Standard 2: Add and subtract multi-digit whole numbers. Build an understanding of multiplication and division operations.

This tutorial will help you to brush up on your multiplication, division and factoring skills with this exciting game. 

Type: Educational Game

This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents.

Various levels of difficulty make this game appropriate for multiple age and ability levels.

Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals.

Multiplication/Division: The multiplication and addition of whole numbers.

Percentages: Identify the percentage of a whole number.

Fractions: Multiply and divide a whole number by a fraction, as well as apply properties of operations.

Type: Educational Game

In this activity, students are quizzed on their ability to estimate sums, products, and percentages. The student can adjust the difficulty of the problems and how close they have to be to the actual answer. This activity allows students to practice estimating addition, multiplication, or percentages of large numbers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Game

In this activity, students solve arithmetic problems involving whole numbers, integers, addition, subtraction, multiplication, and division. This activity allows students to track their progress in learning how to perform arithmetic on whole numbers and integers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Software / Tool

Students are asked to solve two subtraction problems using the standard algorithm.

Type: Formative Assessment

Students are asked to find the error in a partially completed subtraction problem using the standard algorithm and to solve the problem correctly.

Type: Formative Assessment

Students are asked to solve two addition problems using the standard algorithm.

Type: Formative Assessment

Students are given a context for a multiplicative comparison and asked to explain the comparison.

Type: Formative Assessment

Students discuss the relationship between the lengths of two snakes in a multiplicative comparison problem that includes an equation.

Type: Formative Assessment

Students write an equation to match a given word problem.

Type: Formative Assessment

Students read a multiplicative comparison word problem and are asked to write an equation that matches the problem.

Type: Formative Assessment

Students are asked to complete subtraction problems using the standard algorithm.

Type: Formative Assessment

Students consider the solution to a multiplication problem and explain their thinking.

Type: Formative Assessment

Students are asked to explain how the knowing the product of nine and three can help in finding the product of nine and 30.

Type: Formative Assessment

Students are asked to explain why, when multiplying by a power of 10, the product has a zero in the ones place.

Type: Formative Assessment

Students are asked to consider how using an easier, known fact could help them solve a related multiplication problem with a multiple of 10.

Type: Formative Assessment

Students are asked to explain how to use a number line for dividing, in the context of a word problem.

Type: Formative Assessment

Students are asked to illustrate a division problem and write a corresponding equation.

Type: Formative Assessment

Students are given division word problem and asked to determine how it might have been solved and what the quotient means.

Type: Formative Assessment

Students are assessed for fluency with multiplication.

Type: Formative Assessment

Students are assessed for fluency with division.

Type: Formative Assessment

Students are asked to describe two different ways to find the product of two numbers.

Type: Formative Assessment

Students are assessed on their fluency with multiplication facts for the products of two one-digit numbers.

Type: Formative Assessment

Students add four two-digit numbers within the context of a word problem.

Type: Formative Assessment

Students are asked to add four two digit numbers by considering how another student added "friendly" numbers first.

Type: Formative Assessment

The student is encouraged to use compensation to efficiently add multi-digit numbers.

Type: Formative Assessment

Students are asked to complete four subtraction problems (within 1000) using strategies of their own choosing.

Type: Formative Assessment

Students are asked to complete addition and subtraction problems that can be done more easily by using properties.

Type: Formative Assessment

Students are asked to add four different pairs of numbers (within 1000) using strategies of their own choosing.

Type: Formative Assessment

Students are asked to write multiplication word problems prompted by pictures and then to write both an addition and a multiplication expression that can be used to solve the problem.

Type: Formative Assessment

Students are given a context for a multiplication problem and asked to determine how to solve it and what the product means.

Type: Formative Assessment

Students are asked to explain how to use a number line for multiplying, in the context of a word problem.

Type: Formative Assessment

Students are asked to explain what 5 x 7 means and to provide a real-world context for 5 x 7.

Type: Formative Assessment

Students are asked to add four two digit numbers using place value.

Type: Formative Assessment

Students add four two-digit numbers without the context of a word problem.

Type: Formative Assessment

A data table is given listing class donations to a food drive. Students interpret the data and answer questions using addition and subtraction. Students discuss the importance of, volunteerism and ways that they can help their community.

Type: Lesson Plan

Students will use their knowledge of properties of materials and measurement of length to determine how the properties of different surfaces affect the distance traveled by a toy car.

Type: Lesson Plan

During this activity, students will create an incubator to save the last dinosaur eggs. Students will use their knowledge of energy to develop a strategy and choose which materials would be best for their dinosaur egg incubator.

Type: Lesson Plan

This lesson is a hands-on activity that includes multiplication using arrays. The lesson also serves as a great transition from repeated addition to multiplication.

Type: Lesson Plan

Students will solve real-world addition problems within 1,000 using strategies and an algorithm and justify their solutions.

Type: Lesson Plan

Type: Lesson Plan

Students will learn how multiplication is related to repeated addition and use different strategies to find the product of equal groups situations.

Type: Lesson Plan

Students will learn how to represent and count equal groups through the use of literature and situational story problems. Using the book Each Orange Had 8 Slices, students will use manipulatives to find the total number of objects in a collection of equal groups. Students will learn to write corresponding multiplication equations.

Type: Lesson Plan

“How many Circles? How many Stars?” is an activity that will give students a visual representation of multiplication. It will also help students see multiplication as the combining of equal-size groups that can be represented with a multiplication equation.

Type: Lesson Plan

In this lesson, which focuses specifically on the elapsed time portion of the standard, students work in small groups in a "race" to solve real world problems involving time.

Type: Lesson Plan

This lesson builds upon student knowledge of arrays to using the Van de Walle 100-Dot Matrix model to solve multiplication problems involving rows and columns.

Type: Lesson Plan

In this lesson, students will learn to use the structure of array frames to build familiarity and fluency with the array as a tool. Students will explore multiplication by solving several multiplication word problems involving rows and columns situations using the array as a representation.

Type: Lesson Plan

In this model-eliciting activity (MEA), students will work together to determine the best bus for a class trip.  Students will be able to decide between several buses with varying capabilities and costs while practicing their application of multiplying one-digit whole numbers by a multiple of ten.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

This is an introductory lesson to prepare students to move from using repeated addition to using multiplication to represent equal groups situations.

Type: Lesson Plan

In this MEA, students will work in groups to rank books using the following criteria: price, genre, number of pages, reading level and a summary provided for each book. The students must calculate the price for a class set of each book by multiplying each price by 20 students. There is a budget of $100. Students are then given a new budget and a new criteria and asked to re-evaluate their decision.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Batter Up!!! Help the Peace Love Baseball Championship find a home!!! In this interactive Model-Eliciting Activity (MEA), the students will successfully multiply one digit whole numbers by multiples of 10. The students will also work collaboratively to express their opinions, while considering those of their peers.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

In this lesson students will make and complete tables to express larger unit measurements in terms of a smaller unit within one system of units. They will use the chart to make comparisons and explain their reasoning.

Type: Lesson Plan

Students will explore the Zero Property of Multiplication using array and equal-group models for multiplication. Students will model story problems, translate problems into multiplication facts, and identify patterns in a set of multiplication facts to develop understanding of the Zero Property of Multiplication.

Type: Lesson Plan

In this lesson students will explore the Multiplicative Identity Property of 1, using array and equal-group models for multiplication. Students will model story problems, translate problems into multiplication equations, and identify patterns in a set of multiplication facts to develop understanding of the Multiplicative Identity Property of 1.

Type: Lesson Plan

In this lesson, students will use pictures in arrays and groups to write multiplication story problems, write an equation, solve the problem, and identify the factors and products.

Type: Lesson Plan

The lesson uses a movie making theme to teach the characteristics and purpose of arrays, as well as the vocabulary, factor and product.

Type: Lesson Plan

Students will be able to use counters to create equal groups and write multiplication equations to represent these representations.

Type: Lesson Plan

In this lesson students will use various strategies to multiply one-digit numbers by multiples of 10 within the range of 10-90. The strategies will encompass the Distributive, Commutative, and Associative properties, place value, number lines, base-ten blocks, diagrams, hundreds chart. Students will play a game with number cubes to practice this multiplication.

Type: Lesson Plan

The students will compare different nutritional content of chicken nuggets from many restaurants. They will factor in the calories, the total fat, saturated fat, and sodium levels in the nuggets to rank the nuggets from healthiest to least healthy.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Kites for Education is a Modeling Eliciting Activity which presents students with an engineering challenge in which they must analyze data sets and develop a procedure for ranking different kite models. The product ranked as best by the students will hypothetically be sold to customers and the profit used to purchase school textbooks and supplies for school age children impacted by Haiti's devastating earthquake.

Type: Lesson Plan

Students will use the open number line as a strategy to add within 1,000. The lesson begins with a formative assessment that evaluates students' strategies for efficiently solving addition sentences within 1,000. In order for students to have practice reinforcing the skill, students will complete the guided practice with open number lines, as well as playing the game, Jumping Beans. To conclude the lesson, students will evaluate a solution to an open number line problem.

Type: Lesson Plan

This is an introductory lesson to explore the use of arrays to solve multiplication problems. Students build arrays and save the arrays in a class Multiplication Chart. They learn to use arrays to find products and factors, and by placing them in the Multiplication Chart, they learn how to read the chart. They learn how to write equations to represent situations that are modeled with arrays. An overall theme is the organization of the multiplication chart and how it includes arrays within.

Type: Lesson Plan

The definition of the Zero Property of Multiplication will be analyzed, modeled and practiced.   

Type: Lesson Plan

In this lesson, students will learn to solve division problems by relating them to multiplication facts. Practice materials focus on the 6's and 8's multiplication facts.

Type: Lesson Plan

In this lesson, students will deepen their knowledge of using equal groups in multiplication and their ability to visualize the quantity of an item in a given object. They will use problem-solving skills and see the value in using benchmarks.

Type: Lesson Plan

Students will engage with questions to evaluate the students' abilities to select and apply multiplication strategies with fluency and efficiency. The focus of the lesson is decomposing numbers to multiply using the Distributive property and understanding and applying the Commutative property. Then, students will reinforce decomposing of factors while playing Decomposition of Factors. The lesson concludes with a real world application problem on an Exit Slip.

Type: Lesson Plan

In this lesson, students will demonstrate fluency in using a standard algorithm to complete story problems involving subtraction with regrouping using multi-digit whole numbers.

Type: Lesson Plan

Students will learn how to transpose a horizontal addition equation with two-digit addends using a specialized vertical place value work mat. Students will "rip and regroup" to help understand how to regroup ten ones as one ten and move toward using a standard algorithm for addition.

Type: Lesson Plan

In this lesson students will model partitive division through the real-world activity of a pet store owner.

Type: Lesson Plan

Students work together to create arrays to represent given numbers.

Type: Lesson Plan

In this lesson, students will understand the concept of arrays and will be able to create/draw an array for multiplication sentences. Engaging center game is used to help students with concrete visual representation of multiplication sentences.

Type: Lesson Plan

In this lesson students will use Cheerios to solve multiplication equations relating 3 whole numbers from word problems that include missing factors ranging from one through ten. Students will also argue the validity of multiplication equations that include missing factors and products with corresponding word problems.

Type: Lesson Plan

This is a hands-on lesson for introducing and practicing building arrays to create models that represent the distributive property of multiplication, and then using those arrays to draw models of the equations they represent.

Type: Lesson Plan

In this lesson, the students will work in independently or in small groups to write equations to represent situations as well as their own math riddles around the concepts of multiplication. The teacher will use the book, The Grapes of Math by Greg Tang, to support this lesson.

Type: Lesson Plan

This lesson helps students make the connections between area and multiplication using square tiles.

Type: Lesson Plan

Students will add 3-digit numbers by decomposing them by place value.  It is a useful lesson to reinforce place value concepts when adding.

Type: Lesson Plan

In this hands-on math exploration, students will use knowledge of estimation and multiplication to develop strategies for estimating how many seeds are in a medium-sized pumpkin.

Type: Lesson Plan

In this lesson students will be creating, describing, and analyzing arrays as they relate to multiplication. In addition, they will be working on hands on activities that allow them to justify their answers and prove their reasoning.

Type: Lesson Plan

In this lesson, students will learn that in some word problems too much information is given. They will learn to identify what information is needed to solve a single digit multiplication problem and what is "additional information" or way too much! With this information, they will represent their answers using arrays and explain their thinking. This is a good lesson to use after students have become comfortable with multiplication and prior to introducing multi-step problems.

Type: Lesson Plan

Learn how to use a bar graph to summarize voting results at school in this interactive tutorial. 

This is part 2 in a two-part series. Click HERE to open Part 1.

Type: Original Student Tutorial

United States citizens have a responsibility to vote. In this integrated civics and math tutorial, a class collects voting data to display in a table showing the students' and teachers' choices for a new school project. 

Type: Original Student Tutorial

Help Jaliah continue to plan her birthday party and be fluent in her math facts using helpful facts she already knows, and the relationship between multiplication and division in Part 2 of this interactive tutorial.  

This is part 2 of 2-part series, click HERE to view part 1.

Type: Original Student Tutorial

Jaliah is ready to celebrate her birthday and use strategies of doubling and halving and relating multiplication and division for building fluency with multiplication and division facts in this interactive tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Type: Original Student Tutorial

Come play with Marty the monkey as he teaches you how to understand the concept of multiplication in this interactive tutorial. 

Type: Original Student Tutorial

Learn to multiply by multiples of ten, in this interactive tutorial!

This is the second tutorial in a two-part series. .

Type: Original Student Tutorial

Learn how to multiply a 1-digit number by ten using a pattern to help you. This interactive tutorial is Part 1 in a two-part series about multiplying by multiples of ten.

Type: Original Student Tutorial

Learn to add multi-digit numbers using a standard algorithm in this interactive tutorial.

Type: Original Student Tutorial

Help Speedy Sam add and subtract as quickly as possible by using the properties of addition and subtraction in this interactive tutorial.

Type: Original Student Tutorial

Allie learns to be fair when she shares and she learns more about division in this interactive tutorial.

Type: Original Student Tutorial

How are fluency and automaticity defined? Dr. Lawrence Gray explains fluency and automaticity in the B.E.S.T. mathematics benchmarks in this Expert Perspectives video.

Type: Perspectives Video: Expert

What are the components to a good procedure? Dr. Lawrence Gray discusses the role of procedures in the path to fluency in this Expert Perspectives video.

Type: Perspectives Video: Expert

Why do students need "a" good procedure for the arithmetic operations? Dr. Lawrence Gray explains why math may look different than in the past in this Expert Perspectives video.

Type: Perspectives Video: Expert

What roles do exploration, procedural reliability, automaticity, and procedural fluency play in a student's journey through the B.E.S.T. benchmarks? Dr. Lawrence Gray explains the path through the B.E.S.T. maththematics benchmarks in this Expert Perspectives video.

Type: Perspectives Video: Expert

What is fluency? What are the ingredients required to become procedurally fluent in mathematics? Dr. Lawrence Gray explores what it means for students to be fluent in mathematics in this Expert Perspectives video.

Type: Perspectives Video: Expert

Why is it important to look beyond whether a student gets the right answer? Dr. Lawrence Gray explores the importance of understanding why we perform certain steps or what those steps mean, and the impact this understanding can have on our ability to solve more complex problems and address them in the context of real life in this Expert Perspectives video.

Type: Perspectives Video: Expert

Ever wonder why the benchmarks say, “a standard algorithm,” instead of, “the standard algorithm?" Dr. Lawrence Gray explores the role that standard algorithms can play in building and exhibiting procedural fluency through this Expert Perspectives video.

Type: Perspectives Video: Expert

Unlock an effective teaching strategy for representing remainders as fractions in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Unlock an effective teaching strategy for making connections in area models in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Unlock an effective teaching tool that can help students all the way from basic counting principles to multiplying polynomials.

Type: Perspectives Video: Teaching Idea

Unlock an effective teaching strategy for teaching multiplying multi-digit numbers using ten frames in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Both of the questions are solved by the division problem 12÷3 but what happens to the ribbon is different in each case. The problem can be solved with a drawing of a tape diagram or number line. For problem 1, the line must be divided into 3 equal parts. The second problem can be solved by successive subtraction of 3 feet to see how many times it fits in 12.

Type: Problem-Solving Task

This task presents an incomplete problem and asks students to choose numbers to subtract (subtrahends) so that the resulting problem requires different types of regrouping. This way students have to recognize the pattern and not just follow a memorized algorithm--in other words, they have to think about what happens in the subtraction process when we regroup. This task is appropriate to use after students have learned the standard US algorithm.

Type: Problem-Solving Task

The first of these is a multiplication problem involving equal-sized groups. The next two reflect the two related division problems, namely, "How many groups?" and "How many in each group?"

Type: Problem-Solving Task

In this task, the students are not asked to find an answer, but are asked to analyze the problems and explain their thinking. In the process, they are faced with varying ways of thinking about multiplication.

Type: Problem-Solving Task

This task is intended to assess adding of four numbers as given in the standard while still being placed in a problem-solving context. As written this task is instructional; due to the random aspect regarding when the correct route is found, it is not appropriate for assessment. This puzzle works well as a physical re-enactment, with paper plates marking the islands and strings with papers attached for the tolls.

Type: Problem-Solving Task

In this video tutorial from Khan Academy, learn how to subtract in situations that require regrouping twice using the expanded forms of numbers, as well as the standard algorithm.

Type: Tutorial

In this Khan Academy video tutorial, consider an alternate algorithm for subtracting multi-digit numbers mentally. This video is best for students that are already comfortable with using regrouping to subtract using the standard algorithm.

Type: Tutorial