Standard 2: Add, subtract, multiply and divide positive rational numbers.

Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.

Type: Educational Game

Students are asked to explain the relationship between a fraction division word problem and either a visual model or an equation.

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 consider why a number multiplied by 10 to the third power will have three zeros in the product.

Type: Formative Assessment

Students are asked to solve a word problem involving division of a whole number by a decimal using a model or drawing, a strategy based on place value, the relationship between multiplication and division, or properties of operations.

Type: Formative Assessment

Students are asked to complete two fraction division problems – one with fractions and one with mixed numbers.

Type: Formative Assessment

Students are asked to write a story context for a given fraction division problem.

Type: Formative Assessment

Students are asked to write and evaluate a numerical expression involving division of fractions and mixed numbers to model and solve a word problem.

Type: Formative Assessment

In this Model Eliciting Activity, MEA, students will use the provided data to calculate travel time and total cost after tax. Students will consider this data and other provided criteria to assist a travel agent in determining which airline to choose for a client.

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 explores the use of box plots and the mean absolute deviation to compare two data sets and draw inferences.

Type: Lesson Plan

Students will be able to match a 3-D shape with its net, then using the net, they will find the surface area of the shape. They will then be able to apply this knowledge to solve real world application problems, finishing up with a design contest.

Type: Lesson Plan

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

Students calculate the tax, tip, and discount in real-world situations.

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

In this lesson, students will build upon their arithmetic experiences with the distributive property to equate algebraic expressions through a series of questions related to real world situations and the use of manipulatives. Activities include the use of Algebra Tiles for moving the concrete learner to the abstract level and the use of matching cards.
This is an introductory lesson that only includes producing equivalent expressions such as 3(2 + x) = 6 + 3x.

Type: Lesson Plan

In this Model Eliciting Activity, MEA 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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx.

Type: Lesson Plan

The students will use square tiles or cubes to explore the meaning of "squared" and "cubed" numbers. They will model squared and cubed numbers to build a strong foundation for working with exponents. The students will learn the connections between area and volume models and the related positive exponents. This is an introductory lesson.

Type: Lesson Plan

In this lesson, students will explore and apply the use of nets to find the surface area of pyramids.

Type: Lesson Plan

This lesson is the first of two in a unit on surface area. This lesson provides a foundation for understanding the concept of surface area by introducing nets of right rectangular prisms. 

Type: Lesson Plan

Students explore how the formulas for surface area and volume were derived and apply this knowledge to solve problems. Students will be presented with a problem-solving task that incorporates finding the surface area and volume when designing an aquarium.

Type: Lesson Plan

This lesson is primarily formative in nature and is designed to introduce students to the area of a triangle by having them derive the formula themselves using the relationship between rectangles and triangles. During the lesson the teacher will be facilitating their students as they work with their teams and shoulder partners to solve problems.

Type: Lesson Plan

This lesson helps students develop procedural skills in dividing fractions. During this lesson students will discuss prior knowledge of the concept of dividing fractions and will solve problems independently and in pairs using the standard algorithm. The lesson also incorporates music and poster-making to reinforce the learning objective. This lesson was originally designed for a 6th-grade Intensive Math class and should only be used following lessons where students have developed a solid conceptual understanding of dividing fractions. This lesson may take up to 3 days depending on how much practice and extra activities your students require.

Type: Lesson Plan

This lesson provides teachers with a way to show students why multiplying negative numbers results in a positive answer. The lesson starts with a review of decomposition, the distributive property, and finding missing addends. Then, with teacher guidance, groups of students apply these skills in a systematic way to apply properties of operations to discover the rules governing the signs of products for positive and negative factors and to multiply positive and negative numbers in mathematical and real-world problems. Finally, students independently demonstrate mastery of the lesson objectives by completing an independent practice assessment.

Type: Lesson Plan

In this Model Eliciting Activity, MEA, students will work in groups to determine a procedure for ranking companies to build a park for a town. Students will need to calculate the area and cost of the park, make decisions based on a data table, and write a letter to the mayor providing evidence for their decisions. Students will need to trade-off between the size and cost of the park as well as park features such as pond or lake, sports field, and playground.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Students will learn what the "net" of a three-dimensional figure is, draw nets of right-rectangular prisms and right-rectangular prisms, accurately calculate the surface area of nets, and put nets together to create an original “person” or “pet.”

Type: Lesson Plan

Students are presented with the task of evaluating several types of fabric based on each of its characteristics. They need to analyze their current uniform needs and decide by choosing which type of fabric will best fit their uniform needs. Then they have to write a report explaining the procedure they used to analyze their choices, reasoning for their ranking and make the requested recommendations.

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, 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

Meaning of Exponents... Students will write and simplify numerical and algebraic expressions with natural number exponents. Bases are limited to positive integers.

Type: Lesson Plan

In this Model Eliciting Activity, MEA, "Sticks and Stones May Break My Bones", teams of students work as forensic anthropologists and use equations to determine the height and gender of persons to whom a series of newly discovered bones may belong.

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 a lesson designed to teach students how to find the volume and surface areas of right rectangular prisms. It provides an interactive lesson where students get to learn hands-on with cereal boxes and on the computer with a GeoGebra activity.

Type: Lesson Plan

In this activity, students will work in groups to evaluate the measurements of shapes that form three-dimensional composite shapes to compute the surface area.

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

This is the final part of the lesson "Makeover, Home Edition." This lesson is designed to teach students the applicability of finding the area of composite figures as well as understanding the importance of ratios in the real world. Part I (#48705) dealt with determining backyard dimensions for fence installation. Part II (#48967) concentrated on inserting a pool and patio into this backyard. Part III (#49025) dealt with creating a scale drawing of the backyard.

Type: Lesson Plan

This two-day lesson uses a hands-on problem-solving approach to find the volume of a right rectangular prism with positive rational number edge lengths. Students first design boxes and fill with Rubik's Cubes. They create a formula from the patterns they find. Using cubes with fractional edges requires students to apply fractional units to their formulas. 

Type: Lesson Plan

Students will be able to match a 3-D shape with its net, then using the net, they will find the surface area of the shape. They will then be able to apply this knowledge to solve real world application problems, finishing up with a design contest.

Type: Lesson Plan

In this Model Eliciting Activity, MEA, students will evaluate batteries using empirical data and customer comments to help a Taxi Cab Service decide which battery brand to purchase. In this real-world scenario, students will communicate with the client in letter format stating their suggested ranking. They will also provide calculations and justification for each 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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Students will apply and develop strategies to write and solve equations for mathematical and real world situations. Students will be encouraged to use various strategies, including using inverse operations, to find a solution.

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

This lesson requires students to use mathematical data and logic/reasoning to place vendors into retail spaces in a shopping plaza. Students will first rank five vendor types on their profitability (based on average sales and average overhead/upkeep costs), then place the vendor types into the 11-13 retail spaces. They are also required to find the area of each space and calculate the total leasing charges. The plans for the plaza are given on a coordinate plane, so students will need to find the lengths of horizontal and vertical line segments (using the coordinates of the endpoints) to calculate the areas of the rectangular and composite spaces.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

This MEA is a great way to implement Florida State Standards for math and language arts. It also supports cooperative learning groups and encourages student engagement. Students will explore different types of materials to determine which absorbs the least amount of heat. Students will also calculate the surface area to determine the cost for constructing the buildings using the materials.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

This activity has students predict the number of one hundred dollar bills that can fit inside the classroom. The students use volume measurements to explain their estimation.

Type: Lesson Plan

In this lesson, students work cooperatively to find the volume of a right rectangular prisms, using whole and fraction units of measurement, using the volume formula, and using manipulatives to count the number of units necessary to fill the prisms, and compare it with the formula results. 

Type: Lesson Plan

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

Type: Lesson Plan

In this lesson students will find the surface area of three-dimensional figures. Students will use nets to calculate the surface area of right rectangular prisms and right rectangular pyramids.

Type: Lesson Plan

In this activity the students will apply their knowledge of mathematical calculations to solve a real-world problem. They will analyze a collection of shipping boxes to determine which box will ship the most for the $100 allowed.

Type: Lesson Plan

This is a guided inquiry lesson to help students gain greater understanding of the relationship between 2-dimensional and 3-dimensional shapes. Students create right rectangular prisms and problem-solve how to find the flat 2-dimensional surface area. Students are asked to figure out how many party favors (prisms) can be painted with a quart of glow-in-the-dark paint.

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

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

In this introductory lesson to surface area, students will make connections between area of two-dimensional figures and calculating the surface area of rectangular prisms using nets, within the context of wrapping birthday presents! Math is Fun :)

Type: Lesson Plan

In the Sugar Scrub MEA students will analyze 5 sugar scrub formulas. In the first part, students are asked to evaluate each formula based on color, scent, and exfoliation. In the second part, students apply their methodology to a cost analysis of the scrubs.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx.

Type: Lesson Plan

This lesson teaches Least Common Multiples.

Type: Lesson Plan

In this lesson students will extend their knowledge of volume from using whole numbers to using fractional units. Students will work with adding, multiplying, and dividing fractions to find the volume of right rectangular prisms, as well as, determining the number of fractional unit cubes in a rectangular prism.

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 use the 4 operations with decimal numbers and calculate profit (including negative numbers) as well as use the resulting data to help a business owner make decisions about their candy stores.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

This lesson uses a discovery approach to exploring the meaning of volume. The students will work with cubes as they construct and analyze the relationship between the length, width, and height to the total amount of cubes. Students will be able to apply this concept to real world applications of other right rectangular prisms and compare them to determine which will hold the most volume. 

Type: Lesson Plan

Area of a Right Triangle

Type: Lesson Plan

In this Model Eliciting Activity, MEA, students are to decide on a pressure cleaning machine that will provide the Sidewalks and Roof Cleaning Services Incorporated with the best value for their money. Students are asked to provide a "Best Value" pressure cleaner to the company owner and explain how they arrived at their solution.

Model Eliciting Activities are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Students will work in groups to conduct class surveys, using the results of the survey to calculate various measures of central tendency.

Type: Lesson Plan

The students will convert fractions into decimals and multiply to determine the amount of food to feed their assigned cat. Using this amount, they will calculate (division of decimals) the number of servings and the price per serving of cat food. Students will work with three brands of food and enter the data into their charts. Finally, the students will analyze the data to determine the most affordable food.

Type: Lesson Plan

In this lesson students will explore the different methods available for dividing fractions through a student-based investigation. The teacher will facilitate the discussion, but the students will discover the different methods on their own or with a partner as they work through the different steps.

Type: Lesson Plan

This lesson is 2 of 2 and is primarily formative in nature, but includes a summative assessment for students to take during the following class period. 

During the lesson, students will be reviewing for their assessment on the surface area formula for a right rectangular prism. 

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

This lesson allows the students to explore the foundation for dividing fractions as well as correctly solving word problems involving division of fractions. It includes the use of the Philosophical Chairs activity and numerical solutions. Group activities are included to foster cooperative learning.

Type: Lesson Plan

Students will solve problems involving sales tax and tips; students will apply the properties of operations with numbers in decimal, percent, and fraction form. Students will convert between numbers in any form as appropriate.

Type: Lesson Plan

Students will multiply a fraction times a fraction. The students will section off a square through rows and columns that will represent the strategy of multiplying numerators and then denominators.

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

This lesson allows students to derive an algorithm for dividing fractions using visual fraction models and equations to represent the problem.

Type: Lesson Plan

In this lesson, students will explore the relationship between volume and surface area through real-world problem solving. They will work with a partner as they are tasked with finding the least expensive packaging (smallest surface area) for a given number of caramels (volume). Students will justify their packaging strategy in a group discussion.

Type: Lesson Plan

In this activity, students use a house blueprint to find the area of carpeted floor by decomposing composite shapes into rectangles and triangles. As students critique each other's reasoning, they refine their thinking of surface area. 

Type: Lesson Plan

This lesson involves students modeling fraction multiplication with rectangular arrays in order to discover the rule for multiplication of fractions.

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 lesson allows students to derive the formulas for 3D figures by having them build models for nets.

Type: Lesson Plan

Have your students become "Data Doctors" by examining and analyzing means of central tendency. This lesson is a great introduction to mean, median, mode and range. Students will be sets of data, get to work in small groups examining the sets, view a poem that will help them remember each term, and take surveys to get real data sets.

Type: Lesson Plan

This lesson allows a hands-on approach for students to use real-life problem-solving. Students will apply their measurement skills to the concept of surface area. This lesson provides opportunities for students to work cooperatively with others as a team.

Type: Lesson Plan

Students will translate verbal phrases into algebraic expressions. Students are given practice in writing expressions that record operations with numbers and variables. Special attention is given to writing operations in the correct order. Class work and homework worksheets are provided with answer keys for each.

Type: Lesson Plan

Lotsa Lotion Labs requests the help of your team to rank a group of sunscreens, explain the process and justify how you chose which is 'best.' An additional hands-on lesson investigating solar energy and sunscreens is included as an extension activity.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

This lesson explores the creation of box plots to compare two data sets and draw inferences.

Type: Lesson Plan

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. mathematics 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 teaching decimal multiplication in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Why did the math teacher KROS the ocean? Because it made for a wonderful way to engage students and do something unique.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set [.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth [.KML]

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Teaching Idea

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

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 solve a distance problem involving fractions.

Type: Problem-Solving Task

Students are asked to solve a fraction division problem using both a visual model and the standard algorithm within a real-world context.

Type: Problem-Solving Task

Students are asked a series of questions involving a fraction and a whole number within the context of a recipe. Students are asked to solve a problem using both a visual model and the standard algorithm.

Type: Problem-Solving Task

Students are asked to solve a distance problem involving fractions. The purpose of this task is to help students extend their understanding of division of whole numbers to division of fractions, and given the simple numbers used, it is most appropriate for students just learning about fraction division because it lends itself easily to a pictorial solution.

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 use fractions to determine how many hours it will take a car to travel a given distance.

Type: Problem-Solving Task

Students are asked to use fractions to determine how long a video game can be played.

Type: Problem-Solving Task

The purpose of this task is to help students get a better understanding of multiplying and dividing using fractions.

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

The purpose of this task is to help give students a better understanding of multiplying and dividing fractions.

Type: Problem-Solving Task

The purpose of this task is to help students explore the meaning of fraction division and to connect it to what they know about whole-number division. Students are asked to explain why the quotient of two fractions with common denominators is equal to the quotient of the numerators of those fractions.

Type: Problem-Solving Task

This task builds on a fifth grade fraction multiplication task, "Drinking Juice." This task uses the identical context, but asks the corresponding "Number of Groups Unknown" division problem. See "Drinking Juice, Variation 3" for the "Group Size Unknown" version.

Type: Problem-Solving Task

Students are asked to solve a fraction division problem using a visual model and the standard algorithm.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

This instructional task requires that the students model each problem with some type of fractions manipulatives or drawings. This could be pattern blocks, student or teacher-made fraction strips, or commercially produced fraction pieces. At a minimum, students should draw pictures of each. The above problems are meant to be a progression which require more sophisticated understandings of the meaning of fractions as students progress through them.

Type: Problem-Solving Task

The purpose of this problem is to help students deepen their understanding of the meaning of fractions and fraction division and to see that they get the same answer using standard algorithm as they do just reasoning through the problem. These two fraction division tasks use the same context and ask "How much in one group?" but require students to divide the fractions in the opposite order. Students struggle to understand which order one should divide in a fraction division context, and these two tasks give them an opportunity to think carefully about the meaning of fraction division.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

This professional development module shows teachers how to use area models to understand multiplication and division of fractions.

Type: Professional Development

Students communicate mathematical ideas and visually represent ideas by constructing charts, graphs, and scale drawings based on information cards about various marine animals.

Type: Teaching Idea

Students use a scale representation of the top 26 small planets and large moons in the solar system to compare their relative sizes to Earth. Students will use simple fractions to solve real world problems.

Type: Teaching Idea

This interactive resource provides three activities which model the concept of dividing fractions, as well as mixed numbers, by using number lines or circle graphs.  It includes the equation showing the standard algorithm.

Type: Teaching Idea

This Khan Academy tutorial video explains patterns in the placement of the decimal point, when a decimal is multiplied by a power of 10.  Exponents are NOT discussed.

Type: Tutorial

This Khan Academy tutorial video presents the methodology of understanding and using patterns in the number of zeros of products that have a factor that is a power of 10. While the standard does not mention exponents, the place value understanding of multiplying or dividing by powers of ten will help students understand multiplying and dividing by decimals.  

Type: Tutorial

In this tutorial, you will see how mixed numbers can be divided.

Type: Tutorial

This video demonstrates dividing two numbers that are decimals.

Type: Tutorial

This video demonstrates how to multiply two decimal numbers.

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

This tutorial explores the addition and subtraction of fractions with unlike denominators. Using the number line, this mathematical process can be easily visualized and connected to the final strategy of multiplying the denominators (a/b + c/d = ad +bc/bd).  The video number line does show negative numbers which goes beyond elementary standards so an elementary teacher would need to reflect on whether this video will enrich student knowledge or cause confusion.

Type: Tutorial

This five-minute video answers the question "Must one always invert and multiply?" when dividing fractions. An alternative algorithm is presented which works well in certain cases. The video focuses on sense-making in using either method, and on judging the reasonableness of answers.

Type: Tutorial

The video describes how to multiply fractions and state the answer in lowest terms.

Type: Tutorial

When working with fractions, divisions can be converted to multiplication by the divisor's reciprocal. This chapter explains why.

Type: Video/Audio/Animation