5th grade mathematicselementarymath.dmschools.org/.../13224522/g5u3ex.docx · web viewdeveloping...

$: 5th Grade Mathematicselementarymath.dmschools.org/.../13224522/g5u3ex.docx · Web viewDeveloping fluency with addition and subtraction of fractions, and developing understanding$
5th Grade Mathematics

Unit 3: Addition and Subtraction of FractionsTeacher Resource Guide

2012 - 2013

In Grade 5, instructional time should focus on three critical areas:

1. Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions (limited to unit fractions divided by whole numbers and whole numbers divided by unit fractions);

Students apply their understanding of fractions and fraction models (set model, area model, linear model) to represent addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators (¼ + 2/8 = ¼ + ¼). They develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them. Students also use the meaning of fractions and the relationship between multiplication and division to explain why the procedures for multiplying and dividing fractions make sense.

2. Extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations;

Students develop understanding of why division procedures work based on place value and properties of operations. They are fluent with multi-digit addition, subtraction, multiplication, and division. They apply their understandings of models for decimals, decimal notation, and properties of operations to add and subtract decimals to hundredths. Students use the relationship between decimals and fractions, and the relationship between decimals and whole numbers (i.e., a decimal multiplied by anpower of 10 is a whole number) to understand and explain why procedures for multiplying and dividing decimals make sense. They compute products and quotients of decimals to hundredths efficiently and accurately.

3. Developing understanding of volume.Students understand that volume is an attribute of three-dimensional space and can be measured by finding the total number of same-size units of volume required to fill the space without gaps or overlaps. They understand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume. They decompose three-dimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of cubes.

5th Grade Mathematics 2012 - 2013

Unit Time Frame Testing WindowTR

IMES

TER

1 1: Multi-Digit Multiplication and Division 7 weeks 8/22 – 10/12 October 12

2: Measurement/Geometry4 weeks 10/15 – 11/9 November 9

TRIM

ESTE

R 2 3: Addition and Subtraction of Fractions

8 weeks 11/12 – 1/18 January 18

4: Decimals 8 weeks 1/22 – 3/14 March 14

TRIM

ESTE

R 3

5: Multiplication and Division of Fractions9 weeks 3/25 – 5/30 May 30

DMPS Wiki: http://dmps-mathematics.wikispaces.com/

5th Grade 2012-2013 Page 2

http://dmps-mathematics.wikispaces.com/

Unit 3: Addition and Subtraction of Fractions November 24- January 18 (8 weeks)

Big Ideas Essential QuestionsBenchmark fractions help us estimate when adding or subtracting so we can decide if an answer is reasonable.

Why do we use benchmark fractions?

Finding a common denominator makes all the fraction parts the same size so we can add or subtract them.

Why do we find a common denominator?

Identifier Standards Mathematical Practices

STAN

DARD

S

5.NF.2

5.MD.2

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

1) Make sense of problems and persevere in solving them.

2) Reason abstractly and quantitatively.

3) Construct viable arguments and critique the reasoning of others.

4) Model with mathematics.

5) Use appropriate tools strategically.

6) Attend to precision.

7) Look for and make use of structure.

8) Look for and express regularity in repeated reasoning.

5.NF.1

4.NF.1

4.NF.2

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc) / bd.)

Explain why a fraction a/b is equivalent to a fraction (n×a)/(n×b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.



Identifier Standards Bloom’s Skills Concepts

STAN

DARD

S

5.NF.2

5.MD.2

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

Apply (3)

Apply (3)

Evaluate (5)

Solve (word problems, add/sub fraction including unlike denominators)

Use (benchmark fractions & number sense to estimate

Assess (reasonableness of answers)

fractionsdenominatorsnumerators

benchmark fractions

5.NF.1

4.NF.1

4.NF.2

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc) / bd.)

Explain why a fraction a/b is equivalent to a fraction (n×a)/(n×b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Apply (3) Add/Sub fractionsunlike denominators

Add/SubtractFractions (unlike denom)Find equivalent fractions

Transition Plan 2012-2013: Addition and subtraction of fractions with unlike denominators rely heavily on students’ understanding of equivalent fractions. Therefore, the 4 th grade standard relating to equivalent fractions is included as a supporting standard. Instruction will begin with comparing fractions and equivalent fractions before moving into fraction computation.



Instructional Strategies for ALL StudentsCritical Readings for Teachers Prior to Instruction –

Wiki: Math Expressions, Teacher Edition Volume I, Houghton Mifflin, 2009, p. 411L-NWiki: Teaching Student-Centered Mathematics Grades 3-5, Van de Walle & Lovin, Pearson, 2006, p. 144-157 (These pages are included with the additional activities on the wiki)Wiki: Focus in Grade 5 Teaching with Curriculum Focal Points, NCTM, 2009, p. 35-48

Comparing Fractions – Students have a tremendously strong mind-set about numbers that causes them difficulties with the relative size of fractions. In their experience, larger numbers mean “more.” The tendency is to transfer this whole-number concept to fractions: Seven is more than four, so sevenths must be bigger than fourths. The inverse relationship between number of parts and size of parts cannot be told but must be a creation of each student’s own thought process. Telling students that “larger bottom numbers mean smaller fractions” is not only inappropriate but also dangerous to students’ conceptual understanding. Instead students must have many opportunities to make sense of the size of fractions in comparative situations through comparison tasks over time. Many times a standard algorithm is taught for comparing fractions. The usual approach is to find a common denominator. This rule can be effective in getting correct answers but requires no thought about the size of the fractions. If students are taught the common denominator rule before they have had the opportunity to think about the relative size of various fractions, there is little chance that they will develop any familiarity with or number sense about fraction sense. Number sense about fractions is critical to students’ conceptual understanding of operations with fractions which begin in 4th grade and continue through the middle grades. For these reasons, the recommended strategies for instruction in comparing fractions are benchmark fractions, focus on numerator or denominator, and common denominators. (Adapted from Van de Walle, 2006.) Instructional tasks to support students’ conceptual understanding for comparing fractions are listed on p. 6 of this guide and on the wiki.

Equivalent Fractions – The general approach to helping students create an understanding of equivalent fractions is to have them use models to find different names for a fraction. This is typically followed with instruction of an algorithm. However, models alone often do not help students develop the conceptual understanding of equivalent fractions and algorithms are often taught too soon. Rather, it is recommended that multiple tasks are given to students with a focus on finding multiple ways to create fraction equivalencies and reason about the patterns. When students understand that fractions can have more than one name, they can begin to figure out a method for finding equivalent names. Therefore, the recommended strategies for instruction in equivalent fractions are to provide multiple tasks for students to develop conceptual understanding of equivalence followed by instruction of the algorithm. (Adapted from Van de Walle, 2006.) Instructional tasks to support students’ conceptual understanding for equivalent fractions are listed on p. 6 of this guide and on the wiki.

Assess reasonableness of an answer – The ability to assess the reasonableness of an answer is a priority for operations with fractions. This is often viewed as an estimation skill, but can quickly be reduced to rounding. Rounding is the primary estimation strategy in the elementary grades because of an emphasis on whole numbers. However, when adding and subtracting fractions, it is also critical for students to learn how benchmarks can be used to assess the reasonableness of an answer. The use of benchmarks to estimate can lead to an important discussion on whether an estimate is an overestimate of the actual answer or an underestimate. For example, 3/8 + 9/10 could be estimated to 1 ½ since 3/8 is close to ½ and 9/10 is close to 1 whole. This is an example of overestimation because both numbers were increased to the closest benchmark, therefore the actual answer would be less than 1 ½. This is a very helpful skill to develop with students prior to their work with computation of fractions.Addition and Subtraction of Fractions with Unlike Denominators – It is important for students to learn the traditional algorithm to add and subtract fractions with unlike denominators. However, it is also beneficial for students to begin their fraction computation work with informal exploration. Informal exploration with friendly fractions and fraction models provide students opportunities to use their developing understanding of equivalent fractions to reason about combining fraction amounts. This informal exploration will benefit students as they move to more formal instruction with the algorithm for common denominators. Therefore, instruction for addition and subtraction of fractions will begin with an informal exploration followed with instruction of the traditional algorithm. Instructional tasks to support students’ conceptual understanding for adding and subtracting fractions are listed on p. 6 of this guide and on the wiki.



Routines/Meaningful Distributed PracticeDistributed Practice that is Meaningful and PurposefulPractice is essential to learn mathematics. However, to be effective in improving student achievement, practice must be meaningful, purposeful, and distributed.

Meaningful: Builds on and extends understanding Purposeful: Links to curriculum goals and targets an identified need based on multiple data sources Distributed: Consists of short periods of systematic practice distributed over a long period of time

Routines are an excellent way to achieve the mandate of Meaningful Distributed Practice outlined in the Iowa Core Curriculum.. The skills presented during routines do not necessarily reinforce the lesson concept for that day. Routines may be used to address a need for small increments of exposure to a skill or review of skills already taught. Routine activities may be repeated several days in a row, allowing for a build-up of conceptual understanding, or can be visited and re-visited over a period of time. Routines can be inserted as the schedule allows; in short intervals throughout the day or as a lesson opener or closer. Selection of the routine should be made based on informal teacher observation and formative assessments.

Concepts taught through Meaningful Distributed Practice during Unit 3:

Skill Standard ResourceMulti-digit multiplication 5.NBT.5Whole-number division 5.NBT.6Interpreting remainders 4.OA.3 Expressions: Unit 7; Unit 1 Resource Guide Problem Bank p. 14-15Classify 2-D figures based on properties 5.G.4Convert among different-sized standard measurement units 5.MD.1Other skills students need to develop based on teacher observations and formative assessments.



Lesson Progression

Lessons Teacher Directions Teacher’s EditionPages

StandardsAddressed

Wiki: Part and Whole Tasks Activity Do Part and Whole Tasks activity for several days. Combine with Lesson 1. See teacher notes for the activity on Wiki.

5.NF.2, 5.NF.1Math Expressions: Unit 5, Lesson 1, Activities 1-2 412 5.NF.2, 5.NF.1Wiki: Zero, One-Half, or One Activity The three activities are to be done simultaneously for

several days. See teacher notes for each activity on Wiki. Lesson 2 should be done after several days of the activities.

4.NF.7Wiki: Close Fractions Activity 4.NF.7Wiki: About How Much? Activity 4.NF.7Math Expressions: Unit 5, Lesson 2, Activities 1-2 422 4.NF.7Wiki: Ordering Unit Fractions Activity The two activities are to be done for several days. Combine

with Lessons 3, 4, and 5. See teacher notes for the activities on Wiki.

5.NF.1Wiki: Choose, Explain, Test Activity 5.NF.1Math Expressions: Unit 5, Lesson 3, Activities 1-2 430 5.NF.1Math Expressions: Unit 5, Lesson 4, Activities 1-2 438 5.NF.2Math Expressions: Unit 5, Lesson 5, Activity 1 442 4.NF.2Wiki: Mixed Numbers and Improper Fraction Activity Do Mixed Numbers and Improper Fractions activity before

Lesson 6. See teacher notes for the activity on Wiki.Continue the activity throughout the remainder of the lessons in this unit.

4.NF.3cMath Expressions: Unit 5, Lesson 6, Activities 1-2 450 4.NF.3cMath Expressions: Unit 5, Lesson 7, Activities 1-2 456 5.NF.1Math Expressions: Unit 5, Lesson 8, Activities 1-2 462 5.NF.1Math Expressions: Unit 5, Lesson 9, Activities 1-3 468 5.NF.2Wiki: Different Fillers Activity The four activities are to be done prior to Lessons 11-13.

The activities explore fraction equivalency prior to teaching the algorithm.

4.NF1Wiki: Divide and Divide Again Activity 4.NF1Wiki: Missing Number Equivalencies Activity 4.NF1Wiki: Slicing Squares Activity (area model) 4.NF1Math Expressions: Unit 5, Lesson 11, Activities 1-2 482 4.NF1Math Expressions: Unit 5, Lesson 12, Activities 1-2 492 4.NF1Math Expressions: Unit 5, Lesson 13, Activities 1-2 500 4.NF1Wiki: First Estimates Activity Do First Estimates activity before Lessons 14-15. Continue

having students estimate sums and differences before solving a problem. Compare actual answer to estimate to determine reasonableness of answer.

Math Expressions: Unit 5, Lesson 14, Activities 1-2 508 5.NF.2, 5.NF.1Math Expressions: Unit 5, Lesson 15, Activities 1-2 518 5.NF.2, 5.NF.1

Resource Guide: Problem Bank, use fractions in problems for continued practice in add/sub with unlike denominator problems. Focus should be problems in context.

Student will need a lot more practice solving add/sub with unlike denominator problems. Use the Problem Bank onp. 8-18 of this guide for problems in context. Continue to distribute add/sub with like and unlike denominators as review all year!!!!

5.NF.2, 5.NF.1



Math Expressions Activities(use as centers, re-teaching/extension support, etc.)

Activity Standards Activity StandardsActivity Card 5-2 Intervention 4.NF.7 Activity Card 5-11 Intervention, On-Level 4.NF.1Activity Card 5-6 Intervention, On-Level, Challenge 4.NF.3c Activity Card 5-13 Intervention, On-Level,

ChallengeActivity Card 5-7 Intervention 5.NF.1 Activity Card 5-14 Intervention 5.NF.1Activity Card 5-8 Intervention, On-Level 5.NF.1Activity Card 5-9 On-Level 5.NF.2Activity Card 5-15 On-Level, Challenge 5.NF.2, 5.NF.1



Addition/Subtraction Problem BankJoin, Result Unknown / Add to, Result Unknown

Tommy was on page ____ of his book. Then he read ____ more pages. How many pages did Tommy read in all?

Susan collected cans for recycling. She had ____ cans collected already. Then she collected ____ more. How many cans did she collect all together?

Liz has a comic book collection. ____ of her books feature Super Girl. Josh gave her ____ more Super Girl books from his collection. How many Super Girl books does Liz have now?

At Mr. Beal’s fruit stand. There were ____ apples at the stand when he opened. He added ____ more apples to his stand. What is the total number of apples?

A zoo got ____ otters. They then got ____ more otters from another zoo. How many otters does the zoo have now?

Dennis earned money mowing lawns over the summer. He had earned ____ dollars and got _____ more dollars from Ms. Kats for mowing her lawn. How much money does he have now?

There were ____ people in the audience when the concert began. After the first song, ____ more people came in. How many people are in the audience now?

Mr. King had a student council meeting. ____ third graders came in first, then ____ fourth graders came, and finally ____ fifth graders came. How many students came to the meeting?

Jim is selling raffle tickets. He sold ____ tickets. On Monday he sold ____ more. How many tickets did he sell all together?

Central School was having a show. ____ people were sitting in the auditorium. ____ more arrived. How many people were there to see the show? Jerry wanted to buy something for lunch. He spent $_____ and then spent $____ more to get a drink. How much money does Jerry spend in all?

Ji Young had ____ sea shells. Emma gave her ____ more. How many sea shells does Ji Young have now?



Join, Change Unknown / Add to, Change Unknown

Sam had ____ baseball cards. He went to a card show and got some more cards for his collection. Now he has ____ cards. How many cards did Sam buy at the card show?

David is making a comic book. Last week, he finished the first ____ pages. This week, he finished some more pages. He has finished ____ pages in all. How many pages did he draw this week?

Susan collected cans for recycling. She had ____ cans collected already. Then she collected some more. She had ____ at the end of the day. How many more did she collect?

The Robinsons drove ____ miles the first week of their two week trip. Altogether they drove ____ miles. How far did they drive the second week?

Reba had $____. She earned some more money babysitting. Now she has $____. How much did she earn babysitting?

There were ____dogs at the park. Within 30 minutes, more dogs came. Now there are ____ dogs at the park. How many more dogs came to the park.

Zack has ____ songs oh his MP3 player. Luke downloaded some more songs onto Zack’s player. Now he has ____ songs. How many songs did Luke download?

Phillip has ____ DVDs. His sister went through her collection and gave him some. Now he has ____ DVDs. How many did his sister give him?

There were ____ students on the playground. Some more came later. Now there are ____ students on the playground. How many students came later?

Sara has $____. How much more money does she need to save to buy a new t.v. for $____?



Join, Start Unknown / Add to, Start Unknown

Maggie had some pairs of socks. Then she bought ____ new pairs of socks. She has ____ pairs of now. How many pairs of socks did she have to start with?

Sam had some baseball cards. Then he bought ____ more. Now he has ____ cards. How many cards did same start with?

Allegra is building a model from popsicle sticks. Yesterday, she used some popsicles sticks to start her model. Today she used ____popsicles sticks to finish it. Altogether, Allegra used ____ popsicle sticks. How many did she use yesterday?

Dakota had some money. Then she earned $____ at her family garage sale. Now she had $____ . How much money did she start with?

Elsie found some coins in her drawer. She found ____ more coins while cleaning her room. How she has ____ coins. How many coins did she have to start?

Some students left the lunchroom to go to the playground. ____ more students came later. There are ____ students when everyone arrived. How many students went to the playground first?

Tommy had some sheets of paper. He bought ____ more sheets of paper. He now has ____ sheets of paper. How many sheets of paper did he start with?

Greg is been reading a book for class. Yesterday he read ____ more pages. Now he is on page ____. How many pages had Greg read before yesterday?

Sam had some baseball cards. He went to a card show and got ____ more cards for his collection. Now he has ____ cards. How many cards did Sam start with?

David is making a comic book. Last week, he finished the first pages. This week, he finished ____ more pages. He has finished ____ pages in all. How many pages did he have finished the first week?



Separate, Result Unknown / Take from, Total Unknown

There were ____ children on the playground. ____ children came in first. How many children were still outside?

At the start of the track meet, ____ people were in the stands. Then it started to rain and ____ people left. How many people were still in the stands?

Samir had ____ marbles. He gave ____ of them to his little sister. How many marbles does Samir have now?

Samantha collected ____ basketball cards. She traded ____ of them for baseball cards. How many basketball cards does Samantha have left?

A thrift store had ____ hats for sale. A costume designer came in and bought ____ of the hats. How many hats were left?

Kim had ____ stickers. She gave ____ away. How many stickers did she have left?

Rodney had ____ butterflies in his collection. He gave ____ to his friend Jin. How many butterflies does he have now?

Sara had $____ to buy lunch. She spent $____. How much does she have left?

Kristy had ____seeds to plant. She planted ____of them. How many seeds does she still have to plant?

Raj brought $____to the deli. He spent $____ on a turkey sub. How much money did he have left?

Manuel started reading a book with ____ pages. Today he read ____pages. How many pages does Manuel have left to read?

Alicia had ____ coins in her collection. She gave ____to her little brother. How many coins does she have now?

Sam had ____ baseball cards. He went to a card show and sold ____ cards. How many cards does Sam have now?



Separate, Change Unknown / Take from, Addend Unknown

Yolanda had $____ . Then she spent some money on a magazine. She has $____ left. How much did she spend on the magazine?

Ms. Pena brought ____ juice boxes to the class picnic. She gave a juice box to each student at the picnic. She had ____ juice boxes left over. How many students attended the picnic?

Marlena had ____ baseball cards. Her brother gave her some more. Now she has ____ baseball cards. How many did her brother give her?

John had $____ in his savings account. After purchasing a new mountain bike, he had $____ left in his account. How much did he spend on the mountain bike?

____ third graders were playing football at recess. Some left to go play basketball. Now there are ____ third graders playing football. How many left to go play basketball?

There were ____ children on the playground. Then the second-graders came out to play. Now there are ____ children on the playground. How many second graders came?

At the start of the track meet, ____ people were sitting in the stands. Then it started to rain. At the end of the meet, ____ people were still in the stands. How many left when it started to rain?

Samir had ____ marbles. He gave some of them to his little sister. Now he has ____. How many marbles did Samir give to his sister?

Samantha collected ____ basketball cards. She traded some of them for baseball cards. Now she has ____ basketball cards. How many basketball cards did Samantha trade?

A thrift store had ____ hats for sale. A costume designer came in and bought some of the hats. Now there are____ hats left? How many did the costume designer buy?

Jan had ____ flowers. She gave some away. After she gave away the flowers she still had ____ flowers. How many flowers did she give away?



Separate, Start Unknown / Take from, Start Unknown

Ramona made some bracelets. She gave ____ of the bracelets away. Now Ramona has ____ bracelets left. How many bracelets did Ramona make?

Jan had some flowers she wanted to share. She gave away ____ flowers. After she gave away the flowers she still had ____ flowers left. How many flowers did she have to start with?

The furniture store sold ____bookcases in one week. At the end of the week, the store had ____bookcases left. How many bookcases did the store have at the start of the week?

Raj had some CDs. He gave ____ CDs to his friend. How he has ____ CDs. How many CDs did Raj start with?

Joan had some new pencils. She lost ____ of them and has ____ left. How many new pencils did Joan have to start with?

Today the hardware store sold ____ boxes of nails. At the end of the day, ____ boxes were left. How many boxes of nails did the hardware store have at the beginning of the day?

Bob has some minutes on his cell phone plan. He used ____ minutes so far this month. He has ____ minutes left. How many minutes did he start with?

The Tiger Cheerleading squad had some t-shirts to throw out during games. They threw ____ at the first game and had ____ left. How many shirts did they have to start?

Ellen has some money left on her credit card. She paid $____ . Now she has $____ left on her card. How much did Ellen start with?

Zoey had some Legos. She gave ____ away. She now has ____ left. How many Legos did she start with?

Yolanda had some money. She spent $____ on a magazine. She has $____ left. How much did she have to start with?



Part/Part/Whole, Whole Unknown / Put together-Take apart, Total Unknown

The two Scout troops went on a field trip. There were ____ Girl Scouts and ____ Boy Scouts. How many Scouts went on the trip?

At the park, ____ children are playing tag and ____ are playing soccer. How many children are playing tag or soccer?

There were ____woodwind players and ____brass players in the marching band. How many band members were there in all?

Trey has ____ Tootsie Rolls from the parade. Sam has ____ Tootsie Rolls. How many Tootsie Rolls do they have together?

Our class has ____ boys and ____ girls. How many students are in our class?

____ men and ____ women were at the football game. How many people were at the football game?

King school is having an awards ceremony. The school has ____ third-graders and ____ fourth-graders. How many awards will they need if each third and fourth grader get one?

Ali has ____ photos of her pets and ____ photos of her family. How many photos does Ali have all together?

Juanita counted all of her crayons. ____ were broken and ____ were not. How many crayons did she have in all?

The Science Club went to the planetarium. ____ students rode in cars. ____ students took the bus. How many students went to the planetarium?

On Saturday, ____ people rode the Ferris wheel in the morning and ____ rode in the afternoon. How many people rode the Ferris wheel that day?

Joe went shopping at the store. He spent $____on markers and $____on crayons. How much money did he spend?

Rosa went on vacation with her family. She traveled ____ miles by car and ____ miles by plane. How far did she travel?



Part/Part/Whole, Part Unknown / Put together, Take apart, Addend Unknown

Juanita counted all of her crayons. Some were broken and some were not. She had ____ crayons in all. ____ crayons were not broken. How many were broken?

Waleed barbecued some turkey burgers. He had ____ buns. He put a burger on each bun and had ____ left over. How many burgers did he cook?

The drama club sold too many tickets to the play. ____ people bought tickets. ____ people had to stand because there weren’t enough seats. How many seats are in the auditorium?

The ____ members of the Science Club went to the planetarium. ____ students rode in cars. The rest of the students took the bus. How many students rode in cars?

On Saturday, ____ people rode the Ferris wheel at the fair. Of these people, ____ rode during the morning. How many people rode during the rest of the day?

There are ____ notebooks on the store shelf. There are ____ yellow notebooks, and the rest are purple. How many purple notebooks are on the shelf?

Joe spent $____ at the store. He spent $____on markers and the rest on crayons. How much did he spend on crayons?

There are ____students at Prairie Hill School. Of these students, ____ are in the elementary school. The rest are in middle school. How many students are in the middle school?

There were ____ trophies in the trophy case. ____ were tennis trophies, the rest were soccer. How many were soccer trophies?

The teacher has ____ student folders. ____ of them are red, the rest are blue. How many folders are blue?

Dana picked red and green apples. She picked a total of ____ apples. If ____ were red, how many were green?



Compare, Different Unknown / Compare, Difference Unknown

Ms. Molina has ____ paperback books and ____ hardcover books. How many more paperback books does she have?

A furniture store had ____ tables and ____ chairs. How many more chairs did the store have than tables?

Natalie and Olivia are participating in the roadside clean-up day. Natalie’s team collected ____ bags of trash. Olivia’s team collected ____ bags of trash. How many more bags did Natalie’s team collect than Olivia’s team?

____ fans attended Friday’s game. ____ fans attended Saturday’s game. How many fewer fans attended Friday’s game than Saturday’s game?

____ people attended the school musical on Friday night. ____ people attended the musical on Saturday afternoon. How many more people attended the Saturday show than the Friday show?

The Cruz family traveled ____ miles to the beach and ____ miles to the campground. About how many more miles did they travel to the beach than to the campground?

Toshi lives ____ miles from her grandmother and ____ miles from her cousin Kioko. How much farther does Toshi live from her cousin than she does from her grandmother?

Ann’s family went on vacation for a week and ____days. Tye’s family went on a vacation for ____weeks. How many days longer was Tye’s vacation than Ann’s?

Last week, a clothing store sold 113 short sleeve shirts, 209 long sleeve shirts, ____ pairs of pants, and ____ pairs of shorts. How many more pants did they sell than shorts?

Dora has a dog that is ____ inches high. Sam has a dog that is ____ feet high. Whose dog is taller? How much taller?

A train traveled ____ miles. A second train traveled ____ miles. How much farther did the second train travel?



Compare, Compare Quantity Unknown / Compare, Bigger Unknown

On Tuesday, the workers at Tidy Pet Salon groomed ____ dogs. On Wednesday they groomed ____ more dogs than on Tuesday . How many dogs did they groom on Wednesday?

Frankie’s dog weighs ____ pounds. His cat weighs ____ less pounds than his dog. How much does his cat weigh?

Jordan has ____ baseball cards. Hakeem has ____ less than Jordan. How many cards does Hakeem have?

Andy has ____ crayons in his box. Mandi has ____ more crayons in her box. How many does Mandi have in her box?

Jackson had $____. Jazlyn had $____ more than Jackson. How much does Jazlyn have?

Brent has ____cows. Willie has ____fewer cows. How many cows does Willie have?

Ms. Molina has ____ paperback books and ____ fewer hardcover books than paperback books. How many more hardcover books does she have?

A furniture store had ____ tables and ____ more chairs than tables. How many chairs does the store have?

Natalie and Olivia are participating in the roadside clean-up day. Natalie’s team collected ____ bags of trash. Olivia’s team collected ____ more bags of trash than Natalie’s team. How many bags did Olivia’s team collect?

____ fans attended Friday’s game. ____ more fans attended Saturday’s game than Fridays game. How many fans attended Saturday’s game?

____ people attended the school musical on Friday night. ____ less people attended the musical on Saturday afternoon than on Friday. How many people attended the Saturday show?

The Cruz family traveled ____ miles to the beach and ____ more miles to the campground than to the beach. About how many miles did they travel to the campground?



Comparison, Referent Unknown / Compare, Smaller Unknown

Zeke read ____ pages in his Social Studies book. He read ____ fewer pages than Kaya. How many pages did Kaya read?

Jing has ____ baseball pennants. She has ____ more pennants than Max. How many pennants does Max have?

Ahmed and Tray are playing air hockey. Ahmed has made ____goals. He has made ____more goals than Tray. How many goals has Tray made?

Linda has ____ movies. She has ____ more than Nancy. How many movies does Nancy have?

Zoe had $____ to spend for the school trip. She has $____ more than Cameron. How much money does Cameron have?

Sara is ____ inches tall. She is ____ taller than Sami. How tall is Sami?

On Tuesday, the workers at Tidy Pet Salon groomed some dogs. On Wednesday they groomed ____ dogs which was ____ more than on Tuesday . How dogs did they groom on Tuesday?

Rachel has ____ paperclips. She has ____ more than Sydney. How many paperclips does Sydney have?

Trisha has ____ CDs. She has ____ fewer CDs than her sister. How many CDs does her sister have?

Frankie’s dog weighs ____ pounds. His cat weighs ____ more pounds than his cat. How much does his cat weigh?

Jordan has ____ baseball cards. He has ____ less than Hakeem. How many cards does Hakeem have?

Lee has ____ leaves. He has ____ more leaves than Jenny. How many leaves does Jenny have?


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