Cluster 2: Compute fluently with multi-digit numbers and find common factors and multiples. (Additional Cluster)Archived

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

Students are asked to rewrite 36 + 42 in the form a(b + c) where a is the greatest common factor of 36 and 42.

Type: Formative Assessment

Students are asked to multiply multidigit decimal numbers and are assessed for both accuracy and fluency.

Type: Formative Assessment

Students are asked to subtract multidigit decimal numbers and are assessed for both accuracy and fluency.

Type: Formative Assessment

Students are asked to add multidigit decimal numbers and are assessed for both accuracy and fluency.

Type: Formative Assessment

Students are asked to divide multidigit decimal numbers and are assessed for both accuracy and fluency.

Type: Formative Assessment

Students are asked to find the least common multiple of 8 and 12 and to explain how they found their answers.

Type: Formative Assessment

Students are given two whole numbers less than or equal to 100 and asked to find the greatest common factor.

Type: Formative Assessment

Students are asked to complete three long division problems (no remainders) to check for fluency with the standard division algorithm.

Type: Formative Assessment

Students are asked to complete three long division problems (each with a remainder) to check for fluency with the standard division algorithm.

Type: Formative Assessment

Students are asked to complete three long division problems (one with a remainder) to check for fluency with the standard long division algorithm.

Type: Formative Assessment

Most families must buy food and household items that they will need every few weeks. Instead of randomly throwing things into a shopping cart and paying whatever the total is, many families must stick carefully to a predetermined budget to buy all of the items they need. A helpful way to make sure that you are able to buy everything needed is to use a list that is written before going shopping. Families must also determine, if they will purchase "name brand" or "store brand" products. Today, students will practice using a grocery list with a predetermined budget as they add and subtract decimals.

Type: Lesson Plan

In this lesson, students will:

• Investigate how natural disasters have affected human life in Florida.
• Add, subtract, and multiply multi-digit decimals using the standard algorithm.
• Find a percent of a quantity as a rate per 100 and then solve problems involving finding the whole given a part and the percent.

Type: Lesson Plan

This lesson introduces the idea of finding volume. Volume in sixth grade math is very "rectangular" (cubes, rectangular prisms) and this lesson brings to light that volume is simply a measure of available space, but can take on many shapes or forms (cylinders for example - graduated cylinders and beakers) in science. Students will be left to design their own data collection and organizing the data that they collect. They will apply the skill of finding volume to using fractional parts of a number (decimals) and finding the product using the volume formula.

Type: Lesson Plan

Students will analyze data to create a route and itinerary, while following time frame guidelines.

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 explore lodging options for their dream family vacation. Students will plan a vacation for a family of four. With a budget of $5,000 students will prepare a budget to include the cost of transportation, lodging, and attractions. In this lesson, students will focus on preparing the budget for hotel costs. In lesson 1 of this unit lesson, students prepared a budget for transportation. In the subsequent lesson to this one, students will prepare a budget for the entertainment/attractions costs portion of their vacation. Teachers can choose to do one, some, or all lessons as they can be completed independently of one another.

Type: Lesson Plan

This is a interdisciplinary MEA lesson for science, writing, and math. This lesson ask students develop a criteria for selecting headphones and develop an equation that supports their choices.

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

Students will look at a data set to determine which vending machine should be placed in a school. Students have to determine profit and consider other provided data.

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 use their knowledge of division and division strategies to solve problems that have been written in a code where numbers are replaced with symbols. The students are challenged to find out how the traditional algorithm strategy works and how it compares to other strategies they already know. Students are also charged with creating a list of mathematical tools that help make solving division problems easier.

Type: Lesson Plan

In this lesson, students will be given a list of ingredients and prices they must use to create their own snack mix. Students will have to add, subtract, multiply, and divide decimal numbers. The closure of the lesson focuses specifically on the division strategies students used to solve the problem.

Type: Lesson Plan

In this Model Eliciting Activity, MEA, the purpose of this lesson is to provide students with the opportunity to solve real-world problems using addition, subtraction, multiplication, and division of multi-digit decimals. They will write arguments to support claims with clear reasons and relevant evidence. Engage effectively in a range of collaborative discussions.

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

Multiply efficiently and fluently with multi-digit decimals using a standard algorithm for the operation.

Type: Lesson Plan

Students develop a procedure to select a cell phone based on qualities they think their parents value in a cell phone. Students present their solution in writing to a marketing company, who wishes to use the results to market cell phones to parents of elementary students.

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

Short Hop Airlines, a small airline, features flights under 120 minutes. Students are provided a list of songs of varying genre and asked to create a playlist for each of the 9 flights. They will also calculate royalty fees on all songs. Oral presentations of their procedure and song choices will be shared with the class.

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 first define in their own words what the greatest common factor (GCF) and least common multiple (LCM) mean. They will take this understanding and apply it to solving GCF and LCM word problems. Students will then illustrate their understanding by creating posters based on their word problems. There are examples of different types of methods, online games, a rubric, and a power point to summarize this two-day lesson.

Type: Lesson Plan

Students are asked to decide which field trips would be the most cost effective and be the best one(s) for their grade level to attend. They are given a set dollar amount and asked to consider distance, cost of busses per mile, admission costs, food costs, and also consider feedback from other students regarding how fun and how educational the trip will be.

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

Students will be given a list of phone rates of 5 different companies and will have to decide which plan(s) are the best according to cost. They will discuss minutes and monthly plan and the cost of each phone. All of the plans are on the prepayment option.

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

The students will create a package list for a travel company. They must use all operations with decimals as well as compare decimals.

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 Model Eliciting Activity, MEA, students will learn about nutrition and the importance of keeping things balanced on their plate using the FDA recommendations. Students will need to rank meal plans and shake plans in order to help a restaurant catering company keep a successful business going. After students have evaluated and created rankings for their meal choice, they will write a letter explaining their rationale and thinking and find the bundle price. They will then receive a second letter asking for their help in ranking vegetarian shakes from highest to lowest to support an expanded customer base and find the bundle price. Students will now have the chance to learn a little more about vegetarians and their food choices.

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

Students will model how to express an addition problem using the distributive property.

Type: Lesson Plan

This MEA asks the students to decide which company would be the “best and the worst” to use to purchase scuba diving masks for Tino’s Scuba Diving School to provide to their diving certification students. Furthermore, the students are asked to suggest which type of scuba diving masks should be purchased in term of multiple panes – single pane mask, double pane mask, full face mask, skirt color, fit, durability, and price. Students must provide a "top choice" scuba diving mask to the company owner and explain how they arrived at their solution.

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 lesson will show the student how to use the distributive property to express a sum of two whole numbers 1-100.

Type: Lesson Plan

In this Model Eliciting Activity, MEA, the purpose of this lesson is to solve real-world and mathematical problems. Students will also use operations with multi-digit decimals to solve problems. They will write arguments to support claims with clear reasons and relevant evidence. Students will engage effectively in a range of collaborative discussions.

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 lesson teaches Least Common Multiples.

Type: Lesson Plan

Fancy Fractions Catering Company will be hosting a party and need your help to make it happen! Your help is needed to find out how much of each ingredient is needed to feed 200 people and the most economical way of doing this (Brand name brands or store brand). You also have the option of omitting up to three ingredients from the recipe.

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

The students will clip out advertisements or use the attached PowerPoint to determine the better buy between small quantities and large quantities. The students will answer the question, "Which item costs less per unit?" and demonstrate fluency in dividing with decimals.

Type: Lesson Plan

A traveling baseball team coach is asking a group of engineers to provide a travel plan from Boston to Jacksonville, Florida with the hopes of attending Major League baseball games along their route. The students will design the route on a large US map highlighting their travel plan and submit the map and a written rationale of their plan.

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 lesson uses a real-life approach to exploring the use of Greatest Common Factors (GCF). The students will utilize math practice standards as they analyze math solutions and explain their own solutions.

Type: Lesson Plan

This lesson teaches students how to find the GCF and LCM by factoring. This is a different method than is normally seen in textbooks. This method easily leads to solving GCF word problems and using the distributive property to express a sum of two whole numbers.

Type: Lesson Plan

In this Model Eliciting Activity (MEA), students will multiply and divide decimals as well as use the resulting data to make a decision about a candy store.

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 lesson reviews all four operations (adding, subtracting, multiplying, and dividing) with decimals. It is designed to easily provide differentiated instruction for students. The culmination of the lesson is a computer-based assessment which provides a fun change from a typical pencil and paper test.

Type: Lesson Plan

In this introductory lesson, students test how the basic operations performed on the dividend and divisor affect the quotient of a pair of numbers. Students then conclude whether the results of their trials can be applied to solve problems with a decimal divisor.

Type: Lesson Plan

The students will determine what to order at a dinner with friends yet stay within a budget. The students will try to maximize their budgets and order as much food as they possibly can with their given amount of money.

Type: Lesson Plan

This activity provides an introduction to composite numbers and prime numbers through factorization.

Type: Lesson Plan

Use the least common multiple to solve real-life problems with Brady and Natalia in this interactive tutorial.

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

Type: Original Student Tutorial

Sail through subtracting decimals to the thousandths place using a standard algorithm in this interactive tutorial.

Type: Original Student Tutorial

Learn to add decimals to the thousandths using a standard algorithm at the ice cream shop in this interactive tutorial. 

Type: Original Student Tutorial

Explore computer coding on the farm by declaring and initializing variables in this interactive tutorial. You'll also get a chance to practice your long division skills.

Type: Original Student Tutorial

Learn how to find the least common multiple by helping Brady and Natalia work through some homework questions in this interactive student tutorial.

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

Type: Original Student Tutorial

The goal of this task is to give students a context to investigate large numbers and measurements. Students need to fluently convert units with very large numbers in order to successfully complete this task. The total number of pennies minted either in a single year or for the last century is phenomenally large and difficult to grasp. One way to assess how large this number is would be to consider how far all of these pennies would reach if we were able to stack them one on top of another: this is another phenomenally large number but just how large may well come as a surprise.

Type: Problem-Solving Task

The purpose of this task is to gain a better understanding of factors and common factors. Students should use the distributive property to show that the sum of two numbers that have a common factor is also a multiple of the common factor.

Type: Problem-Solving Task

The purpose of this task requires students to apply the concepts of factors and common factors in a context. A version of this task could be adapted into a teaching task to help motivate the need for the concept of a common factor.

Type: Problem-Solving Task

The purpose of this task is for students to solve problems involving decimals in a context involving a concept that supports financial literacy, namely inflation. Inflation is a sustained increase in the average price level. In this task, students are asked to compare the buying power of $20 in 1987 and 2012, at least with respect to movie tickets.

Type: Problem-Solving Task

This problem uses the same numbers and asks similar mathematical questions as "The Florist Shop" file, but that task requires students to apply the concepts of multiples and common multiples in a context.

Type: Problem-Solving Task

Given the fact 13 x 17 = 221, students are asked to reason about and explain the decimal placement in multiplication and division problems where some of the numbers involved have been changed by powers of ten.

Type: Problem-Solving Task

Students are asked to reason about and explain the placement of decimals in quotients.

Type: Problem-Solving Task

The purpose of this task is for students to solve problems involving multiplication and division of decimals in the real-world context of setting financial goals. The focus of the task is on modeling and understanding the concept of setting financial goals, so fluency with the computations will allow students to focus on other aspects of the task.

Type: Problem-Solving Task

Students are asked to solve a real-world problem involving common multiples.

Type: Problem-Solving Task

There are two aspects to fluency with division of multi-digit numbers: knowing when it should be applied, and knowing how to compute it. While this task is very straightforward, it represents the kind of problem that sixth graders should be able to recognize and solve relatively quickly. Easily recognizing contexts that require division is a necessary conceptual prerequisite to more complex modeling problems that students will be asked to solve later in middle and high school.

This task also has a natural carryover to work with ratios and rates, so students should also be building connections between these kinds of division problems and finding unit rates.

Type: Problem-Solving Task

This problem uses the same numbers and asks essentially the same mathematical questions as "Bake Sale," but that task requires students to apply the concepts of factors and common factors in a context.

Type: Problem-Solving Task

Students are asked to solve problems from context by using multiplication or division of decimals.

Type: Problem-Solving Task

The purpose of this task is to use the computation shown below to find the products. Understanding of place value is necessary for successful completion.

Type: Problem-Solving Task

Students are asked to add or subtract decimals to solve problems in context.

Type: Problem-Solving Task

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

In this problem solving activity, students will practice measuring and making calculations in the context of providing nutrients to a baby whale that was rescued.

Type: Teaching Idea

• Given data about sharks and the amount of food they eat, students will be able to solve for the unknown in percentage problems.
• Given information about a shark's growth, students will be able to graph coordinates and interpret a linear graph.
• Given the conversion factor, students will be able to convert from metric to English units.

Type: Teaching Idea

This video demonstrates the prime factorization method to find the lcm (least common multiple).

Type: Tutorial

This video demonstrates dividing two numbers that are decimals.

Type: Tutorial

This video demonstrates how to multiply two decimal numbers.

Type: Tutorial

This video demonstrates adding decimal numbers to solve a word problem.

Type: Tutorial

Let's show subtracting with digits up to the thousandths place in this tutorial.

Type: Tutorial

Watch as we align decimals before subtracting in this tutorial.

Type: Tutorial

Learn how to add decimals and use place value in this tutorial. 

Type: Tutorial

Use long division to find the percent in this tutorial.

Type: Tutorial

Here we have a couple of word problems searching for the least common multiple and the other for the greatest common factor. 

Type: Video/Audio/Animation