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Answer KeyBridges Grade 4Home Connections Volumes 1 & 2Unit 1Unit 3Number Line Puzzles .1Models for Multiplication .3Modeling Multiplication & Division .5Factors & Tea Lights .7Multiplication Fact Strategies .9Multiplying by 8 & 9 .11Multiples, Flowers & Cards .13Arrays & Factors .15Measuring Lengths.17Mass & Volume Story Problems .19Skills Review 2 . 49Fraction & Division Story Problems . 51Thinking About Fractions . 53Brownie Dessert . 55Planning a Garden . 57Fractions & More Fractions . 59More Comparing Decimals & Fractions.61Decimals, Fractions & Story Problems . 63Equal, Not Equal . 65Frankie’s Fractions & Decimals . 67Unit 2Unit 4Multiplicative ThinkingMulti-Digit Multiplication & EarlyDivisionMeasuring in Centimeters . 21More Multiplying by Ten . 25Which Operation? . 27Coins & Arrays .31Multiplication Strategies . 33Multiplying by Multiples of Ten . 35Design a Floor Pattern. 37Multiplying & Dividing .41Multiplication & Division Puzzles . 43Moolah on My Mind. 45Bridges in Mathematics Grade 4 Home ConnectionsFractions & DecimalsAddition, Subtraction & MeasurementNumber Riddles & Stories . 69Big Numbers . 71Addition Algorithm & More. 73Think Before You Add. 75Number Cards . 77Thinking About Subtraction . 79Which Measurement Is Best? . 81Running the Race. 83Unit 4 Review 1 . 85Unit 4 Review 2 . 87 The Math Learning Center mathlearningcenter.org

Answer KeyUnit 5Geometry & MeasurementReviewing Area & Perimeter . 89Angles & Rectangles . 91Protractor Practice . 93Drawing Two-Dimensional Figures . 95Symmetry . 99Classifying & Drawing Quadrilaterals . 101Area & Perimeter Review . 103Area, Perimeter & Multiplication . 105Clock Angles & Shape Sketches . 107Unit 5 Review .109Unit 6Unit 7Reviewing & Extending Fractions,Decimals & Multi-Digit MultiplicationConversion Tables . 131Multiplication Review &Fraction Comparisons . 133Sketch & Compare Fractions . 135Fraction Action . 137Decimals on Number Lines & Grids . 139Standard Algorithms. 141Choose Your Strategy . 143Variables & Expressions . 145Unit 7 Review . 147Multiplication & Division, Data &FractionsUnit 8Area & Perimeter Story Problems .111Fraction Stories .113Conrad’s Room .115Paloma’s Picture .117Frankie’s Fairground.119Perimeter & Area . 121Rope Climb Results & Skills Review . 123Bakery Bundles . 125Danny’s Data. 127Unit 6 Review . 129Another Grassy Field. 149Ten-Foot Seesaw . 151Circle Explorations . 153Most Important Items . 155Pricing Playground Equipment . 157Measurement & Decimal Review. 159Drawing the Playground . 161Playground Map . 163Designing Playground Equipment. 165Bridges in Mathematics Grade 4 Home ConnectionsPlayground Design The Math Learning Center mathlearningcenter.org

Answer KeySession 2Unit 1 Module 1NAME DATENumber Line Puzzles page 1 of 2Note to FamiliesStudents can use number lines to review the multiplication facts they learned in third grade. Number lines can help studentsuse facts they know to help them figure facts they don’t remember. Talk together about relationships between facts thatyou see in the two number lines below, such as numbers that double.1Fill in the blanks in the number lines.ab2 43 44 48 49 48121632362 83162244 88 832649 872 44010 880Complete the facts.8 2163 8108 4328 8648 10808 9727 10707 963Roger’s little brother, Saul, wants to know if 5 7 7 5. If you were Roger, howwould you explain to Saul whether the equation is true?Work will vary, it is true that 5 7 7 5.(continued on next page)Bridges in Mathematics Grade 4 Home Connections1 The Math Learning Center mathlearningcenter.org

Unit 1 Module 1Answer KeySession 2NAME DATENumber Line Puzzles page 2 of 245Each of the 29 students in Mr. Brown’s fourth grade brought 2 notebooks to class thefirst day of school. How many notebooks was that in all? Show your thinking withnumbers, sketches, or words. Then write an equation that represents your work.29 students 2 notebooksper student 58 notebooks58 notebooksEquationAnswer, labeled with correct unitsEach of the students in Mr. Smith’s class also brought in 3 pocket folders. Mr. Smithwrote a multiplication equation to compare the number of students to the number ofpocket folders they brought in. Fill in the bubble to show what this equation means.87 3 29!687 is 3 morethan 29!87 is 3 times asmany as 29!29 is 3 times asmany as 87If 5 students each brought in 8 boxes with 10 pencils per box, and 10students each brought in 8 boxes with 5 pencils per box, how many total pencils didthe students bring in? Show your thinking with numbers, sketches, or words.CHALLENGE(5 8 10) (10 8 5) 800800 pencilsEquationBridges in Mathematics Grade 4 Home ConnectionsAnswer, labeled with correct units2 The Math Learning Center mathlearningcenter.org

Unit 1 Module 1Answer KeySession 4NAME DATEModels for Multiplication page 1 of 2Write a story situation to go with each multiplication model.Multiplication ModelexStoryKeith’s dog, Spot, ate 2 cans of dog food everyday for 3 days in a row. Spot ate 6 cans ofdog food in 3 days.2 3 610714212835Work will vary. Example:A grasshopper jumps 7times, and each jump is 6feet, for a total of 42 feet.427 6 422Work will vary. Example:There were 4 kids. Eachkid ate 4 brownies. Theyate 16 brownies in all.4 4 163Work will vary. Example:A number grid is 4 feetwide and 6 feet long. Itstotal area is 24 sq. ft.4 6 244Number of124Number of612 24Work will vary. Example:One ant has 6 legs. Forany number of ants,multiply by 6 to find thetotal number of legs.8(continued on next page)Bridges in Mathematics Grade 4 Home Connections3 The Math Learning Center mathlearningcenter.org

Unit 1 Module 1Answer KeySession 4NAME DATEModels for Multiplication page 2 of 2Multiplication ModelStory5Work will vary. Example:Five rows with 6 tiles perrow cover a floor. Thefloor is covered by 30 tiles.5 6 306 8 8 8 8 8 8 8 8 8Work will vary. Example:Mrs. Smith has 9grandchildren. She gaveeach grandchild 8. Shegave them 72 in all.8 9 727There are 4 rows of crayons in this box. Each row has the same number of crayons.How many crayons are in the box? Show your thinking.64 Crayons8Teachers collected 5 from each of the 130 fourth grade students at the beginning ofthe year for field trips. The first field trip cost 120. The second field trip cost 250.How much can they spend on the last field trip if they need to have 25 left over towash the bus? Show your thinking using words, numbers, or pictures. 255Bridges in Mathematics Grade 4 Home Connections4 The Math Learning Center mathlearningcenter.org

Unit 1 Module 1Answer KeySession 6NAME DATEModeling Multiplication & Division page 1 of 2For problems 1 and 2, complete the sketches and write the equations.4312565 4 20318 6 3Copy one equation from above and write a story problem to go with it.exI bought 5 packs of pencils. Each pack had 4 pencils in it. How many pencilsdid I get? (5 4 20)Work will vary.Complete the number line and ratio table.452 53 54 55 56 51015202530123456736912 151821 248(continued on next page)Bridges in Mathematics Grade 4 Home Connections5 The Math Learning Center mathlearningcenter.org

Unit 1 Module 1Answer KeySession 6NAME DATEModeling Multiplication & Division page 2 of 26Mr. Still’s class has music for 50 minutes and then independent reading for 20 minutes.Music starts at 8:30. What time does Mr. Still’s class finish independent reading?9:407Ms. Ford’s class starts art at 9:30 and finishes at 10:15. They spend twice as muchtime in math class. If they start math at 1:10, what time do they finish math?2:40Bridges in Mathematics Grade 4 Home Connections6 The Math Learning Center mathlearningcenter.org

Unit 1 Module 2Answer KeySession 2NAME DATEFactors & Tea Lights page 1 of 21Imagine using 48 tiles to build each rectangle below. Write in the missingdimensions on the rectangle sketches.4814824236488481648124248The factors of 48 are:481 and3 ab242 and124 and68 and316 andIs 48 a prime number or a composite number?CompositeHow do you know?Work will vary. Example:It has many factors.4Study your list of factors for 48. What patterns do you observe?Work will vary. Example:If you double one factor, you halve the other to makefactor pairs. You can have one odd and one even factoror two even factors. You cannot have two odd factors ina factor pair.(continued on next page)Bridges in Mathematics Grade 4 Home Connections7 The Math Learning Center mathlearningcenter.org

Unit 1 Module 2Answer KeySession 2NAME DATEFactors & Tea Lights page 2 of 25Write the missing parts on this number line:3 721683 243 93 27103 113 33301236Tea light candles are being packaged 6 to a box. Fill in the table:Number of Boxes45678910Total Number ofCandles24303642485460For the problems below, use numbers, words, or labeled sketches to explain your answers.7Jane has 7 tea light candles. Aisha has 5 times more candles than Jane. How manycandles does Aisha have?35 candles8Theo has 50 tea light candles. Madeline has half as many candles as Theo. Howmany candles does Madeline have?25 candlesBridges in Mathematics Grade 4 Home Connections8 The Math Learning Center mathlearningcenter.org

Unit 1 Module 2Answer KeySession 4NAME DATEMultiplication Fact Strategies page 1 of 2Doubles Plus One Set FactsWhen one of the factors is 3, you can think about the Doubles fact, and then add one more set of thenumber being doubled. For example, 6 3 is 6 doubled (12) plus one more set of 6.3 6 (2 6) 612 6 187 3 (7 2) 1414 7 21You can use this strategy with larger numbers, too:3 25 1(2 25) 2550 25 75150 3 300 150 450Shade in the areas and complete the equations.3 5 152(2 150) 1503 8 24If you had 2 boxes of 8 crayons and your teacher gave you another box of 8 crayons,how many crayons would you have?24 crayons3Cody bought 2 bags of 5 apples. He already had 1 bag of 5 apples at home. Howmany apples does Cody have in all?15 apples4Write a story problem for a Doubles Plus One Set ( 3) fact.Work will vary.(continued on next page)Bridges in Mathematics Grade 4 Home Connections9 The Math Learning Center mathlearningcenter.org

Answer KeySession 4Unit 1 Module 2NAME DATEMultiplication Fact Strategies page 2 of 2Tens Facts5Circle the groups of 10 in the arrays below, and solve the equations.707 10 9010 9 When you understand place value, multiplying larger numbers by 10 can be easy, too.10 25 250670 10 6700Half-Tens FactsWhen one of the factors is 5, you can multiply the other factor by 10 and then divide the answer in half.6Fill in the blanks below.Half-Tens Facts5 6 307896 10 60Half of 60 is30n 10 512345610203040506051015202530Max had 6 dimes in his pocket. How much money did he have?60 Jose had 7 nickels in his pocket. How much money did he have?35 If Suzie bought 9 baskets with 5 large peaches in each basket, how many peachesdid she buy?45 peachesBridges in Mathematics Grade 4 Home Connections10 The Math Learning Center mathlearningcenter.org

Unit 1 Module 2Answer KeySession 6NAME DATEMultiplying by 8 & 9 page 1 of 21Circle all the Double-Double-Doubles facts ( 8) in blue. Then solve them and use aregular pencil to write each product.2Circle all the Tens Minus One Set facts ( 9) in red. Then solve them and use aregular pencil to write each product.6 97 87 95 854365663403 94 89 68 89 9273 a9 432546481Pick one fact from above and write it here: .Work will vary.bColor in the array for that fact on the grid below.cLabel the array to show how you found the product, and use equations orwords to explain your work.Work will vary.(continued on next page)Bridges in Mathematics Grade 4 Home Connections11 The Math Learning Center mathlearningcenter.org

Unit 1 Module 2Answer KeySession 6NAME DATEMultiplying by 8 & 9 page 2 of 24Shade in and label the arrays of two more Double-Double-Double facts in the gridsbelow. Write an equation for each fact.Work will vary.5Shade in and label the arrays of two more Tens Minus One Set facts in the gridsbelow. Write an equation for each fact.Work will vary.Bridges in Mathematics Grade 4 Home Connections12 The Math Learning Center mathlearningcenter.org

Unit 1 Module 3Answer KeySession 2NAME DATEMultiples, Flowers & Cards page 1 of 212When you count by a number, you are naming the multiples of that number. Forexample, if you skip-count by 5s, you are naming the multiples of 5: 5, 10, 15, 20, 25,and so on. In each sequence below, fill in the missing multiples.ex20 25, 30,355, 10, 15, ,a9 12, 15, 18, ,21 243, 6, ,b6, ,12 18, ,24 30c9, 18, ,27 36, 45, ,54 63Circle all the multiples of the number in each 19ace2567814 21 10722 33 21 14 16 42 35321 35 18 36 44 12 29Fill in the missing numbers. 9 93 94 42 67 881271612563769314 530 4366 26 46 86 166 3212244896192824 2 412(continued on next page)Bridges in Mathematics Grade 4 Home Connections13 The Math Learning Center mathlearningcenter.org

Unit 1 Module 3Answer KeySession 2NAME DATEMultiples, Flowers & Cards page 2 of 24Four friends were making cards to sell at the holiday sale. Each friend made 9 cards.They put all their cards together and then bundled them in groups of 6 cards to sell.How many bundles of 6 cards did they make? Show all your work.6 bundles5Zack measured a rectangular garden at the park. The longer sides eachmeasured 15 feet and were 3 times longer than the shorter sides. If Zack walked allthe way around the garden, how far did he walk?CHALLENGE40 feetBridges in Mathematics Grade 4 Home Connections14 The Math Learning Center mathlearningcenter.org

Answer KeySession 4Unit 1 Module 3NAME DATEArrays & Factors page 1 of 21Draw and label a rectangular array to show two factors for each number. Do not use 1 asa factor. Then write the fact family that goes with each array that you draw.exa 16Work will vary.Example:84822484288 4 28 2 4 332 2b 18Work will vary.Example: 62 8 163 6 188 2 166 3 1816 8 218 6 316 2 818 3 6List all the factors of each number below.ex12b17d91, 2, 3, 4, 6, 121, 171, 3, 9Circle the prime number(s) in problem 2.aa16c24e361, 2, 4, 8, 161, 2, 3, 4, 6, 8, 12, 241, 2, 3, 4, 6, 9, 12, 18, 3617Draw a square around the square number(s) in problem 2.9, 16, 36(continued on next page)Bridges in Mathematics Grade 4 Home Connections15 The Math Learning Center mathlearningcenter.org

Unit 1 Module 3Answer KeySession 4NAME DATEArrays & Factors page 2 of 24Is the number 25 prime or composite? How do you know?Composite. Work will vary, Example: it has 3 factors. 1, 5, 25.5Judy has a collection of 30 stamps. She can divide the stamps into 2 equal groups of 15stamps. What are two other ways she could divide the stamps into equal groups?Work will vary, Example:3 groups of 10 (or 10 groups of 3)5 groups of 6 (or 6 groups of 5)15 groups of 26Judy’s brother Sam has a collection of 96 comic books. What are the tenways Sam could divide his comic books into equal groups?CHALLENGE2 groups of 48 (48 groups of 2)3 groups of 32 (32 groups of 3)4 groups of 24 (24 groups of 4)6 groups of 16 (16 groups of 6)8 groups of 12 (12 groups of 8)Bridges in Mathematics Grade 4 Home Connections16 The Math Learning Center mathlearningcenter.org

Unit 1 Module 4Answer KeySession 1NAME DATEMeasuring Lengths page 1 of 212Would you use centimeters or meters to measure the length ofametersyour bedroom?bcentimetersyour big toe?cmetersa car?da mouse? centimetersethe gym? metersFill in the table below to convert between centimeters and meters. The first 2 rowsare done for you.centimeters (cm)meters (m)100 cm200 cm300 cm1m2m800 cm2500 cm3100 cm33m8m25 m31 mFor each of the following story problems, show your work using numbers, labeledsketches, or words. Write an equation, including the answer labeled with the correctunits, to represent your work.aChloe is a baby who is 24 inches tall. Her father is 3 times as tall as she is. Howmany inches tall is Chloe’s father?72 inches24 inches 3 72 inches(continued on next page)Bridges in Mathematics Grade 4 Home Connections17 The Math Learning Center mathlearningcenter.org

Unit 1 Module 4Answer KeySession 1NAME DATEMeasuring Lengths page 2 of 2bChloe’s dog, Wilson, is 27 inches long. Chloe’s hammock is 4 times as long asWilson. How many inches long is the hammock?108 inches27 inches 4 108 inches4A small table is 2 feet by 3 feet. A large table is twice as long and twice aswide as the small table. What is the area of the large table in square feet?CHALLENGE24 sq. ft.Bridges in Mathematics Grade 4 Home Connections18 The Math Learning Center mathlearningcenter.org

Unit 1 Module 4Answer KeySession 3NAME DATEMass & Volume Story Problems page 1 of 2For each problem, show your thinking with numbers, sketches, or words. Then write anequation that represents your work.1DJ and Tyler are watering plants. DJ uses 18 liters of water. Tyler uses 5 times asmuch water. How much water does Tyler use?18 liters 5 90 liters90 litersEquation2Answer, labeled with correct unitsChris and Jocelyn are building a patio out of bricks. Chris uses 23 kilograms ofbricks. Jocelyn uses 6 times as many kilograms. How many kilograms of bricksdoes Jocelyn use?23 kg 6 138 kg138 kgEquation3Answer, labeled with correct unitsThe mass of one bouncy ball is 14 grams. Tracy has 8 bouncy balls. What is themass of all 8 bouncy balls?14 g/ball 8 balls 112 g112 gramsEquation45Answer, labeled with correct unitsTrue or False?aTA liter is 1,000 times as much as a milliliter.bA gram is 300 times smaller than a kilogram.FcFThere are 99 centimeters in a meter.Fill in the bubble to show which unit you would use to measure the amount of waterin a very large inued on next page)Bridges in Mathematics Grade 4 Home Connections19 The Math Learning Center mathlearningcenter.org

Unit 1 Module 4Answer KeySession 3NAME DATEMass & Volume Story Problems page 2 of 267Fill in the bubble to show which unit you would use to measure the mass of a mouse.!centimeter!!gramliter!kilogramAnna has 15 stickers. Rosa has 3 times as many stickers as Anna. Dawnhas 3 times as many stickers as Rosa. Sara has 17 fewer stickers than Dawn.CHALLENGEaHow many stickers does Rosa have? Show your work.45 stickersbHow many stickers does Dawn have? Show your work.135 stickerscHow many stickers does Sara have? Show your work.118 stickersBridges in Mathematics Grade 4 Home Connections20 The Math Learning Center mathlearningcenter.org

Unit 2 Module 1Answer KeySession 2NAME DATEMeasuring in Centimeters page 1 of 3Note to FamiliesThis Home Connection asks students to measure common items at home in centimeters. If you have a ruler or tape measureat home marked in centimeters, have your child use it. If not, you can cut out the strips below and tape or glue themtogether to create a measuring tape.Measuring in CentimetersFind a ruler or tape measure that is marked in centimeters. You can also cut out thestrips below and tape or glue them together to make your own measuring tape.2By yourself or with a family member or two, measure the items listed on theworksheet and record your 1525354555657585960glue or tape glue or tape glue or tape glue or tape glue or tape1(continued on next page)Bridges in Mathematics Grade 4 Home Connections21 The Math Learning Center mathlearningcenter.org

Answer KeyBridges in Mathematics Grade 4 Home Connections22 The Math Learning Center mathlearningcenter.org

Unit 2 Module 1Answer KeySession 2NAME DATEMeasuring in Centimeters page 2 of 3Please measure the following objects in centimeters and record the results.Object To Be Measured1width of your bed2width of a doorMeasurement in CentimetersWork will vary, example:102 cmWork will vary, example:104 cm3height from thefloor to the seatof your favorite chair4length of a telephoneor cell phone5dimensions of yourfavorite book (lengthand width)6width of your refrigeratorWork will vary, example:46 cmWork will vary, example:15 cmLorettalsand PaWork will vary, example:14 cm 21 cmWork will vary, example:102 cm7dimensions of a towel(length and width)8length of yourtoothbrushWork will vary, example:75 cmWork will vary, example:19 cm(continued on next page)Bridges in Mathematics Grade 4 Home Connections23 The Math Learning Center mathlearningcenter.org