warm-up To find change, subtract the price from the money paid. Example 1: Grandpa: the shopkeeper buys a pack of seeds for 25 cents and a ruler for 61 cents. How much do they cost together? Grandchild: 86 cents. Example 2: Mariam buys 5 badges at 29 cents each. What is the total cost? That comes to 145 cents. Example ...
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Facts to know 2165 − 26 = 2139 52 - 14 = 38 14 minus 6 is 8 979 - 2 = 977 8 * 11 = 88 The difference between 8 and 2 is 6 2 multiplied by 6 is 12 35 divided by 5 is 7 34 + 8 = 42 42 − 23 = 19 9 + 51 = 60 The difference between 330 and 49 is 281 6 minus 3 is 3 Subtracting 11 from 98 gives 87 573 less than 3397 is 2824 8...
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Story time math Each day, Dr. Cruz walks 5 blocks. In 7 days, Dr. Cruz walked ____. Missing: 35 blocks. Soren has 57 toy trains. Amir has 44 more than Soren. How many do they have together? We add 57 and 44: 57 + 44 = 101. 57 + 101 = 158. The two of them have 158 toy trains. My cousin owned 72 paper flowers. My cousin ...
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Solve these (1) Arthur buys a bookmark for 43 cents and a carton of milk for 95 cents. Together they cost 138 cents. (2) Ben picked 90 paper clips. Rosie picked 24 paper clips. Ben has this many more: 66 paper clips. (3) Leila scored 89 points and Andre scored 1 points. How many more points does Leila have than Andre? ...
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Problem of the day 1) 3 groups of 4 make 12. 2) Tutor: Ross owned 7 bottles. Then, he lost 6 bottles. How many bottles does he have now? Learner: 1 bottle. 3) Ezra bought 9 notebooks priced at $1.55 apiece. The bill came to $13.95. 4) Coach Suzuki has 1 nickel and 3 pennies. How much money is that? 1 × 5 = 5. 3 gro...
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Warm-up Exercise: The cupboard had 78 lids in it. 41 went missing. Then 51 more arrived. How many lids are in the cupboard now? Answer: 88 lids. There are 5 rows of mugs, and each row has 12. How many mugs are there? That comes to 60 mugs. A bar graph of favorite snack shows 14 for crackers, 31 for popcorn, 20 for yogu...
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Show your work (1) A board is 10 centimeters long. In millimeters, that is 100 millimeters. (2) 16 divided by 2 is 8. (3) There were 93 cookies in a drawer, and 92 were removed. The drawer was left with 1 cookie. (4) 17 + 33 = 50, 50 + 11 = 61 (5) This morning, Joy had 52 dolls. The next day, Joy unpacked 56 more....
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Problem of the day 1) Jia shared 12 rubber ducks equally among 3 friends. Every friend receives 4 rubber ducks. 2) Ivan kept 75 dominoes in a toy chest. He left 28 at school. How many dominoes does he have now? 75 - 28 = 47. The amount he kept was 47 dominoes. 3) Umar picked 17 mugs. Santiago picked 38 mugs. How man...
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Lesson notes There were 6 feathers in the sack. 3 were sold. That makes 3 feathers. Ray scored 91 points and Luis scored 5 points. How many fewer does Luis have? Take 5 away from 91: 91 - 5 = 86. The gap between them is 86 points. A rug is 13 feet by 9 feet. What is the area of the rug? Step 1: 13 × 9 = 117. The rug co...
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Practice page 1. There are 51 shirts on Carter's table and 78 shirts on Fatima's table. How many shirts are there altogether? 2. There were 27 birds on the fence. First 11 flew away. Then 2 more flew down. How many birds are there now? 3. Cleaning up lasts 82 minutes. Iris has done 44 minutes so far. How many minutes a...
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Math class notes 90 divided by 10 equals 9. 141 + 10 = 151 Asher has 87 friendship bands and Ray has 35 friendship bands. How many fewer does Ray have? The gap between them is 52 friendship bands. 24 friendship bands are packed into bags, 3 to a bag. How many bags are there? We divide 24 by 3 to get 8. That fills 8...
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Story time math Teacher: There were 4 guests at the party. Then 6 more arrived. How many guests are there now? Student: 10 guests. Paolo scored 23 points and Jose scored 878 points. Paolo would need 855 more. 4 less than 168 is 164.
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Homework A scarf is 5 meters long. How many centimeters is that? We multiply 5 by 100 and get 500. In centimeters, that is 500 centimeters. Task: Count by 20s starting at 130: 130, 150, 170, 190, 210. What number comes next? Result: 230. Tutor: Of Bianca's 73 cups, 36 are large. The others are white. How many cups a...
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Problem of the day Area is the space inside a shape. For a rectangle, multiply the length by the width. Example 1: A shape is made of two rectangles. One is 7 units by 5 units. The other is 3 units by 2 units. Together they cover 41 square units. Example 2: Charlotte covers a bathroom wall with 2 rows of tiles, 10 tile...
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Math corner Problem 1: 6045 − 4944 = 1101 Problem 2: A crayon box costs 39 cents and a carton of milk costs 65 cents. The bill is 104 cents. Problem 3: There were 48 shoppers in the store. First 11 went out. Then 28 more came in. How many shoppers are there now? In the end there were 65 shoppers. Problem 4: 6 times...
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Math corner (1) The third grade voted on their favorite season: winter 10, spring 9, summer 29, fall 13. How many votes for spring and winter? 9 + 10 = 19. Spring and winter together got 19 votes. (2) Thomas filled 3 cupboards, putting 12 dolls in each one. How many dolls are there in all? 3 × 12 = 36. The total is 36 ...
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Homework #1 Survey of favorite color | Choice | Votes | | Orange | 7 | | Purple | 18 | | Red | 19 | | Green | 34 | | Yellow | 29 | Altogether the votes add up to 107 votes. #2 Dalia buys 6 pack of seedses at 13 cents each. Dalia pays 78 cents. #3 Diego counted 3 spinning tops. He shared 1 with Kwame. What is the number...
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Show your work At first, Wren had 69 glasses. The next day, Wren earned 94 more glasses. They now have 163 glasses altogether. Problem: In the morning the art teacher found 474 sticks. In the afternoon he found 8 sticks. How many sticks is that in all? Answer: 482 sticks. Bianca buys a balloon for 68 cents and pays ...
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Warm-up (1) Look at the pattern: 2, 4, 8, 16. What number comes next? Multiply: 16 × 2 = 32. The number after 16 is 32. (2) 59 birds were on the fence. 8 more flew down. How many birds are there now? Add: 59 + 8 = 67. That makes 67 birds. (3) Task: A shape is made of two rectangles. One is 4 units by 6 units. The other...
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Quick practice 49 + 44 = 93 8 + 7 = 15 120 ÷ 10 = 12 399 plus 45 is 444 203 − 73 = 130 61 - 2 = 59 3 + 73 = 76 6838 + 33 = 6871 Subtracting 3 from 98 gives 95 The product of 5 and 3 is 15 56 fewer than 313 is 257
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Quiz practice Rohan has 2 fewer badges than Daniela, who has 21. Rohan has 19 badges. There are 4 oranges, each cut into 5 pieces. How many pieces? Result: 20 pieces. A shape is made of two rectangles. One is 2 units by 8 units. The other is 7 units by 6 units. Together they cover 58 square units.
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Solve these 48 / 8 = 6 Word problem: Tina covers a bathroom wall with 7 rows of tiles, 4 tiles in each row. How many tiles are used? Solution: The number of tiles is 28 tiles. Try this: Liv sorted paper planes into two piles: 6 blue and 16 paper. How many paper planes are there in all? Answer: Altogether she has 22 ...
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Math class notes (1) The difference between 29 and 19 is 10. (2) 898 + 1 = 899 (3) The librarian has 24 pom-poms to share fairly with 3 bags. How many does each get? Split 24 into 3 equal parts: 24 ÷ 3 = 8. Each share is 8 pom-poms. (4) A gardener cut a sheet of paper into 4 equal pieces and gave away 3 of them. Ho...
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Math journal 1) Question: Carlos paid for a $0.52 lunch with a 1-dollar bill. How much change did the cashier give back? Answer: $0.48 back. 2) Reading starts at 8:14 and lasts 49 minutes. When does it end? The clock will read 9:03. 3) Talia is holding 82 flags. Kalani is holding 29 flags. How many flags do Talia an...
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Math centers 1) Ethan came to the zoo with 63 napkins. Ethan handed out 34 of them. The number left is 29 napkins. 2) Parker started with 4 snowballs. They spotted 42 more snowballs. How many snowballs does Parker have now? Right now Parker has 46 snowballs. 3) Sophie had a crayon 104 centimeters long and cut off 84 ce...
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Mental math #1 Naomi read 9 pages. Jules read 748 pages. How many more pages does Jules have than Naomi? So the answer is 739 more pages. #2 A bus left the depot with 48 riders. At the first stop 3 got off, and at the second stop 9 got off. Still on board were 36 riders. #3 Sasha's sandcastle is 110 centimeters tall. S...
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Think and solve (1) Tutor: Dina had 14 crayons. She forgot 1 at the park. How many crayons does she have now? Learner: That left she with 13 crayons left. (2) Question: The art club met from 8:30 to 9:05. How long did the meeting last? Answer: 35 minutes. (3) At the playground, waffles are set out in 9 rows with 4 i...
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Practice page 1) Zuri looked in the toy chest and saw 44 cans. Zuri stacked 6 more in it. How many are in the toy chest after that? The toy chest now has 50. 2) Grandpa: A kitchen floor is 2 tiles long and 3 tiles wide. How many tiles are used? Grandchild: The number of tiles is 6 tiles. 3) Albert's collection had 74 p...
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Practice set Area is the space inside a shape. For a rectangle, multiply the length by the width. Example 1: A table top is 11 tiles long and 2 tiles wide. In all, there are ____. Missing: 22 tiles. Example 2: A table top is 9 tiles long and 8 tiles wide. How many tiles are used? We multiply 9 by 8 and get 72. The numb...
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Morning work #1 Cesar had 63 cents and earned 76 cents more by walking a dog. How much money is there now? #2 Hannah bought 8 packs of mugs. Every pack has 11. How many mugs are there in all? #3 Georgia has 51 seashells and George has 30 seashells. How many seashells do Georgia and George have together? #4 A shape is m...
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Math practice Puzzle: There are 36 friendship bands, and Uncle Bennett gives away a quarter of them. How many is a quarter of 36? Answer: 9 friendship bands. At first, Naomi had 84 clay pots. After that, she shared 18 with Irene. How many clay pots are left? There were still 66. A shape is made of two rectangles. One i...
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Quick practice 74 - 64 = 10; 76 plus 1 is 77; 9 × 2 = 18; 108 ÷ 9 = 12; 90 − 6 = 84; 27 / 9 = 3; 95 + 70 = 165; 55 divided by 11 is 5
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Warm-up Try this: Anika's tomato plant was 36 centimeters tall. Over the month it grew 13 centimeters. How tall is it now? Answer: 49 centimeters. Bianca collected 96 bananas. Bo collected 23 bananas. How many bananas do Bianca and Bo have together? So in all there are 119 bananas. Q: Mr. Clarke has 59 paper clips. ...
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Brain teasers A patio is 7 units long and 9 units wide. What is the area? The librarian has 8 hamsters. Abigail has five times as many hamsters. How many hamsters does Abigail have? The desk had 50 apples on it. 33 more were dropped in. Then 8 were taken out. How many apples are on the desk now? One bowl has 147 rabbit...
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Homework Area is the space inside a shape. For a rectangle, multiply the length by the width. Example 1: A rectangle measures 7 centimeters by 12 centimeters. Its area comes to 84 square centimeters. Example 2: On grid paper, a rectangle covers 7 squares across and 2 squares down. The space inside is 14 square units.
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Math practice The difference between two numbers is how much bigger one is than the other. Example 1: Ricardo picked 39 rocks. Yara picked 1 rock. The gap between them is 38 rocks. Example 2: Tom picked 872 roses. Ezra picked 3 roses. Ezra has fewer by 869 roses. Example 3: Yosef picked 48 kittens. Lee picked 844 kitte...
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Story problems There were 54 toy trains in the crate. Jane poured in 47 more. How many toy trains does the crate hold now? Edith buys 4 erasers at 48 cents each. What is the total cost? Tobias's collection had 64 mugs. Tobias donated 27 mugs. Later, he donated 20 mugs. What is the number of mugs Tobias has at the end? ...
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Think and solve 1. At the park, blueberries are set out in 4 rows with 3 in each row. How many blueberries are there? 2. Piano practice started at 10:17 and ended at 11:17. How long did it take? 3. The teacher made 163 jigsaw puzzles. Ada made 97 jigsaw puzzles. How many jigsaw puzzles do they have in all? 4. Grandpa's...
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Lesson notes #1 Penny has 99 photos. At first, Penny returned 24. How many photos does she have left? The answer is 75 photos. #2 Puzzle: Alexis needs 91 mugs for a project and has 8 so far. How many more mugs are needed? Answer: 83 mugs. #3 Rahim buys a whistle for 28 cents and pays with one dollar. Rahim gets back...
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Math corner Dad: Paper flowers are lined up in 12 rows of 10. How many paper flowers are there? Child: The total is 120 paper flowers. Count by 100s starting at 195: 195, 295, 395, 495, 595, 695. The number after 695 is 795. The sides of a rectangular picture frame are 29 centimeters and 18 centimeters. What is the per...
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Math corner Puzzle: Savannah wants to collect 77 walnuts. She already has 17. How many more walnuts are needed? Answer: The number still needed is 60 more. There were 91 chestnuts in the bag. Molly took out 21. Now the bag holds 70. Nathan filled a pail with 26 cones. He handed 14 to Brooke. This leaves 12 cones. 3...
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Think and solve A table top is 2 feet by 13 feet. The table top covers 26 square feet. 12 * 7 = 84 33 ÷ 3 = 11 A garden hose was 54 centimeters long. Rachel cut 53 centimeters off it. How long is it now? What is left measures 1 centimeters. Chen's collection had 8 screws. Chen traded for 7333 more screws. How many scre...
arith_v2
0
82
Math practice Jacob had 64 horses. He gave 13 to Yara. Later, he gave away 28. How many horses does he have? We subtract: 64 - 13 = 51. Find the difference: 51 - 28 = 23. So he has 23 horses. Bailey cuts a scarf into 9 pieces, each 20 centimeters long. The whole length was 180 centimeters. Question: A square tile has s...
arith_v2
0
83
Show your work 1. 100 − 82 = 18 2. Frida started with 37 coins. She used up 11 of them. Later, she unpacked 8 more. What is the number of coins Frida has at the end? Result: 34 coins in all. 3. Priya owns 5238 puppies, and Jamie owns 11 puppies. What is the total number of puppies? To find the total, add 5238 and 11, w...
arith_v2
0
84
Weekend practice 5 × 10 = 50, 4 * 1 = 4, 50 + 4 = 54 My aunt scored 1370 points and Brooke scored 2 points. Brooke has fewer by 1368 points. Survey of favorite fruit | Choice | Votes | | Grapes | 29 | | Cherries | 20 | | Apples | 3 | | Mangoes | 7 | | Bananas | 15 | Combined, bananas and grapes have 44 votes.
arith_v2
0
85
Classroom notes A fraction names equal parts of a whole. Half of something is one of two equal parts. Example 1: Word problem: A chocolate bar is cut into 18 equal pieces. One sixth of the chocolate bar is eaten. How many pieces? Solution: The number of pieces eaten is 3 pieces. Example 2: Ask: A sandwich was cut into ...
arith_v2
0
86
Warm-up 76 + 56 = 132 60, 57, 54, ... The next number is 51. 80 take away 23 is 57. 57 and 35 more is 92.
arith_v2
0
87
Drill 9 times 2 equals 18 38 plus 73 is 111 Subtracting 62 from 521 gives 459 Subtracting 82 from 851 gives 769 84 - 3 = 81 11 times 2 is 22 46 − 5 = 41 110 divided by 10 is 11 814 + 70 = 884 4 × 8 = 32 50 take away 21 is 29 8 * 12 = 96 983 add 82 is 1065 3 + 94 = 97 5 × 10 = 50 27 split into 3 equal groups is 9 in eac...
arith_v2
0
88
Problem of the day 1) Tutor: Week 1 has 54, week 2 has 65, week 3 has 76, week 4 has 87. What comes next? Learner: 98 chairs. 2) A board game took 59 minutes. Then swim class took 17 minutes. How many minutes in all? Put the two amounts together: 59 + 17 = 76. Together they took 76 minutes. 3) That evening, Logan ha...
arith_v2
0
89
Story problems 1. Salma's bean plant was 26 centimeters tall. Over the month it grew 13 centimeters. How tall is it now? 26 + 13 = 39. Now it is 39 centimeters. 2. One wire is 80 centimeters. Another is 93 centimeters. They are joined. How long are they together? Final answer: 173 centimeters. 3. 4 x 10 = 40
arith_v2
0
90
Weekend practice One meter is 100 centimeters. Lengths add up when things are laid end to end. Example 1: Ask: A stick is 11 centimeters long. How many millimeters is that? Reply: 110 millimeters. Example 2: A pencil was 118 centimeters long. Iris cut 103 centimeters off it. Now it is 15 centimeters. Example 3: Amos cu...
arith_v2
0
91
Practice set To find change, subtract the price from the money paid. Example 1: One pack of seeds costs 8 cents. Leila wants 8 of them. What is the total cost? 8 of them cost 64 cents. Example 2: One muffin costs 60 cents. Ethan wants 8 of them. Ethan pays 480 cents.
arith_v2
0
92
Math centers (1) My uncle cut a pan of brownies into 16 equal pieces and ate 14 of them. Now there are 2 pieces left. (2) The difference between 54 and 46 is 8. 8 add 14 is 22. (3) 5 more than 43 is 48. (4) A hall is set up with 6 rows and 13 chairs in each row. How many chairs are set up? Step 1: 6 * 13 = 78. The ...
arith_v2
0
93
Practice sheet Each day, Quinn bakes 9 loaves of bread. After 4 days, they has baked 36 loaves of bread. 31 lemons are put into bags of 3. Only full bags count. Left over there are 1 lemon. Henry has 32 forks and Omar has 14 forks. The gap between them is 18 forks. 87 + 965 = 1052 Isaac read 66 pages. Joanna read 7261 ...
arith_v2
0
94
Warm-up One hour has 60 minutes. To find how long something took, count the minutes from start to end. Example 1: Soccer practice started at 4:34 and ended at 6:54. It took 140 minutes. Example 2: 1 groups of 60 make 60. 60 plus 23 is 83. Example 3: A nap took 2 hours and 10 minutes. Written in minutes, it is 130 minut...
arith_v2
0
95
Problems for today Neil has 56 daisies. Nell has 3 more than Neil. Both of them together have 115 daisies. The puppet show started at 3:05 and ended at 3:15. How long did it take? 3:15 - 3:05 = 10 minutes The puppet show lasted 10 minutes. There were 92 folders in the barrel. 8 more were added. Now the total in the ...
arith_v2
0
96
Mental math (1) Gideon had 66 cents and spent 18 cents on a carton of milk. How much money is left? That leaves 48 cents. (2) The scouts's lunch box had 3 worksheets in it. They stacked 4 more in it. How many are in the lunch box after that? Add: 3 + 4 = 7. Now there are 7 worksheets. (3) Exercise: Gardening started at...
arith_v2
0
97
Math corner The difference between two numbers is how much bigger one is than the other. Example 1: Coach Rivera has 94 bracelets and Nolan has 98 bracelets. How many more bracelets does Nolan have than Coach Rivera? The answer is 4 bracelets. Example 2: Bea scored 8 points and Leah scored 19 points. How many more poin...
arith_v2
0
98
Homework 1) Kendall's bean plant was 69 centimeters tall. Over the month it grew 24 centimeters. How tall is it now? 2) Nora picked up 2 pots on Wednesday. On Thursday, she picked up 99 more. How many pots is that in all? 3) Aurora divided 14 dominoes into 2 equal groups. How many does each get? 4) Amira has 64 sunflow...
arith_v2
0
99
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Mantis-50M synthetic arithmetic

The synthetic grade-school arithmetic text that Mantis-50M was trained on, published so anyone can check it. It is decoded from the exact token shards used in training, not regenerated.

Config What Train docs Validation docs Train tokens
v2 (default) All of the decay-phase data (12% of the decay mix) 1,129,331 2,000 299,478,229
v1-sample 1 of the 20 stable-phase shards (7% of the stable mix) 305,306 2,000 99,362,627

The decay drew about 214M tokens from v2, under one pass. The full v1 data is 20 shards like v1-sample (6.1M documents, 2.0B tokens). Validation documents were held out of training. Tokens are Mantis-50M tokens, counting one <|endoftext|> per document.

from datasets import load_dataset

v2 = load_dataset("kash8080/Mantis-50M-arith", "v2", split="train")
print(v2[0]["text"])

Fields

Field Meaning
text One training document, exactly as trained (without the `<
generator arith_v2 or arith (v1)
shard Training shard index. Each shard is one seeded run of the generator
doc Position in the shard, in training order

How it was made

Both generators are plain Python in src/slm50m/arith/: generator.py (v1) and generator_v2.py with lexicon.py (v2). They fill templates from general English word lists: names, objects, containers, gain and loss verbs, lead phrases. Every number is computed, so every answer is correct. Documents are worksheets, drills, answer keys, dialogues and stories with one or more problems each.

  • v1 covers addition, subtraction, multiplication, division, sequences, money, time, measurement and tallies, with 50 names and a small set of fixed wordings
  • v2 was written after v1's skill turned out to work only in v1's own wording. It has ~500 names with pronoun agreement, ~200 objects, ~90 verbs, ~110 lead phrases and ten answer formats (story, question and answer, worked steps, equation, dialogue, fill-in and others). It covers the usual grade-school topics, which overlap with ArithMark-3's
  • This dataset was decoded from the training shards on the Modal Volume. Each shard's document and token counts match the training manifests, and every 100th document re-encodes to the same token ids

Decontamination

  • No benchmark item was used to write the generators
  • Zero exact matches and zero 13-gram matches with ArithMark-3 over ~54,000 (v1) and ~55,000 (v2) generated problems in every format
  • Every v2 document also went through the 13-gram filter against HellaSwag, ARC-Easy, ARC-Challenge, PIQA and ArithMark-3 before training: zero documents dropped

What it does and does not teach

Training on v2 raised Mantis-50M's ArithMark-3 score from 37.3% to 85.7%. On grade-school word problems written by other people (ASDiv and SVAMP, 232 problems that no training data paraphrases) the gain is much smaller: 31 to 41% against 25% chance, up 10 to 20 points. Details in the model card. Wider wording does not by itself give general arithmetic.

Known issues

The text is unedited generator output. It has occasional grammar slips ("That left she with 22") and odd pairings of objects and containers (horses shared into bags). The arithmetic itself is always correct.

Licence

CC-BY-4.0. The generator code is Apache-2.0.

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