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Addition word problems (1-3 digits)

Addition word problems with numbers under 1,000.

These grade 2 word problem worksheets are solved by forming addition equations involving 1, 2 or 3 digit numbers.   Sums are under 1,000.  Most questions have only 2 addends though some have 3.  

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Check Out These 50 Second-Grade Math Word Problems of the Day

Hunter has 47 baseball cards in his collection.

Opening your daily math lesson with a Math Word Problem of the Day is an excellent way to set the stage for learning. We all know that word problems are difficult for young learners to grasp, even when the mathematical operation portion of the problem is basic. Incorporate these second grade math word problems one day at a time at the start of your math block to build confidence, critical thinking skills, and a learning community!

Topics covered include addition, subtraction, multiplication, even/odd, three digit numbers, and time. All you need to do is post one of these second grade math word problems on your whiteboard or projector screen. Then let kids take it from there!

Want this entire set of second grade math word problems in one easy document? Get your free PowerPoint bundle by submitting your email here .

50 Second Grade Math Word Problems

1. trey has 5 squishy toys. he gets 4 more for his birthday. how many squishy toys does he have in all.

2. Stephanie brings donuts to give out to her classmates on her birthday. She brings in 8 powdered donuts, 8 glazed donuts, and 10 chocolate donuts. How many donuts did she bring in all?

3. Sara goes to the library. She is allowed to check out 10 books. She chooses 5 picture books and 3 chapter books. How many more books can she choose?

4. David plants 8 pineapple seeds, 5 strawberry seeds, and 2 blueberry seeds. How many seeds does he plant in all?

5. Paige has 10 crayons. Mike has 6 more crayons than Paige. Jon has 9 crayons. How many crayons do they have in all?

6. Jeff has 21 marbles in his collection. Eddie has 39 marbles in his collection. How many marbles do they have in all?

7. Vicki goes to the zoo and sees 8 flamingos. Next, she sees 15 ducks, before seeing 22 ibises. How many birds did she see in all?

8. Joshua sells 26 tickets to the school play. Nina sells 39 tickets to the school play. How many tickets did they sell in all?

9. The second grade goes on a field trip to the aquarium. There are 7 teachers, 62 girls, and 59 boys. How many people go on the field trip in all?

10. Some apples are in an apple orchard. 38 apples are picked. Now there are 52 left. How many apples were there to start?

11. Blake swam 18 laps on Monday. He swam 22 laps on Tuesday. He swam 27 laps on Wednesday. How many laps did he swim in all?

12. enzio reads for 25 minutes on monday. he reads for 33 minutes on tuesday. he reads for 35 minutes on wednesday. how many minutes does he read for in all.

13. Dana has 15 yummy cookies. He eats some of the cookies. Dana has 7 cookies left. How many cookies did Dana eat?

14. Eric had 12 toy cars. He gave 5 of the cars to his friend, Darren. How many toy cars does he have now?

15. Carolyn saw 15 beautiful birds in a tree. Some birds flew away. Now there are 4 birds in the tree. How many birds flew away?

16. Christina sold 32 boxes of girl scout cookies. Lea sold 44 boxes of girl scout cookies. How many more boxes did Lea sell than Christina?

17. Mimi has 23 more crayons than markers. She has 15 markers. How many crayons does she have?

18. Carrie has 36 pieces of candy. She gives 13 pieces to Tommy. How many pieces of candy does Carrie have left?

19. Dahlia has 28 dolls on a shelf. She moves some to her dollhouse. Now 15 dolls are on the shelf. How many did she move to the bed?

20. Jerry has 12 soccer balls. Bob had 17 soccer balls, but gave 8 of them to Phil. How many tennis balls do Jerry and Bob have now?

21. John has 54 pieces of candy. He eats 7 pieces on Monday. On Tuesday, he eats 11 pieces. On Wednesday, he gives 17 pieces away to friends. How many pieces of candy does he have left?

22. Maria has 29 marbles. Sam has 56 marbles. Rachel has 67 marbles. How many more marbles does Rachel have than Ella?

23. Steven buys 52 strawberries. He eats 12 of them for a snack. He eats 15 of them later that evening for dessert. How many strawberries are left?

24. Diana collects stickers. She has 48 stickers in an album. She buys 27 more stickers. She then gives 18 stickers to her friend Judy. How many stickers does she have now?

25. Hunter has 47 baseball cards in his collection. Ryan has 39 cards in his collection. How many more cards does Hunter have?

26. There are 95 people on a train. 19 people get off at the first stop. 24 people get off at the second stop. How many people are still on the train?

27. Daryl loves to collect comic books with superheroes. He has 5 comic books on his desk. He has 3 comic books in his backpack. Does Daryl have an even number or odd number of comic books?

28. Kim collects special seashells at the beach. She puts 8 shells in a pail. She puts 7 more shells in a jar. Does Kim have an even or odd number of seashells?

29. Leslie plants red peppers in her garden. Her garden has 6 rows with 5 peppers in each row. How many tomatoes are in her garden?

30. Marc puts 16 photos in an album. If there are 4 cards in each column, how many columns are there?

31. Ms. Sanders wanted to treat her class to a pizza party. There are 8 slices of pizza in each pizza pie. If she has 29 students, how many pizza pies does she need to order?

32. Four friends want to share a pumpkin pie. How could they cut the pie so each friend gets an equal share? Draw a picture to help you show your thinking.

33. Choose a three-digit number. Draw models to show the hundreds, tens, and ones to explain your thinking.

34. Liam is thinking of a number with three digits. It has 7 hundreds, 4 tens, and 6 ones. What is his number? Draw a model to explain your thinking.

35. Juliana has 257 stickers in her collection. She wants to explore this number further. First, she draws a model of the number by drawing base ten blocks. Then she writes it out in expanded form. Last, she writes it out in word form. Show how she does all three of these ways to explain 257.

36. Caleb is skip counting. He writes 160, 165, and 170 on a whiteboard. What are the next 5 numbers in his pattern?

37. The Florida Gators Football Team won their last 4 football games. They scored 25 points in the first game, 58 points in the second game, 33 points in the third game, and 77 points in the fourth game. How many points did they score in all?

38. Nolan collects Pokemon cards. He has 402 cards in his collection. He gives 25 cards to his friend Charlotte. He then gives 32 cards to his friend Maria. How many cards does he have left?

39. A school is having a bake sale. Dhomini’s mom brings 82 cupcakes. Amelia’s dad brings 75 cookies. Lorenzo’s mom brings 100 brownies. How many items are at the bake sale in all?

40. Kristella is reading a Magic Treehouse Book for her book report. She reads 24 pages on Monday. She reads 39 pages on Tuesday. She reads 37 pages on Wednesday. How many pages does she read in all?

41. Erica is reading James and the Giant Peach. The book has 144 pages. She reads 30 pages on Monday. She reads 42 pages on Tuesday. How many pages does she have left in the book?

42. Alana and her family are going to Disney World for her birthday. It is a 425 mile drive from her house. Her dad drives 127 miles before they stop for a snack. He drives another 233 miles before they stop for lunch. How many more miles do they have left until they arrive at Disney World?

43. The high school band is having a holiday concert. Peggy sells 75 tickets. Diana sells 101 tickets. Judy sells 135 tickets. How many tickets do they sell in all?

44. Mr. Axelrod’s class is tracking how many picture books they read each month. They read 329 books in March. They read 471 books in April. They read 450 books in May. How many books did they read in all?

45. The museum has 792 visitors over the weekend. 382 people visited the museum on Saturday. How many people visited the museum on Sunday?

46. Luna sells copies of the school newspaper. There are 500 copies. On Monday, she sold 122 copies. On Tuesday, she sold 198 copies. How many copies are left?

47. The second grade classes are going on a field trip to a play. Ms. Anastasio’s class has 29 students. Mr. Gordon’s class has 31 students. Mr. Fishman’s class has 33 students. Ms. McConnell’s class has 30 students. How many students go on the field trip in all?

48. Carlos is going to New York City on vacation. His plane leaves the airport at 2:30 p.m. The flight is 3 hours and 30 minutes long. What time does he land in New York City?

49. Juanita is watching the movie Harry Potter and the Sorcerer’s Stone. She starts the movie at 5 p.m. The movie is 2 hours and 32 minutes long. What time does the movie end?

50. Harry, Ron, and Hermione are on their way to Hogwarts. The train leaves the station in London at 9 a.m. It takes 7 hours to get to Hogwarts. What time do they arrive at Hogwarts?

Enjoying these second grade math word problems? Check out our second grade hub for even more resources.

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2nd Grade Math Word Problems

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Word problems  can be challenging for students, especially second-graders, who may still be learning to read. But, you can use basic strategies that will work with nearly any student, even those who are just starting to learn written-language skills.

Instructions and Strategies

To help second-grade students learn to solve word problems, teach them to use the following steps:

• Survey the math problem:  Read the word problem to get an idea of its general nature. Talk with your students about the problem and discuss which parts are most important.
• Read the math problem:  Read the question again. This time, focus on the specific details of the problem. Which parts of the problem relate to each other?
• Ask questions about the operations involved:  Reflect again. Determine the specific math operations the problem is asking you to perform, and list them on paper in the order they are to be performed.
• Question yourself about the steps taken:  Review each step you took. Determine if your answer seems reasonable. If possible, check your answer against the book's answers to determine if you are on the right track.
• Wrap it up:  Scan through the text of the word problems you will be solving to identify any words you do not recognize. List them and determine their meanings before solving the problems. Write brief definitions of the terms for your reference during problem-solving.

Solving the Problems

After reviewing these strategies, use the following free word-problem printables to let the students practice what they've learned. There are only three worksheets because you don't want to overwhelm your second-graders when they are just learning to do word problems.

Start slowly, review the steps if needed, and give your young learners a chance to absorb the information and learn word problem-solving techniques at a relaxed pace. The printables contain terms with which young students will be familiar, such as "triangle," "square," "staircase," "dimes," "nickels," and the days of the week.

Worksheet 1

This printable includes eight math word problems that will seem quite wordy to second-graders but are actually quite simple. The problems on this worksheet include word problems phrased as questions, such as: "On Wednesday you saw 12 robins on one tree and 7 on another tree. How many robins did you see altogether?" and "Your 8 friends all have 2 wheeled bicycles, how many wheels is that altogether?" 

If students seem perplexed, read the problems aloud together with them. Explain that once you strip out the words, these are actually simple addition and multiplication problems, where the answer to the first would be: 12 robins + 7 robins=19 robins; while the answer to the second would be: 8 friends x 2 wheels (for each bike) = 16 wheels.

Worksheet 2

On this printable, students will work six questions starting with two easy problems followed by four more of increasing difficulty. Some of the questions include: "How many sides are on four triangles?" and "A man was carrying balloons but the wind blew 12 away. He has 17 balloons left. How many did he start with?"

If students need help, explain that the answer to the first would be: 4 triangles x 3 sides (for each triangle) = 12 sides; while the answer to the second would be: 17 balloons + 12 balloons (that blew away) = 29 balloons.

Worksheet 3

This final printable in the set contains slightly more difficult problems, such as this one involving money: "You have 3 quarters and your pop cost you 54 cents. How much money do you have left?"

To answer this one, have students survey the problem, then read it together as a class. Ask questions such as: "What could help us solve this problem?" If students are unsure, grab three quarters and explain that they are equal to 75 cents. The problem then ​becomes a simple subtraction problem, so wrap it up by setting up the operation numerically on the board as follows: 75 cents – 54 cents = 21 cents.

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2nd grade math skills: Find out what you need to know for your student

Want to help your second-grader master the basics of 2nd grade math ? Here are some of the skills your child will be learning in the classroom.

Counting up to one thousand

Count forward within 1000. Count by 5s. Count and add by 10s and 100s. For any given number between 100 and 900, mentally add 10 or 100, or subtract 10 or 100.

Odd and even numbers

Understand odd and even numbers. Tell whether there are an odd or even number of objects in a group (of as many as 20 objects) by putting them into pairs, and/or counting by two.

Parenting Guides 2nd grade math tips: Here's how to help your student

Reading and writing large numbers

Read and write numbers through 1000, using numbers (352, 621, 1000) and number names ( “three hundred fifty-two,” “six hundred twenty-one,” “one thousand” ).

Relationship between larger numbers

Understand the relationship between ones, tens and hundreds: ten ones equal one ten; ten tens equal one hundred, ten hundreds equal one thousand. Understand that in a three-digit number, the first digit represents the amount of hundreds, the second digit represents the amount of tens, and the third digit represents the amount of ones– for example, 843 equals 8 hundreds (800), 4 tens (40), and 3 ones (3).

Comparing large numbers

Compare three-digit numbers using the symbols > (greater than or more than), = (equal to), and < (less than or fewer than) and explain using hundreds, tens, and ones.

Addition, subtraction, multiplication, & division

Large numbers

Quickly and accurately add numbers that total 20 or less, and subtract from numbers up to 20.

One- and two-step problems

Solve one-step and two-step word problems by adding or subtracting numbers, through 100.

Adding large digit numbers

Understand that in adding two three-digit numbers, you are adding hundreds and hundreds, tens and tens, and ones and ones and you may need to compose a new ten or a new hundred. Use models or drawings and explain your written method.

Adding within 1,000

Learn to add within 1,000.

Subtracting large digit numbers

Understand that in subtracting one three-digit number from another three-digit number, you are subtracting hundreds from hundreds, tens from tens and ones from ones and you may need to get more tens and ones in order to subtract. Use models or drawings and explain your written method.

Subtracting within 1,000

Learn how to subtract within 1,000.

parenting-guides 2nd Grade Parenting Guides

Measurement & data.

Reading digital and analog clocks

Read circular “face” clocks and digital clocks to tell time to the nearest five minutes. Understand the concept of a.m. and p.m. in a 24-hour day. Be able to tell the time aloud and write the time in various ways, using a.m. and p.m.

Measuring and estimating lengths

Measure and estimate lengths of lines or objects in standard units, such as inches, feet, centimeters, and meters. Write out and read measurements in inches (in.) or centimeters (cm). Compare measurements (how many more, how many less).

Solving word problems

Solve addition and subtraction word problems involving lengths in the same units (within 100).

A new roll of ribbon contains 72 inches of ribbon. Sara needs 26 inches of ribbon to wrap a birthday present. If she cuts 26 inches from the beginning of the new roll, how many inches of ribbon will be left?

Solving problems involving money

Solve addition and subtraction word problems involving money – coins (penny, nickel, dime, quarter) and dollar bills.

Antony has a quarter, two dimes, and five pennies. He wants to buy a whistle that costs one dollar. How much more money does he need? What combination of coins would give him the money he needs?

Picture and bar graphs

Read and create picture graphs and bar graphs to show measurements, quantities, or other data in up to four categories. Solve addition, subtraction, and comparison word problems using information presented in a bar graph.

Identifying common shapes

Identify triangles (three-sided shapes), quadrilaterals (four-sided shapes), pentagons (five-sided shapes), and hexagons (six-sided shapes). Analyze shapes by number of sides and corners (angles).

Dividing shapes

Divide a rectangle into several rows of same-size squares, and count to find the number of squares. Divide circles and rectangles into halves, thirds, or fourths.

For tips to help your second-grader in math class, check out our second grade math tips page .

TODAY's Parenting Guides resources were developed by NBC News Learn with the help of subject-matter experts and align with the Common Core State Standards.

How to Master Math: Strengthen Mental Math Skills

Parent Toolkit is a one-stop resource for parents produced by NBC News Learn.

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Second Grade Math Problems

Welcome to the Second Grade Math Problems page. We have a wide selection of longer math problems requiring a wide range of math skills to solve.

These problems are also a great way of developing perseverance and getting children to try different approaches in their math.

On this webpage are our selection of longer, more in-depth problem solving sheets for 2nd grade.

Typically, there is just one problem on each page with maybe a follow up problem in some cases.

The sheets cover a wide range of Math topics, from place value and number fact knowledge to geometry and logic problems.

The following worksheets have been designed to develop a wide range of skills and problem solving techniques such as:

• making lists or tables
• drawing pictures to help solve problems
• working systematically
• logical thinking
• number fact knowledge
• persevering until all solutions have been found

An answer sheet is available for each worksheet provided, where appropriate.

These sheets can be used in many different ways:

• to challenge more able pupils
• to use as a way of developing strategies to explore more in-depth problems, such as making lists or tables
• to use as an extension activity for children who finish early
• to use as part of a Maths challenge board
• Broken Calculator Problem 1

The Broken Calculator problem is a number problem involving using an imaginary broken calculator with only the 2, 3, + and = buttons working to make different totals.

There are 2 versions of the problem sheet, one with a pre-prepared template for filling in, and a second blank version for children to show their own recording system.

• No table version
• PDF version

Anyone for an Ice Cream?

Anyone for an Ice Cream is a money activity which involves using silver coins only to make a total of 40¢ . The aim is to find all the possibilities.

• Anyone for an Ice-cream?
• Anyone for an Ice Cream? UK version
• Tyger's Coin Challenges

Tyger's Coin Challenge is a money activity. The aim is to see whether or not different amounts of money can be made from a number of coins.

• Captain Salamander's Letter

This 2nd grade math problem sheet involves working out which totals of money can be made using only 3¢ and 5¢ stamps. It is a good activity for developing perseverance and logical thinking.

• Balloon Pairs #2

Balloon Pairs is a number adding activity where the aim is to find different totals by adding the balloon numbers together. The totals are then sorted in order of size using a table.

• Balls in the Bucket Challenge #2

This challenge involves working out how different scores were made in the balls-in-the-bucket game. It is a 'finding all possibilities' type of problem.

• Birthday Girl

Birthday Girl is an activity which involves finding the correct ages of all the people in the challeges using the clues that are given.

• Climb the Mountain

This is one of our second grade math problems that involves finding all the possible paths up to the top of the mountain using the routes provided.

• Dilly's Eggs #1

Dilly's eggs is a sharing problem - drawing it out is a good strategy for tackling this problem. The aim is to find the number of eggs Dilly had using the clues provided.

• Odd Square Out

This is a good activity for developing noticing skills and recognising shapes that have been rotated or reflected.

• Parking Lots #2

Parking Lots is an activity where the aim is to find as many combinations as possible for the cars to park. Systematic working could be an area of focus for this activity.

• Pick the Cards #2

Pick the Cards is an adding game where the aim is to use combinations of numbers to reach a given total. This activity is good for adding three or four small numbers together to make a given total.

• Place It Right #2

Place It Right is a place value activity to support children with their place value learning. The aim is to make a range of 3 digit numbers with different properties.

• Share the Treasure #2

Share the Treasure is a logic acitivity where the aim is to share some treasure according to certain criteria.

• Who Chose Which Shape #2

Who Chose Which Shape is a logic problem where children have to work out which salamander chose which shape from the clues given.

Looking for some easier word problems

We have a range of easier word problems at our parent site, math-salamanders.com

The problems on this page are at a simpler level than those here.

Many of the problems, e.g. Dilly's Eggs, Pick the Cards and Share the Treasure have easier versions on this page.

Using the link below will open our main site in a new tab.

• First Grade Math Problems

Looking for some harder word problems

We have a range of more challenging word problems at our parent site, math-salamanders.com

The problems on this page are at a trickier level than those here.

Some of the problems, e.g. Place It Right and Share the Treasure have harder versions on this page.

• 3rd Grade Math Problems

Addition and Subtraction Puzzles

The puzzles in this section mainly focus on adding and subtracting numbers.

The puzzles start with adding and subtracting to 20, and progress on to harder levels and more complex puzzles.

Using the puzzles in this section will help your child to:

• develop their adding and subtracting skills;
• develop trial and improvement strategies;
• improve problem solving skills.

All the second grade math problems in this section will help your child to learn their addition and subtraction facts and become more confident with handling numbers mentally.

• Free Math Puzzles - Addition and Subtraction

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Grading Guide

Here is the grading guide for our worksheets.

White: the easiest level for children at their early stages in 2nd grade.

Orange: medium level of difficulty for children who are working at the expected level in 2nd grade.

Purple: this is the hardest level for children who need that extra challenge.

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Series: Focus on the Child

Second grade problem solving with child 5.

March 15, 2016 This is a Video - for grade levels 1st Grade , 2nd Grade , 3rd Grade Tagged Correction , Problem Solving , Child 5

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This second grader works to make sense of a non-routine problem with several addends. She makes a graph to model when trying to trying to think though the math problem. This is one unique way to solve math problems for 2nd grade.

Focus on the Child videos are taken from one-on-one interviews with individual children. The interviews are designed to elicit evidence of children’s mathematical thinking. They are not teaching episodes or formal assessments.

Why is this important?

After an initial error, this second grader works to make sense of the problem. Her choice to construct a graph indicates that she understands the +1 growing pattern of the story. Once she’s made sense of the problem situation, she arrives at the correction solution easily.

Common Core Alignment

Foundational math topics.

Read more about Pattern

Read more about Number Operations

More in the Focus on the Child series

Recognizing Quantity with Child 1

A child selects a card with a given number of dots.

Estimating Quantity with Child 8

A child estimates the number of cubes in a collection.

Recognizing Shapes with Child 13

A child describes examples (and non-examples) of common 2-D shapes.

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180 Days of Problem Solving for Second Grade – Build Math Fluency with this 2nd Grade Math Workbook (180 Days of Practice) 1st Edition

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• ISBN-10 1425816142
• ISBN-13 978-1425816148
• Edition 1st
• Publisher Shell Education
• Publication date October 3, 2016
• Part of series 180 Days of Practice
• Language English
• Dimensions 8.5 x 0.5 x 11 inches
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180 Days Workbooks for Grades K - 6

For over 40 years, TCM’s resources have been used by educators across the U.S. and in 89 different countries. Offering a broad range of innovative curriculum resources, TCM’s products support reading, writing, mathematics, social studies, science, technology, test preparation, and professional development for Grades K-12.

180 Days of Problem Solving Workbook

2nd grade (208 pages).

The '180 Days of Problem-Solving' workbook offers purposeful, daily practice that will engage 2nd-grade students throughout the school year. Great for homeschooling or learning in classrooms, these workbooks also help kids retain educational knowledge during the summer or stay-at-home learning.

• Offers a variety of engaging math subjects: geometry, word problems, and multiplication
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• Improves math skills as it builds confidence in struggling math students

Practice for Every Day of the School Year

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• Publisher ‏ : ‎ Shell Education; 1st edition (October 3, 2016)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 224 pages
• ISBN-10 ‏ : ‎ 1425816142
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• Reading age ‏ : ‎ 6 - 8 years
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Real World Problem Solving in Second Grade Mathematics

Introduction.

Edgewood Magnet School in New Haven, Connecticut is an arts magnet school, integrating the arts across the curriculum. Students in this environment are encouraged to use the strategies of observation, interpretation, and analysis to increase their thinking skills in every subject. With that mission, both teachers and students use unique and exciting approaches to “the basics” and work together to ensure that all learners are included.

For most second graders, the beginning of the year is a time for refreshing knowledge and skills from first grade. The summer away from direct instruction and opportunities for practice and guidance sometimes means a loss of solid understanding of learned concepts in mathematics. This three- to four-week unit is designed to review and build new understanding of one-step word problem solving using addition and subtraction as students develop skills and strategies they will use all year. The students, through a series of mathematical scenarios, will use the problem types identified in Table 1 of the Common Core Mathematics Glossary which covers addition and subtraction. 1

The Common Core concentrates on a clear set of math skills and concepts. Students learn concepts in an organized way during the school year as well as across grades. The standards encourage students to solve real-world problems. 2

The Common Core calls for greater focus in mathematics. Rather than racing to cover many topics in a mile-wide, inch-deep curriculum, the standards ask math teachers to significantly narrow and deepen the way time and energy are spent in the classroom. This means focusing sharply on the major work of each grade, which for grades Kindergarten through second grade includes concepts, skills, and problem solving related to addition and subtraction.

The New Haven Public School district uses the Math in Focus Singapore Approach, a Common Core-based curriculum for students from Kindergarten to Fifth Grade. The student books and workbooks follow an instructional pathway that includes learning concepts and skills through visual lessons and teacher instruction for understanding the how and why; consolidating concepts and skills through practice, activities and math journals for deep math understanding, hands-on work in pairs and in small groups; and, applying concepts and skills through extensive problem solving practice and challenges to build real world problem solvers. 3

This approach embeds problem solving throughout each lesson and encourages frequent practice in both computation and problem solving. The word problems appear throughout each chapter and progress from 1-step to 2-step to multi-step. Each chapter concludes with a challenging problem or set of problems that require students to solve some non-routine questions. To solve these problems, the students need to draw on their deep prior knowledge as well as recently acquired concepts and skills, combining problem solving strategies with critical thinking skills, including classifying, comparing, sequencing, identifying parts and whole, identifying patterns and relationships, induction and deduction and spatial visualization.

The second grade text begins with numbers to 1000. Students begin by expressing numbers in standard form (231), expanded form (200 + 30 + 1), and word form (two hundred thirty-one). This is accompanied by concrete representations via base ten blocks, and, for two digit numbers and a few three digit numbers, representation by trains of rods, of lengths 1, 10 and 100. This initial chapter also includes sequencing numbers and comparing using greater than and less than terminology, and then moving right into addition and subtraction of two- and three-digits numbers. Here the take-away should be, if you have more hundreds, the tens and ones don’t make any/much difference; and if you have the same number of hundreds, but more tens, then the ones don’t make any/much difference. Most of my students (if not all) struggle from the start! They do not seem to have a solid foundation of understanding numbers to 100 or the concept of place value in general. This unit is designed to get ahead of the frustration that the students feel when pushed too quickly before they have a firm understanding of principles of place value and the properties of operations.

This unit launches the school year with 1-step addition and subtraction problems of all types using numbers to 10. The goal is to spend time practicing basic computations with numbers that student can work comfortably with before jumping right into the district curriculum. Once there is a level of understanding with these problem sets (numbers to 10), students will move on to solving 1-step problems using teen numbers and then onto numbers to 100. Most of the curriculum problems at the start of the year require addition and subtraction of 3-digit numbers. Some students will move quickly through the problem sets with numbers to 100 and will be ready to work with the regular curriculum.

For the duration of the unit, the focus will be steadily on solving and later constructing a collection of word problems that provide robust and balanced practice. Problems sets will be based on a scenario which will provide the substance of the story. Each scenario will allow us to extract several problems, changing the numbers and ensuring each set of numbers makes a reasonable problem. This idea looks like the following: John has 8 crayons in his box. He shares 3 with Sam. How many crayons does John have left in the box? John has some crayons in his box. He shares 3 with Sam. John has 5 crayons left in his box. How many crayons did John start with? John has 5 crayons. Sam has 2 fewer than John. How many crayons does Sam have? John and Sam are sharing crayons. John has 5 and Sam has 3. How many crayons do the friends have together? The two students participate in several crayon-sharing stories that use the same set of numbers but in slightly different situations. Some situations are more obvious and direct while others take more thinking. It is important to provide opportunities for students to work with and solve the different problem types that can be created from one set of numbers. 4

Background: Problem Types

The taxonomy of addition and subtraction problem types as identified in the Common Core State Standards of Mathematics Glossary is a framework that sorts one-step problems into three broad classes: change , comparison , and part-part-whole . Each of the three classes is then separated further into a total of 14 problem types sorted out as follows: change , in which some quantity is either added to or taken away from another quantity over time; comparison , in which one amount is described as more or less than another amount; and part-part-whole , in which an amount is made up of two parts. 5

Within the group of change problems, there are two subgroups: change-increase , in which a quantity is added to an initial amount and change-decrease , in which a quantity is taken from an initial amount. We might recognize these subgroups more familiarly as “add to” or “take from.” Additionally within each of these subgroups, there are three possible unknown quantities. One scenario to show change-increase : 2 kittens were playing with some yarn. 3 more kittens join them. Now there are 5 kittens playing with the yarn. Using these quantities, the unknown might be the result (2 + 3 = ?), an unknown quantity of change (2 + ? = 5) or an unknown initial amount (? + 3 = 5). In the change-decrease subgroup, there are again three possible unknowns. A scenario for this example: 5 birds are sitting on the branch. 2 fly away. Now there are 3 birds sitting on the branch. Here again the students might solve for the final amount (5 – 2 = ?), the amount of change (5 - ? = 3), or the initial amount (? – 2 = 3). This gives in all six types of change problems.

Similarly comparison problems can also be categorized into two subgroups: comparison-more , in which one quantity is described as more or greater than another, and comparison-less, in which one quantity is described as less or fewer than another. Here again, each of these two subgroups has three possible unknowns, for a total of 6 types. Sam has 6 marbles. James has 8 marbles. James has 2 more marbles than Sam. The unknown quantity may be the lesser amount (? + 2 = 8), an unknown greater amount

(6 + 2 = ?), or the unknown difference (8 – 6 = ?) one quantity that is more and one that is less. Using this same scenario for a set of comparison-less problems, the language need to change from “more than” to “less than.” Here is a way to present this set with the language adjustment: Sam has 6 marbles. James has 8 marbles. Sam has 2 fewer marbles than James.

Part-part-whole problems are a set of two quantities, the parts that, when put together, make up a whole quantity.  This problem type seems very like to change category but in this problem type there is no change over time. The two parts play equivalent roles, which allow for only two possible unknown categories: either a part is unknown or the whole is the unknown. There are 4 large dogs and 3 small dogs. There are 7 dogs in all. One of the parts may be unknown (4 + ? = 7 or ? + 3 = 7) or the unknown may be the size of the whole (4 + 3 = ?). Since the parts are interchangeable, there are only 2 types in this class of problems.

The following chart sort these classes and categories into the framework. Located in Appendix A of this unit is a set of example problems illustrating each of these 14 types.

The Scenarios of the Problems

For second graders, life at school is a large part of their world. Most of my students arrived at Edgewood for their Kindergarten year and stayed through First Grade making the year in second grade essentially their third year at the same school. They are comfortable in the building and know many of the other students. They will become the active players in the math stories that I, and we together, will construct. Activities that occur in the classroom, in the cafeteria, on the playground, and on the bus seem to be recognizable situations that will help with the basic understanding of context.

Additionally, there are opportunities for students to incorporate the topics and learning that occur in the other subjects, such as science, social studies, literacy, art, music and, in our school, dance and drama. One example might be to create set of story problems centered on the life cycle of the butterfly, a unit of study each year in second grade. With the common knowledge the students will be obtaining, this content could become the scenarios for word problems. An example might be: Seven caterpillars climbed up the branch and formed their chrysalises. Later that day, three more caterpillars climbed up the branch and formed their chrysalises. How many chrysalises are hanging from the branch? Similarly, using the characters in a book read together as a class could provide the characters in a new set of problems. Curious George had a bunch of bananas. He ate 4 of them. Now he has 3. How many bananas did Curious George begin with? The use of common or thematic content will not only connect all the thinking and practicing, it will provide tangible and real situations. With an established scenario, students will work with a set of numbers, determining the unknown within each of problems types.

Creating the Problems

A question that is frequently answered with a guess is “What should we do to answer the question to solve the word problem?” The fundamental understanding of what is being asked is not apparent to the students, making the solution inaccessible. Most first graders entering second grade have a basic understanding when the story (problem) is categorized as final unknown or whole unknown , but most other components of the taxonomy are unfamiliar to them or just too difficult to decode. To begin to help them with their thinking, they will use concrete models, such as themselves (2 children are sitting at the reading table, 4 more join them) acting out scenarios. Many basic materials in the classroom – pencils, notebooks, folders, crayons – can be used to create and design scenarios, with each type of problem represented.

Solving the Problems

Following the overall plan of the Singapore Math program, the students will solve problems using the concrete, pictorial and abstract approach. Because this is a standard approach in our district mathematics instruction throughout the year, the students will begin with this set of strategies to solve problem sets.

Word problems are written as stories and scenarios making language a consideration in crafting the problems for the beginning second graders. Word problems are as much about language and reading as they are about math. If the story is not understandable, how can students begin the know what to do with the numbers they’ve been given and the question they’ve been asked? Thus, words and vocabulary need to be appropriate and useful for the variety of reading levels of the incoming students.  The structure of word problems should be understandable and clear, accessible in language as well as numbers. Also, the language, especially the words that express the relationship between the quantities involved, should be discussed to ensure that it is familiar to all students.

This is a clear integration of Language Arts and Mathematics and a method in which students can connect math to the real world, in this case, through the activities they engage in at school. Reading skills and computation skills come together with even the simplest of word problems.

Structure of Problem Collection

The content introduction over the duration of this unit includes a certain sequencing and scaffolding to guide students through the 14 problem types. To begin the unit, students will only be working with numbers to 10. This is an important starting place to ensure that understanding is occurring. Most of my second graders are capable with addition and subtraction to 10, but are not so comfortable with the word problem language. So first, students will be challenged more by the language than the arithmetic. Students will practice figuring out what exactly the problems are asking with problems that they are familiar with before moving on to a new step. Practicing all the problem types will improve and increase strategies and confidence!

With addition and subtraction within 10 mastered, the next phase of the unit moves to numbers to 20. The key is to continue with scenarios that are obvious and repeated as new numbers are introduced. An example of this transition would be these parallel problems:

6 students got on the bus at the first stop. 3 students got on the bus at the second   stop. After the second stop, how many students are on the bus? ( change-increase, final unknown)

Some students got on the bus at the first stop. 3 students got on the bus at the second stop. Now there are 9 students on the bus. How many students got on at the first stop? ( change-increase, initial unknown)

These now become:

11 students got on the bus at the first stop. 7 students got on the bus at the second stop. After the second stop, how many students are on the bus? ( change-increase, final unknown)

Some students got on the bus at the first stop. 7 students got on the bus at the second stop. Now there are 18 students on the bus. How many students got on at   the first stop? ( change-increase, initial unknown)

When working with numbers to 20, it is essential that students understand that the “teen” numbers (11-19) are really 10 and some ones. Students should work with numbers within 20, creating equations using their knowledge and skill of making a ten first. In the case of 7 + 6, making a new ten looks like this:

7 + 6 = 7 + 3 + 3 = 10 + 3 = 13

Because 7 needs a 3 to make ten, and 6 is composed of 3 + 3, this equation shows the progression of making 10 and some more. Practicing this method using two ten frames demonstrates the process concretely. In the example above, students use the ten-frames to show 7 and 6 separately. To make the new 10, students will move 3 from the 6, which now shows 10 and 3 more or 13.

As mentioned earlier, it is obvious that the most accessible problem types for students entering the second grade are the change-increase or change-decrease, result unknown and part-part-whole, whole unknown. The general go-to strategy for solving a word problem seems to be to just take the two numbers you see and add them together, or maybe subtract, but often the students are just unsure. It seems that these are the most practiced problem types, which leaves students without balanced experience with all 14 types and ultimately without some strategies to employ as they problem-solve. Students need to see a broad range of problems to gain a strong understanding of how addition and subtraction are used and how they are related to each other. The notion of example sufficiency means students should be exposed to a wide array of examples to provide well-rounded practice with the concept. 6

Teaching Strategies

The approaches for this curriculum unit vary to reflect the learning styles of all students.

The general format is based on the workshop model. The concepts and skills are taught through a series of mini-lessons focused on the objective with the following methods used throughout:

Experiential Learning: Most young students need to begin with hands-on learning. Using concrete models to work out math stories allows students to see the problem and manipulate the pieces as the story progresses. This type of learning is an important first step.

Differentiated Instruction: Lessons and activities will be targeted to maximize learning. The students will use a variety of approaches, working sometimes individually and sometimes in small groups, determined by the complexity of the work. Some students will move more quickly as they master skills and some will need more opportunities for practice.

Cooperative Learning: The students will be given opportunities to work as cooperative groups to create math stories to present to the class. This strategy will allow students to work collaboratively taking on various roles necessary to complete the work, with a focus on success for all.

Classroom Activities

Activity 1: sequenced problem types – problems to 10.

The introduction (and review) portion of the unit covers all problem types but in a sequenced manner. The objective is for students to read and interpret a word problem with guided instruction followed by independent practice. Because of the many problem types, this part will take several days of review and practice before students are comfortable beginning to write their own sets of problems. Based on student need and pace of understanding, I expect this section to be a four- to six-day set of lessons, more if needed.

The sequence is as follows: part-part-whole ; change-increase and change-decrease ; and finally, compare-greater and compare-fewer . The following introductory sessions are designed as a whole group activity, with students either at their desks or gathered on the rug close to the board or easel. The whole group portion should be 20 minutes at most. At the close of each session, I will give students between 5 and 10 similar problems to solve. More capable students can begin to generate their own problems during the independent work time.

Beginning with the fundamentals provides a good opportunity to get to know students’ skills which is helpful in preparing differentiated work and creating groups,

In this lesson, students will interpret real world problems and with the help of manipulatives and pictures, solve part-part-whole stories using addition and subtraction.

6 girls are playing

3 boys are playing with them.

How many children are playing in all?

Begin the story with the whole unknown as in this example. This type of story is perfect for students to act out right in the classroom. Write the story on the board or chart paper and have students volunteer as actors. Once the students have solved the problem, write the math sentence to show what happened: 6 + 3 = 9 students. Explain that the 2 parts (boys and girls) have made a whole (children). With the students still in acting position, present a new approach to this scenario:

9 students are playing.

6 of them are girls.

How many boys are playing?

With this visual example, students should see right away how many. The important concept to demonstrate is that the parts can be determined when the whole and one part are known, in this case 9 is known as the whole and 6 as one part. Again, write the math sentence to show this calculation: 6 + ? = 9 and include the strategy of starting with the whole to determine the missing part as a subtraction sentence 9 – 6 = 3. Practicing both approaches to the solution will help students connect addition and subtraction and recognize how they are used together.

Since this lesson requires students to read story problems, I will pair fluent readers with those who are less fluent, provide counters for those who want them, and allow partners to work together to solve and problems and share the strategies that they used.

I will use two more examples, like the ones below, to demonstrate, remembering to write the word problem on the board as well as the math sentence. I will also reword the problems to have the part as the unknown.

Hannah has 5 red markers.

She has 3 blue markers

How many markers does Hannah have in all?

7 students are drawing with crayons.

2 students are drawing with colored pencils.

How many students are drawing?

Continuing with this same idea, the next set of problem types includes change-increase and change-decrease . Although part-part-whole is language that students can adopt and use while discussing their work, the change-increase and change decrease language is a bit trickier. The use of the word change is more appropriate for students to demonstrate that some amount has been either added or subtracted from an initial amount.

Introduce the word problem below which is an example of the unknown result in the change-increase category.

Jason had 8 “caught being good” stickers on his chart at the beginning of the day.

During the school day, he earned 2 more stickers.

How many stickers does Jason have on his chart at the end of the day?

Student can solve the problem as written and, using the same scenario, challenge them to create the change-unknown and initial unknown story. One example might be:

Jason had some “caught being good” stickers on his chart at the

beginning of the day.

At the end of the day, he has 10 stickers.

How many stickers did Jason have at the beginning of the day?

This is an oral activity, with me writing the adjusted version across the board, placing the math sentence underneath. It is important to allow students to work on composing the problem so they can begin the see the relationship between the problems and what the problems are asking.

The goal is for students to understand and not just solve. I can informally assess during the discussion of rewriting the text of the word problem, with more formal assessment later in the unit.

The next category to introduce is the change-decrease problem types. Following the same format as before, I will introduce the result unknown, change unknown and then initial unknown.

Crystal collected 7 leaves for her project.

2 leaves blew away in the breeze.

How many leaves does Crystal have left for her project?

Again, the goal is for students to understand and not just solve.

The third broad class, compare, is more difficult for my 2 nd grade students. This requires the text of the word problems to be very straight-forward. Students should not get tangled up when they are learning to take the data from the problem. Remember that using the exact terminology is not the goal, but rather understanding what the problem is asking. Here are three ways I will present a scenario that shows the problem types comparison-more , and three ways to show comparison-less. Students need to be exposed to and have opportunities to practice all types. Of course, not all of these examples should be used at one time. As I write the problems out on chart paper and post them in the classroom, the students can begin to see and do their own comparing and contrasting as one scenario is explained in different ways. The use of the words “more” and “fewer” should be highlighted and explained as the problem set is introduced and worked on. My role here is to let the students begin to notice the subtle differences in the wording and how it changes the thinking. Simpler is better to start with!

Throughout these introductory sessions, the students and I will brainstorm scenarios that can eventually be used in own word problems. Ideas should generate from school activities and materials, guiding students to think of what students can actually use for manipulatives or, as in the first scenario, be able to act out to solve. By keeping a list of ideas on chart paper as reference material, students won’t struggle with vocabulary or appropriate scenarios; they will be on to the task of crafting their problems. This list will prepare the students for the second part of the unit.

Activity 2: Classroom / school scenarios

As stated earlier, words and vocabulary should be accessible to students and not a challenge or hurdle. The goal is to get to the thinking of the stories and plugging in the information that was gathered during the brainstorming session. To begin this portion, review the charts and add more if students have new ideas. It may be helpful for the purposes of composing word problems to have the information in categories, such as these:

Materials We Use

Classes We Attend

Activities at School

Classmate’s Names

I will create groups of two or three students to have them write problems of their own to share with the class.  Since this lesson requires students to read and write story problems, again, fluent readers and writers with those who are less fluent, provide counters for those who want them, and allow partners to work together to solve and problems and share the strategies that they used.

The goal during this period of time is to challenge students to write the same problem but try it another way, choose a different type as they tell the story. The timing for the student groups to work together will be during arrival time as morning work and during the math workshop portion of math instruction time. This will allow students to work as much as 30 minutes per day with their partners to create some math stories.

I will stress that it is important to keep their collection together as much of their work will become part of the workbook they will create at the end of this unit. Folders and math journals can be helpful, or my collecting the work-in-progress daily is another option.

Activity 3: Science Scenarios

The first unit in 2 nd grade science is investigation and research on the life cycle of the butterfly. Students receive caterpillars at the start of the semester and observe and record the changes the caterpillar’s life. The work that the students do during their science lessons can become the information and scenarios they can use for crafting word problems.

Using all different problem types, we will write several together as a class.  This is an additional opportunity to integrate math very specifically into our science research and work. It is important for students to recognize that, although their learning has been compartmentalized into subject areas, it is essentially impossible to separate it all out into categories. So this portion of the unit uses math, science and reading to help students learn about the life cycle of a butterfly (and other animals as well).

Students will create problem sets that use their daily experiences tracking their caterpillars. Each student has 2-3 caterpillars to observe and record information on, which can become the start of word problems. Examples to start: If Table 3 has 8 caterpillars and 2 caterpillars join that group, how many caterpillars are being observed at Table 3? Here are 28 students in the class. Each student need one cup of caterpillar food.  There are 30 cups of caterpillar food. How many more cups of food are there than students?

There are often students who have great interest in other areas of science. This is an area to encourage if students are excited about sharing their knowledge. Some students will be more inclined to use the unit of study going on in class, but throughout the literacy portion of the day, students are exposed to a great deal of non-fiction, or informational text, that could certainly enrich our science word problems.

Throughout the duration of the science unit, students will continue to write word problems of various types to eventually include in our final project, the workbook. These problems can be written during the morning work session, during math workshop, and at the end of science class. By the end of the unit, each student should have two problems to add to the Science chapter of the workbook.

Activity 4: Creation of Workbook / Publishing Celebration

The goal of this portion of the unit is to sort the word problems into “chapters” and create a workbook to share at the Publication Celebration. Chapters will be titled by subject or category, depending on student choice and teacher suggestion. Ideas include Beginning Stories, Classroom Activities, Playground Fun, Science & Math, and Social Studies Connections. Let students be creative with titles!

Students will submit their work which will include at least one word problem for each chapter. They must also submit the solutions to their problems so that they can be included in an answer key. Each chapter will have at least 25 problems, with examples of all types and with varying levels of difficulty. Word problems can either be typed or hand-written for the final workbook, depending on what the students decide as a class. One workbook per student will need to be copied and bound in some manner for the Celebration.

Two weeks before the Publication Celebration, students will create an invitation to give to their family and friends, inviting them to come for a “Celebration of Problem Solving.” Parents and other VIP guests will spend some time working on word problems, moving around the room, visiting many students. The students will share their own specific work with the guests (the word problems they themselves created) and “help” their visitors figure out the answers.

Each student will have a “Comments” sheet for guests to sign and leave comments on their experience working with the student. I will encourage visitors to stop to talk with each student or as many as they can during their visit.

Additionally, this is an opportunity to have some students work as editors and publishers. Creating the workbook will require review and assembly time and these tasks can be delegated and shared by the students who are interested.

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2nd Grade Problem And Solution

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1. Problem/Solution Explicit Comprehension Lesson Second Grade

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