Classwork 16 Problem 1. dm dm Convert decimeters into centimeters: 2 dm = cm 4 dm = cm 6 dm = cm 3 dm = cm 5 dm = cm 8 dm = cm Convert centimeters into decimeters: 50 cm = dm 70 cm = dm 60 cm = dm 10 cm = dm 90 cm = dm 40 cm = dm Problem 2 a) We cut 3 dm piece of rope and found that there are 4 dm left. How long was the rope before we cut it? b) Caitlin brought 9 dm of ribbon for the craft project, and Fiona brought 80 cm. Whose ribbon was longer? Problem 3 Very very old problem. The man was traveling with wolf, goat and cabbage. He had to cross the river, but the boat was so small, it could hold only the man himself and just one more thing or creature (either wolf, or goat, or cabbage). But if you leave the wolf with the goat (without the man watching over them), the wolf will eat the goat. And if you leave the goat with cabbage, the goat will eat the cabbage. The man managed to cross the river after all. Can you explain how he did it? 1
Problem 4 There were a books on the first shelf. There are b books on the second. How many books are on two shelves together? There were a books on the first shelf. There are b books on the second. How many more books the first shelf holds? There are c books on the first shelf. This is d books less than on the second. How many books are on the second shelf? There are c books on the first shelf. Second shelf holds m books less. How many books are on two shelves together? There were a books on the first shelf and b books on the second. How many books will be on these shelves after we take away c from the second shelf? We took m books from the first shelf and n books from the second. After that there were k books left. How many books were on both shelves together in the beginning? There were a books on two shelves. We took b books from the first shelf and c books from the second. How many books are left on the shelves? 2
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Problem 6 4
Classwork 17 Problem 1. Complete the table using examples on the first row as a guide: 3 tens 5 ones + 1 ten 2 ones = 4 tens 7 ones tens ones - tens ones = tens ones Problem 2. 3t 4o + 2t 3o = t o 4t 5o + 2t 1o = t o 7t 8o - 2t 8o = t o 6t 2o - 3t 0o = t o Problem3. Same thing without words. 25 + 12 = 48 + 30 = 36 22 = 62 42 = Problem3. Equations with shapes and funny letters on the blackboard. Problem 4. Formation of numbers from to 5
Problem 6. 1. 2. 3. 4. 5. 6. I have a liters of water in the first pail, and b liters less in the second one. How many liters of water are in the second pail? I have a liters of water in the first pail. This is b liters less than in the second one. How many liters of water are in the second pail? I have a liters of water in the first pail, and b liters more in the second one. How many liters of water are in the both pails together? I had a liters of water in the pail, than used b liters to water the garden and c liters to water indoor plants. How many liters of water left in the pail? I took a liters of water from the pail, than took b liters more. After that c liters to water were left. How many liters of water were in the pail in the beginning? There were a liters of water in the first pail, and b liters in the second. We used c liters to water some plants. How many liters of water left in both pails? Problem 7. Multiplication expressions. rows of Equals rows of Equals rows of Equals 6
Problem 8. How many legs do three bugs have? How many legs do 3 octopuses have? How many ears do 6 rabbits have? How many arms do 2 starfish have? How many paws do 6 cats have? How many horns do 3 bison's have? Problem 9. Reversed problems. a) There were children playing behind the fence. We see 8 feet. How many children were there? b) There were ducks swimming in the pond. Clever fish counted 12 feet paddling the water. How many ducks were swimming? c) There were students hiding under the tables but then raised both their hands up. The teacher saw 18 hands. How many homework assignments should she prepare? 7
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Classwork 18 Problem 1. Problem 2. There were A cars in the parking lot. B more cars arrived. How many cars are now in the parking lot? There were C cars in the parking lot. D cars left. How many cars are now in the parking lot? There were E cars in the first parking lot. The second parking lot had F cars more than the first. How many cars were in the second parking lot? There were A cars in the first parking lot. The second parking lot had B cars more than the first. How many cars were in two parking lots together? There were C cars in the first parking lot and D cars on the second. How many more cars did the second parking lot have than the first? There were E cars in the first parking lot, which is F less than on the second. How many cars are in the second parking lot? 9
Problem 3. On the left plate put 2 more fruit, and on the right plate put 2 times more fruit. Fill in the rectangles so the number on the bottom is 2 more than the number on the top. And now the number on the bottom is 2 times more than the number on the top. 10
Problem 4. 11
Problem 5. Division 12
Classwork 19. Problem 1. How many polygons can you find on the pictures below? Problem 2. A boys and B girls went to the circus. How many kids went to the circus in total? There were C boys sitting in the first row, and 5 more girls than boys sitting in that same row. How many girls were sitting in the first row? During intermission the girls bought A servings of ice cream. It was 6 servings less than the boys bought. How many servings did the boys buy? During the performance the kids saw C clowns and 8 more acrobats than clowns. How many acrobats and clowns were there in total performing that evening? 10 tigers entered the circus arena, and C less lions than tigers. How many lions and tigers together were there in all? 13
Problem 3. 14
Problem 4. How many roads do you need in order to connect 5 houses with each other? Answer: Problem 5. Solve the equations below and check your answer: x - 11 = 34 12 + x = 45 x + 14 = 65 15
Problem 6. Circle the elements belonging to the one set. Name this set. Problem 7. Finish the drawings of the cubes below. 16
Classwork 20. Problem 1. < review the problem from homework > We have three plates with apples on the table. There are 8 apples on one plate, 3 apples on the second plate and 1 apple on the third one. You have to make the number of apples the same on each plate, but you need to follow two rules. First: you can move apples from one plate to another as many times as you want, but you can take apples from only one plate at a time and put them on one plate only. Second: you can put as many apples on the plate as it already has (for example, on the second plate you can only put 3 apples right now, not 1 or 2 or 4 ). Problem 2. During the lesson Andrew gave the right answer N times, and Fiona 2 times less than Andrew. How many answers did Fiona give? How many did Andrew and Fiona give together? Jeffrey spent С minutes doing his homework. That was 10 minutes less than James. Who completed his homework quicker Jeffrey or James? How many minutes did James spend? Marc solved A problems, and Brandon 3 problems more than Mark. How many problems did they solve together? Jameson broke 4 pencils during the lesson, and Carson broke B pencils less. How many pencils did the boys break together? Taylor memorized Р multiplication facts, which is 2 more than Sarena. How many multiplication facts did Sarena learn? 17
Problem 3. Problem 4. Multiplication and division using the table. New: multiplying and dividing by 10. 18
Problem 5. Show your sister game. you are my brother you are my sister Can you figure out who are boys and who are girls in these pictures? Figure out who are boys and who are girls. Who is a brother to whom? Are there any missing arrows? Fill in the circles properly and add missing arrows. Try to figure out who is whose brother, and are there any girls in the picture? Fill in the circles properly and add missing arrows. 19
Problem 6. Kids are going sledding. Give them sleds (draw the lines) Look at the diagram (graph) Sleds Kids Give cabbage to each kid (draw the lines) Draw the diagram (graph) Cabbage Kids 20
Problem 1. Review of addition, subtraction. Review of handshake problem. Blitz Problems from Peterson on the blackboard Tangram at the end. Classwork 21. Problem 2. Sets in ovals: 1) All the kids, pupils; Books, fiction books 2) Put names in: kids from our class, boys 3) Fix mistakes: animals-birds-crows; animals, tigers; daisies-plants, flowers. Problem 3. 21
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Classwork 22. Problem 1. Samantha and Andrew were playing a game called Where is the princess. Andrew found the princess N times, and Samantha found the princess 3 times more than Andrew. How many times did Samantha find the princess? John and Emily were eating cookies. John ate 6 cookies, which is B more than what Emily ate. How many cookies did the friends eat together? Sophie and Michael together brought C pencils to class. Michael brought 4 pencils. How many pencils did Sophie bring? Lea and Michelle were playing tic-tac-toe. Lea played R times. How many times did Michelle play? There were D students in art class one day. That was 4 students less than in the math class. How many students were in the math class? Problem 2. One birthday candle burns completely in 20 minutes. We lit up 10 candles simultaneously. How long are they going to burn? Each alien has 3 hands. 10 aliens stayed in line holding hands with each other. How many hands are free and can wave at us? Python tried to measure his length with the help of his friends. First he asked Monkey, and figured out that he is as long as 4 monkeys. Then he asked Elephant and found that he needed 2 elephants to cover his length. Then Parrot wanted to measure Python and they figured out that he is as long as 12 parrots. How long are Monkey, Elephant and Parrot, if later Python used the measuring tape and found that he is 12 feet long? 25
Problem 3. Problem 4. Solve using the number line. Compare solutions for 3) and 4). Which one was easier and quicker to do? Problem 5. John had 3 videogames. For his birthday, his mom bought him 2 more, and he received 7 as gifts from friends. How many games does he have now? How many did he get for his birthday? How many more did he receive from his friends than from his mom? he had friends mom Problem 6. Split in half, so you have a sum of two addends that are the same. 26
Problem 7. Draw the hands of the clocks below so they show correct time. 27
Problem 8. How many angles does each shape have? 28
Problem 9. Draw 2 things in each set, including the intersection RED THINGS FLAGS 1) Give a name to each set. 2) How many elements are there in each set? 3) How would you name an intersection of two sets? 4) How many elements are there in the intersection? Name an intersection of the sets below and give an example of something that belongs to this intersection: 1) Green things; edible things. 2) Flowers; red things. 3) Animals; grey things. 4) Toys, round things. 29
Classwork 23. Problem 1. Problem 2. What question can you ask to make following number stories into problems? 1) Dad planted 10 trees today, and his son Micky planted 2 trees. 2) The bag held 18 pounds of potatoes. We took away 8 pounds. 3) Mom bought 10 apples, 4 lemons, and 5 pears. Problem 3. Andrew built a tower from 10 blocks for his brother. The brother took away C blocks. How tall is the tower now? The combined age of Marc and Carson this year is N. What would be their combined age next year? The year after? Sofia and Sara were counting steps on the staircase. Sofia counted M steps, which was 5 steps more than Sara counted. How many steps did Sara count? Both girls together? Caitlin found 30 beautiful stones on the beach. She gave her mom 5 stones, and she brought X stones to school. How many stones did she leave at home? 30
Problem 4. There were 10 passengers on a bus. On each stop 4 passengers got off, and 6 passengers got on the bus. How many passengers were in the bus between 4 th and 5 th stops? Problem 5. Some first graders went to the museum on a field trip. The teacher asked them to line up by threes. Brandon, James and Jeffrey noticed, that their trio is 5 th, if you count from the beginning, and 3 rd, if you count from the end. How many students went to the museum? Problem 6. Connect the dots using a ruler, so your lines won t intersect. What kind of shapes will you get? (discuss sides, angles, diagonals) 31
Problem 7. How many elements are in each set? How many elements are in the intersection? Color the circles that represent sets that do not intersect. Find thr proper place for each shape. QUADRILATERALS BLACK SHAPES 32
Problem 8. 1) Circle the object that belongs to the intersection of sets: VEHICLES and GREEN THINGS 2) Cross out the object that does not belong to any of these sets. 1) Circle the object that belongs to the intersection of three sets: MADE FROM METAL, BELONGS IN THE KITCHEN and CYLINDRICAL THINGS 2) Cross out the object that do not belong to any of these sets. Draw sets as ovals. Which of them intersect? 1) PEOPLE and KIDS 2) PEOPLE and ANIMALS 1) GIRLS and STUDENTS 33
Classwork 24. Problem 1. Solve: 9 + 3 = 10 + = 7 + 5 = 9 + 6 = 8 + 8 = 10 + = 8 + 6 = 6 + 5 = Problem 2. 9 kids from our school took part in the Math Olympiad competition. 4 of them were girls. 7 boys and 3 girls competed from a different school. How many of the following took part in Math Olympiad: 1) boys from our school; 2) kids from the other school; 3) kids from both schools together; 4) boys from both schools together; Which school had more boys competed and by how many? Problem 3. Compare without calculating: Problem 4. Some girls entered a running competition. Fiona finished earlier than Caitlin, but later than Sofia, Sara finished earlier than Sofia, and Sarena came later than Caitlin. Who finished first? Last? What was the order of the girls in which they crossed finish line? 34
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Problem 6. A B C D E F Problem 7. C D E F 36
Game The Flower You and your opponent should take pencils of different colors. In one turn you can color either one petal or two neighboring petals. The person who colors the last petal wins! Won your game? Color the petal of the score flower on the right with your color. 37
Classwork 25. Problem 1. 1. Sofia had A bows in her hair, and Sara had 5 bows more. How many bows did the girls have together? 2. Caitlin put N strawberries on her plate, and Fiona M strawberries less than Caitlin. How many strawberries did the girls have on their plates together? 4. On his way to school Andrew counted C steps on the stairs. How many steps will Marc count if he comes to school the same way? 6. Brandon has Z pencils and Y pens in his backpack. He also has rulers: 2 less than the pens and pencils together. How many rulers does Brandon have in his backpack? 4. Sarena got 6 stickers in school today. She received 2 stickers for each lesson. How many lessons did Sarena have in school today? Problem 2. Make up your own problems according to the drawings: Problem 3. Find and correct the mistakes that Cat in the Hat made below: 38
Problem 4. Subtraction. Make 10 first. Check with addition. Problem 5. Check: Check: Check: Problem 6. There were 4 children playing soccer in the park. Their names were Andrew, Phillip, Sam and Julien. In order to make the teams as fair as possible, they all told each other each of their ages. It turned out that Andrew was older than Sam, Sam was the same age as Julien and Phillip was younger than Julien. Who is older, Andrew or Phillip? 39
Problem 7. Color in squares: Problem 8. 40
Problem 9. The bus stop is black on the outside and white on the inside. Color properly. Problem 10. Make up equations and solve them. 41
Problem 11. Alex 42
Classwork 26 Problem 1. Sofia and Sara were growing flowers in the garden. Sofia grew 5 tulips and 6 daffodils, and Sara grew b flowers less than Sofia. How many flowers did Sara grow? James and Jeffrey had tree pollen allergies. James sneezed 18 times, which was а more than Jeffrey. How many times did Jeffrey sneeze? Carson and Jameson found a duck nest in the garden. Carson counted m eggs in this nest. How many eggs did Jameson count later, if by that time 2 ducklings already hatched? Jan and Andrew were building birdhouses. Jan made k green ones and n yellow ones, and Andrew made 3 birdhouses less than Jan. How many birdhouses did the boys build together? Marc noticed a family of rabbits in his garden. He counted 4 big ones, and c less small ones. How many rabbits did Marc see total in his garden? Problem 2. Solve and explain how you did it. 7 + 8 = 11 7 = 13 4 = 9 + 6 = Problem 3. Make a helpful drawing and solve: 1) Caitlin found 48 seashells. She used 23 for the necklace and gave 15 to her friend. How many seashells does she has left? 2) In the school library there were 30 books on the first shelf, 25 books on the second shelf, and 32 books on the third shelf. The students checked out 42 books today. How many books remained on the shelves? 43
Problem 4. Add your own questions to the number story and solve: Fiona and Sarena were planting flowers. Fiona planted 5 roses and 6 tulips. Sarena planted 12 flowers altogether, 3 of them were roses, and the rest were tulips. Problem 5. Compare if you can: 23 kg 5 kg 68 in 86 in 3 dm 16 sm 18 l 37 l 3 sm 56 km 7 f 8 lb Problem 6. Solve the first problem in the column and find the answer to the second using this result. Problem 7. How many triangles? Problem 8. Draw as many triangles as you can- going through the points below: 44
Problem 9. Neighboring regions have common section of border (see the picture to the left) and should be colored differently on the map. Not neighboring regions (see the picture on the right) can be colored the same. Try to color maps below using only two colors, so neighboring regions will always be colored differently. 45
Problem 10. Multiplication and division by 9. You may use the Peasant s trick (using numbered fingers of both hands) 46
Classwork 27. Problem 1. Here is the menu of a restaurant. There are no prices listed on the menu, the only thing known is that a bagel costs $2. Try to figure out the cost of the other dishes from the clues on the right: Menu Hamburger..... $ Chicken.. $ Fish.... $ Hamburger costs the same amount as Spaghetti and Pizza together Chicken costs the same as 4 Bagels Hamburger twice as expensive as Chicken Spaghetti.... $ Chicken and 2 Bagels cost the same as 2 Pizzas Pizza... $ Rice $ Bagel.. $ 2 Fish and 1 Bagel cost the same as Hamburger and 3 Bagels Rice is two times cheaper than the Fish Problem 2. What is common in numbers: 16, 23, 50? What does not belong with the other two and why? Try to find different answers. Problem 3. Add 3 more numbers in each cell, continuing the pattern. 1, 3, 5, 7, 35, 30, 25, 900, 800, 700, 10, 20, 30, 7, 17, 27, 105, 115, 125 47
Problem 4. Group by shape and write all the possible addition and subtraction expressions. C A How else you can group them? Problem 5. Insert a number in the place of the to make expressions true. Is it always possible? Problem 6. Winnie the Pooh loves honey. He noticed that jug with honey weights 36 lb, and empty jug only 5 lb. How many pounds of honey are in the jug? Problem 7. Did Winnie make mistakes in comparing the expressions below? 84 + 15 < 15 + 84 36 11 > 36 13 45 + 12 > 45 + 14 Problem 8. Multiplication by 6. 48
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Problem 10. How many rectangles do you see on each picture? (Do not forget that squares are rectangles too!) Problem 11. Now let s share these chocolates fairly between you and your friend. You can only divide in full squares. How many squares will each of you get? Are there chocolates that you cannot break equally in half this way? How can you recognize them? Now we don t have full chocolate bars any more, but still let s try to divide them equally in two parts. 50
Classwork 28 Problem 1. Father took 15 nails from the box. He used 8 to fix a bookshelf, 2 to hang picture on the wall, and gave the rest to his son. How many nail did his son get? Mother bought 8 pounds of potatoes, and 5 pounds less of carrots. How many pounds of vegetables did she buy altogether? There were 12 apples in a basket, 6 apples on a plate, and 10 apples in a bag. How many apples less does the basket hold than the bag and plate together? The store had 15 white and 12 brown bags for sale. During the day 8 white and 4 brown bags were sold. Ask your own questions about this number story and answer them. Problem 2. Using the weights 3 lb, 5 lb and 8 lb, measure 16 lb, 11 lb, 10 lb and 6 lb. Problem 3. Closed regions. Regions with holes. Draw a straight line where you can cut the region on the left to make two regions without holes. Draw these regions below: Problem 4. 51
Problem 5. Every food item hides a number. The sum of all numbers in a row is written on the right, and the sum of all numbers in a column is written under it. Find out what item hides which number. Hint: look at the 4 th row. It holds 5 hamburgers, and the sum is 10. What do you think hamburger hides? 52
Problem 6. Mark all the empty seats on the chart to the right. Chart: Stage Mark all occupied seats on the chart to the right. Chart: Stage 53
Mark the places where girls sit with the red circles, and those where boys sit with the blue circles. Color the circles appropriately on the left, where you look at the hall from the back (or you can imagine that the theater had turned around). Chart: Stage Find the seats according to the tickets. Follow the examples below. row seat row seat row seat row seat row seat row seat row seat Rows: 54