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Unit 1: add and subtract within 20, unit 2: place value, unit 3: add and subtract within 100, unit 4: add and subtract within 1,000, unit 5: money and time, unit 6: measurement, unit 7: data, unit 8: geometry, course challenge.

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Math Workbooks for Grade 2

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Second Grade Math Worksheets

Free grade 2 math worksheets.

Our grade 2 math worksheets emphasize numeracy as well as a conceptual understanding of math concepts . All worksheets are printable pdf documents.

Grade 2 math topics:

Skip Counting

Place Value & Rounding

Counting Money

Telling Time

Data & Graphing

Word Problems

mathematics problem solving for grade 2

Sample Grade 2 Math Worksheet

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MATH Worksheets 4 Kids

2nd Grade Math Worksheets

Our printable 2nd grade math worksheets with answer keys open the doors to ample practice, whether you intend to extend understanding of base-10 notation, build fluency in addition and subtraction of 2-digit numbers, gain foundation in multiplication, learn to measure objects using standard units of measurement, work with time and money, describe and analyze shapes, or draw and interpret picture and bar graphs, there's something to interest kids and keep them engaged. Our free math worksheets for grade 2 kids definitely need to be added to your must-try list!

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Explore 4,000+ Second Grade Math Worksheets

Adding with Base Ten Blocks

Adding with Base Ten Blocks

Pique your child’s interest in addition using the place value blocks. Let kids in grade 2 count the unit blocks and rods, figure out the addends, and add them up.

pdf 1

Subtracting Single-Digit from 2-Digit Numbers | No Regrouping

Ensure solid practice with our 2nd grade subtraction worksheet pdfs. Accurately and effortlessly subtract single-digit numbers from 2-digit numbers without regrouping.

printable 1

Multiplication Models | Equal Groups

Get the basics right by relating multiplication to the sum of equal groups. Kids multiply the number of objects in a group by the total number of groups and answer questions based on the model.

exercise 1

Converting Base Ten Blocks into Hundreds and Tens

Crack this batch of printable 2nd grade math worksheets by trading rods for flats. Count the rods depicting the tens place and group them into flats, count the flats formed and the leftover rods.

easy 1

Ordinal Numbers Chart | 1 to 50

Talking about positions or the order of things becomes simpler with this chart. Print this cheat sheet and have a quick review of the names and abbreviations of the first to fiftieth ordinal numbers.

Chart

Growing Patterns

Analyze the pattern that gradually increases in each set of figures in our math worksheet pdfs for grade 2 kids, identify the rule, and draw the picture that comes next in the sequence.

worksheet 1

Measuring Length of Objects using a Ruler | Quarter Inches

Join in the fun of measuring objects and develop a vital life-skill. Note the point that corresponds to the edge of the object; count the smaller divisions to measure the length to the nearest one-fourth inches.

practice 1

Telling time | Increment of 5 Minutes

Make every minute count with our math worksheets for grade 2 kids. Practice telling time to the nearest minutes by observing the minute and hour hands on each analog clock.

Identifying the Coins and Their Values

Identifying the Coins and Their Values

Watch the little bankers observe each coin; identify the coin based on the picture on its face and write its name and the value in cents in the space provided.

Reading Pictographs

Reading Pictographs

Bringing order to chaos, these grade 2 math pdfs have information organized into pictographs. Read the pictograph, comprehend the information, make comparisons, and answer the questions that follow.

Identifying and Labeling 2D Shapes

Identifying and Labeling 2D Shapes

Get kids excited about the wondrous world of shapes around them. Whether it is identifying or labeling 2D shapes, our printable worksheets have both skills covered.

Worksheet

Two-Digit Addition | No Regrouping

Great to use as instant practice, these 2nd grade math worksheet pdfs help kids find the sum of 2-digit addends and apply the concept to solve word problems as well.

worksheet 4

Subtracting 1-Digit from 2-Digit Numbers | Regrouping

Elevate skills to the next level as kids subtract a single-digit numeral from a 2-digit numeral, regrouping in the ones place. Try solving some subtraction word problems too!

Repeated Addition and Multiplication

Repeated Addition and Multiplication

Relating multiplication to repeated addition, our printable 2nd grade math worksheets get kids to count how many times a number is repeated, complete the multiplication equation, and find the product.

Reading 3-Digit Numbers on an Abacus

Reading 3-Digit Numbers on an Abacus

Abacus is a great way to help your eager-to-learn kid understand place value. Write the 3-digit number displayed on the abacus by counting the number of beads in the hundreds, tens and ones place.

pdf 4

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mathematics problem solving for grade 2

Find help from our team of math teachers who are here to help struggling students with their math skills. Find on-demand videos for every second-grade skill to teach students how to best tackle math problems. Teachers break down the concepts in an easily understandable format for younger students who need help with their math skills.

2nd Grade Math Word Problems

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:

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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Elementary Math

In Think Math! , second graders extend and deepen their understanding of the base-ten system. They represent numbers (up to 1000) in expanded form using objects, pictures, sounds, and numbers. They experiment with grouping and regrouping, noticing that sometimes it is necessary to compose a ten or hundred. Children build their repertoire of addition and subtraction strategies and come to understand addition and subtraction as inverse operations. They explore measurement in the context of linear measurement, telling time, weight, and capacity – and describe and analyze shapes, considering their attributes.

All student materials can be accessed through the table below as PDFs by chapter.

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2nd Grade Math Problems

mathematics problem solving for grade 2

Information

Second grade is the time for 7 – 8-year-olds to review what they have learnt in first grade and strengthen their foundation in the subject. Check out our collection of  second grade math problems to give the little ones some  math practice !

Help your young learner get better at reading analog clocks with this simple time worksheet, “Clock Work”. Students find out more about others’ routines and answer a few questions about their own in this fun worksheet for kids. See more

The Car Trains of Gridlokia

Help the traffic police manage Gridlokia’s traffic by solving the math problems and letting them know how many cars can be joined to form each train. See more

Cat and Rat

‘Cat and Rat’ is a cool geometry worksheet that shows kids how to design a maze of their own using only a grid and some tracing paper! See more

Calculator Match

Test your mathematical ability by solving math problems and comparing your answers with the calculator’s in ‘Calculator Match’. See more

Beautiful Butterflies

In this math worksheet, students practice adding and subtracting to balance equations as they put each of the beautiful butterflies in their right places. See more

Broken Glass

When the king ordered for cut glass triangles, he didn’t mean for them to be broken! Unfortunately, now only a skilled multiplier can help put the broken pieces together again. Do you think you’re up to the task? See more

In this math worksheet, students must figure out how many glasses of orange juice, grapefruit juice and apple juice to fetch for the passengers on the ferry. See more

Bag of Beans

“Bag of Beans” is a fun math worksheet that will have your students competing to complete subtraction problems. See more

A Penny for Your Name

With values for each letter, students add the values of the letters in their names to find out whose name is the most valuable. See more

Free Math Problems for Second Graders

In this grade, kids need to be familiar with the concepts of addition and subtraction. While they may not be able to solve really tough problems, they should be comfortable with simple addition and subtraction of two- and three-digit numbers. Second grade math also includes basic geometry - being able to identify and draw different shapes like circles, quadrilaterals, triangles, parallelograms, etc. Kids are introduced to the concept of perimeter and learn to estimate and measure length, weight, and capacity.

Free and printable 2nd grade math problems are a great way to get the kids to practice the subject. It is important for homeschooling parents as well as teachers to monitor each child’s progress, identify their problem areas, and help them grow to like the subject. You can also engage the kids with printable 2nd grade math worksheets to gauge their understanding and get a better idea of what their problem areas are.

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mathematics problem solving for grade 2

Grade 2 Word Problems

Free grade 2 word problems to help your students in mathematics. These free worksheets will help your students apply their knowledge to problem solve. Word Problems are often a challenge for students. They can comfortably do simple equations, but struggle to apply that knowledge to solve real life situations. It is important to do word problems daily to ensure your students get the repetition they need. Use these free worksheets to help you! They are scaled easy to hard (left to right).

mathematics problem solving for grade 2

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Addition Word Problems

Grade 2 word problems

A bundle of the 3 resources.

mathematics problem solving for grade 2

Grade 2 & 3

A bundle of 6 Grade 2 & 3 resources. Click to Preview.

Subtraction Word Problems

Grade 2 word problems

3 weeks of free daily mental maths. Click to Preview.

Grade 2 Mental Maths

10 weeks of daily mental maths. Click to Preview.

Grade 2 Mental Maths

70 weeks of grade 2 & 3 mental maths. Click to Preview.

Grade 3 Word Problems | Draw a Picture

mathematics problem solving for grade 2

Word problems in grade 3 are very important. These 20 grade 3 word problems will engage students as they draw pictures to solve the questions! Drawing pictures is an effective strategy for solving problems in Mathematics. As students get older, they begin to visualize word problems. Drawing is the foundation for this! Get your students engaged in Mathematics with drawing during problem solving!

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Grade 4/5 Word Problem Task Cards

Word Problems

Daily Math Word Problems are vital to student development in Mathematics. This resource has 50 task cards, available in worksheet form with answers. Applying mathematical knowledge to solve word problems is extremely important. Some students understand how to solve equations but struggle to apply their knowledge when solving word problems. Doing daily word problems has helped my class a lot and I hope these flash cards will help yours!

Need More Grade 2 Worksheets?

For more grade 2 worksheets, check out grade 2 mental maths . There are some great worksheets there! For more 2nd grade worksheets, check out Dad Worksheets . They have a bunch of wonderful free worksheets that are helpful and easy to access. 

Grade 2 daily mental maths to help students develop their mental maths skills.

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mathematics problem solving for grade 2

Two Step Word Problems 2nd Grade Worksheets

Two-step word problems 2nd grade worksheets are curated to give students an idea of how to approach word problems and develop the skillset required to solve them. You can expect to find simple addition and subtraction word problems, sums on multiplication and mixed fractions, and money problems, etc.

Benefits of 2nd Grade Two-Step Word Problems Worksheets

One of the major benefits associated with two-step word problems 2nd grade worksheets is that students get the chance to build the speed and accuracy that is required while attempting word problems of any kind. These 2nd garde math worksheets also consist of questions that are arranged in increasing order of difficulty. Thus, as kids progress from a simpler section to more complicated problems, they can develop confidence in solving these sums.

Printable PDFs for Grade 2 Two-Step Word Problems Worksheets

Another benefit of the two-step word problems grade 2 worksheets is that they are easy to use, interactive, and free to download.

Explore more topics at Cuemath's Math Worksheets .

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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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5 Teaching Mathematics Through Problem Solving

Janet Stramel

Problem Solving

In his book “How to Solve It,” George Pólya (1945) said, “One of the most important tasks of the teacher is to help his students. This task is not quite easy; it demands time, practice, devotion, and sound principles. The student should acquire as much experience of independent work as possible. But if he is left alone with his problem without any help, he may make no progress at all. If the teacher helps too much, nothing is left to the student. The teacher should help, but not too much and not too little, so that the student shall have a reasonable share of the work.” (page 1)

What is a problem  in mathematics? A problem is “any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific ‘correct’ solution method” (Hiebert, et. al., 1997). Problem solving in mathematics is one of the most important topics to teach; learning to problem solve helps students develop a sense of solving real-life problems and apply mathematics to real world situations. It is also used for a deeper understanding of mathematical concepts. Learning “math facts” is not enough; students must also learn how to use these facts to develop their thinking skills.

According to NCTM (2010), the term “problem solving” refers to mathematical tasks that have the potential to provide intellectual challenges for enhancing students’ mathematical understanding and development. When you first hear “problem solving,” what do you think about? Story problems or word problems? Story problems may be limited to and not “problematic” enough. For example, you may ask students to find the area of a rectangle, given the length and width. This type of problem is an exercise in computation and can be completed mindlessly without understanding the concept of area. Worthwhile problems  includes problems that are truly problematic and have the potential to provide contexts for students’ mathematical development.

There are three ways to solve problems: teaching for problem solving, teaching about problem solving, and teaching through problem solving.

Teaching for problem solving begins with learning a skill. For example, students are learning how to multiply a two-digit number by a one-digit number, and the story problems you select are multiplication problems. Be sure when you are teaching for problem solving, you select or develop tasks that can promote the development of mathematical understanding.

Teaching about problem solving begins with suggested strategies to solve a problem. For example, “draw a picture,” “make a table,” etc. You may see posters in teachers’ classrooms of the “Problem Solving Method” such as: 1) Read the problem, 2) Devise a plan, 3) Solve the problem, and 4) Check your work. There is little or no evidence that students’ problem-solving abilities are improved when teaching about problem solving. Students will see a word problem as a separate endeavor and focus on the steps to follow rather than the mathematics. In addition, students will tend to use trial and error instead of focusing on sense making.

Teaching through problem solving  focuses students’ attention on ideas and sense making and develops mathematical practices. Teaching through problem solving also develops a student’s confidence and builds on their strengths. It allows for collaboration among students and engages students in their own learning.

Consider the following worthwhile-problem criteria developed by Lappan and Phillips (1998):

Of course, not every problem will include all of the above. Sometimes, you will choose a problem because your students need an opportunity to practice a certain skill.

Key features of a good mathematics problem includes:

Needlepoint of cats

Problem solving is not a  neat and orderly process. Think about needlework. On the front side, it is neat and perfect and pretty.

Back of a needlepoint

But look at the b ack.

It is messy and full of knots and loops. Problem solving in mathematics is also like this and we need to help our students be “messy” with problem solving; they need to go through those knots and loops and learn how to solve problems with the teacher’s guidance.

When you teach through problem solving , your students are focused on ideas and sense-making and they develop confidence in mathematics!

Mathematics Tasks and Activities that Promote Teaching through Problem Solving

Teacher teaching a math lesson

Choosing the Right Task

Selecting activities and/or tasks is the most significant decision teachers make that will affect students’ learning. Consider the following questions:

mathematics problem solving for grade 2

Low Floor High Ceiling Tasks

By definition, a “ low floor/high ceiling task ” is a mathematical activity where everyone in the group can begin and then work on at their own level of engagement. Low Floor High Ceiling Tasks are activities that everyone can begin and work on based on their own level, and have many possibilities for students to do more challenging mathematics. One gauge of knowing whether an activity is a Low Floor High Ceiling Task is when the work on the problems becomes more important than the answer itself, and leads to rich mathematical discourse [Hover: ways of representing, thinking, talking, agreeing, and disagreeing; the way ideas are exchanged and what the ideas entail; and as being shaped by the tasks in which students engage as well as by the nature of the learning environment].

The strengths of using Low Floor High Ceiling Tasks:

Examples of some Low Floor High Ceiling Tasks can be found at the following sites:

Math in 3-Acts

Math in 3-Acts was developed by Dan Meyer to spark an interest in and engage students in thought-provoking mathematical inquiry. Math in 3-Acts is a whole-group mathematics task consisting of three distinct parts:

Act One is about noticing and wondering. The teacher shares with students an image, video, or other situation that is engaging and perplexing. Students then generate questions about the situation.

In Act Two , the teacher offers some information for the students to use as they find the solutions to the problem.

Act Three is the “reveal.” Students share their thinking as well as their solutions.

“Math in 3 Acts” is a fun way to engage your students, there is a low entry point that gives students confidence, there are multiple paths to a solution, and it encourages students to work in groups to solve the problem. Some examples of Math in 3-Acts can be found at the following websites:

Number Talks

Number talks are brief, 5-15 minute discussions that focus on student solutions for a mental math computation problem. Students share their different mental math processes aloud while the teacher records their thinking visually on a chart or board. In addition, students learn from each other’s strategies as they question, critique, or build on the strategies that are shared.. To use a “number talk,” you would include the following steps:

“Number Talks” can be used as an introduction, a warm up to a lesson, or an extension. Some examples of Number Talks can be found at the following websites:

Light bulb

Saying “This is Easy”

“This is easy.” Three little words that can have a big impact on students. What may be “easy” for one person, may be more “difficult” for someone else. And saying “this is easy” defeats the purpose of a growth mindset classroom, where students are comfortable making mistakes.

When the teacher says, “this is easy,” students may think,

Instead, you and your students could say the following:

Tracy Zager wrote a short article, “This is easy”: The Little Phrase That Causes Big Problems” that can give you more information. Read Tracy Zager’s article here.

Using “Worksheets”

Do you want your students to memorize concepts, or do you want them to understand and apply the mathematics for different situations?

What is a “worksheet” in mathematics? It is a paper and pencil assignment when no other materials are used. A worksheet does not allow your students to use hands-on materials/manipulatives [Hover: physical objects that are used as teaching tools to engage students in the hands-on learning of mathematics]; and worksheets are many times “naked number” with no context. And a worksheet should not be used to enhance a hands-on activity.

Students need time to explore and manipulate materials in order to learn the mathematics concept. Worksheets are just a test of rote memory. Students need to develop those higher-order thinking skills, and worksheets will not allow them to do that.

One productive belief from the NCTM publication, Principles to Action (2014), states, “Students at all grade levels can benefit from the use of physical and virtual manipulative materials to provide visual models of a range of mathematical ideas.”

You may need an “activity sheet,” a “graphic organizer,” etc. as you plan your mathematics activities/lessons, but be sure to include hands-on manipulatives. Using manipulatives can

Adapted from “ The Top 5 Reasons for Using Manipulatives in the Classroom ”.

any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific ‘correct’ solution method

should be intriguing and contain a level of challenge that invites speculation and hard work, and directs students to investigate important mathematical ideas and ways of thinking toward the learning

involves teaching a skill so that a student can later solve a story problem

when we teach students how to problem solve

teaching mathematics content through real contexts, problems, situations, and models

a mathematical activity where everyone in the group can begin and then work on at their own level of engagement

20 seconds to 2 minutes for students to make sense of questions

Mathematics Methods for Early Childhood by Janet Stramel is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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    Problem solving in mathematics is one of the most important topics to teach; learning to problem solve helps students develop a sense of solving real-life problems and apply mathematics to real world situations. It is also used for a deeper understanding of mathematical concepts.

  21. ‎Toancap1

    iPad. iPhone. Level 1 math software is adapted from the completely free grade 1 textbook math program, helping children to practice, achieve good results, learn math better. Types of problems include: - Decimals, calculations with decimals. - Geometry. - Measurement of time, math of uniform motion...