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Lesson Plan
Illustrative Mathematics

Making Hot Cocoa, Variation 2

For Teachers 6th - 7th Standards
Learners are introduced to dividing by fractions in a visual way. Setting up groups from the information in the problem allows them to see what we divide and why. Use with the previous instructional activity, which can be found in...
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Lesson Plan
Illustrative Mathematics

Making Hot Cocoa, Variation 1

For Teachers 6th - 7th Standards
Dividing with fractions can be a confusing task to some, but the activity illustrates how to make groups out of the problem and look at it visually. Use this problem with the lesson in the Additional Materials section to practice this...
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Lesson Plan
EngageNY

Interpreting and Computing Division of a Fraction by a Fraction—More Models II

For Teachers 6th Standards
No more inverting and multiplying to divide fractions. Applying concepts of measurement division from the previous lesson, pupils consider partitive division using fraction bars and number lines. They first convert fractions to like...
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Lesson Plan
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Illustrative Mathematics

Fractions and Rectangles

For Teachers 3rd - 5th Standards
Visual models are excellent teaching tools when explaining equivalent fractions. Looking at a rectangle cut into twelfths, students first identify the shaded fraction, and then explain whether the fraction is equal to one-fourth....
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Lesson Plan
Illustrative Mathematics

How Many _______ Are In. . . ?

For Teachers 5th - 7th Standards
Help your learners gain meaningful understanding of dividing fractions using fraction models. The activity includes nine problems which are sequenced to show how the fraction division algorithm evolves. Have students use graph paper or...
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Lesson Plan
EngageNY

The Division Algorithm—Converting Decimal Division into Whole Number Division Using Fractions

For Students 6th Standards
Knowing the standard algorithm opens up a whole new world of division. Scholars learn how to convert division involving decimals to division involving whole numbers to use the standard algorithm. Knowing how to multiply with powers of...
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Lesson Plan
EngageNY

The Relationship of Multiplication and Division

For Teachers 6th Standards
Take any number, multiply it by five, and then divide by five. Did you end up with the original number? In the same vein as the previous instructional activity, pupils discover the relationship between multiplication and division. They...
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Lesson Plan
EngageNY

The Relationship Between Visual Fraction Models and Equations

For Teachers 6th Standards
Ours is to wonder why, not just to invert and multiply. The seventh installment of a 21-part module uses fraction models to help pupils understand why the invert-and-multiply strategy for dividing fractions works. They then work on some...
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Lesson Plan
Illustrative Mathematics

How Many Containers in One Cup / Cups in One Container?

For Teachers 5th - 7th Standards
The object is to model fraction division by asking “How many are in one group?” It is a difficult concept to understand, but developing the model that shows one cup to a certain amount of container or one container to a certain amount of...
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Lesson Plan
Illustrative Mathematics

Half of a Recipe

For Teachers 4th - 6th Standards
Kids love to cook! What is a better place to learn mixed numbers than with a recipe? It is up to learners to decide how they want to divide this recipe in half. They may choose to model the mixed number and then divide the model by two....
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Lesson Plan
Illustrative Mathematics

How Many Servings of Oatmeal?

For Teachers 4th - 6th Standards
Here is another way to illustrate division of a whole number by a unit fraction. In this case, the problem is asking if there are so many servings per cup, how many servings are in a package of multiple cups. Learners are to model their...
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Assessment
Los Angeles County Office of Education

Assessment for the California Mathematics Standards Grade 3

For Students 3rd Standards
Assess scholars' knowledge with a 22-page assessment that covers place value, patterns, probability, estimation, measurement, geometric figures; and their ability to add, subtract, multiply and divide proficiently. 
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Assessment
EngageNY

End-of-Module Assessment Task: Grade 6 Math Module 2

For Students 6th Standards
Give learners a chance to shine. The last installment of a 21-part series is an end-of-module assessment. Scholars show their understanding of operations with decimals and division of fractions by solving problems in the context of a...
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Assessment
EngageNY

Mid-Module Assessment Task: Grade 6 Math Module 2

For Students 6th Standards
Make sure scholars know all about fractions and decimals — not just a fraction of the information. The 12th installment of a 21-part series is a mid-module assessment. Learners solve problems in the context of a birthday party and a...
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Assessment
Los Angeles County Office of Education

Assessment for the California Mathematics Standards Grade 5

For Students 5th Standards
Test young mathematicians' knowledge with an assessment aligned to California's fifth grade state standards. The exam covers a multitude of concepts including fractions and decimals, positive and negative numbers, measurement; and how to...
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Lesson Plan
Illustrative Mathematics

Making Cookies

For Teachers 5th - 7th Standards
Hooray for chocolate chip cookies! Ask your mathematicians to triple a chocolate chip cookie recipe and then reduce the recipe by one-fourth. Your class may need two days to complete, tripling the recipe the first day and reducing the...
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Activity
Illustrative Mathematics

Origami Stars

For Teachers 4th - 6th Standards
This one problem concentrates on the important concept of dividing a whole number by a unit fraction. Here, young mathematicians use pictures they draw to help answer this problem. Insight into the connection between multiplication and...
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Lesson Plan
Illustrative Mathematics

Converting Decimal Representations of Rational Numbers to Fraction Representations

For Teachers 7th - 9th Standards
A rational number is a ratio of two integers. Discuss with your class how to convert the rational numbers of repeating decimals to fractions. A good commentary on letting x equal the repeating decimal and multiplying each side of such...
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Activity
Illustrative Mathematics

How Much Pie?

For Teachers 5th Standards
The connection between fractions and division is not always intuitive for 5th graders. Pie, on the other hand, is something 5th graders can connect with. Multiple pies divided among multiple people provide the platform for your class to...
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Activity
Illustrative Mathematics

Running a Mile

For Teachers 4th - 6th Standards
The single question in this activity has multiple ways to be solved. Two boys ran a mile. Their times were similar, except one time was a fraction of the other. Who ran faster? In demonstrating the answer to this problem, upper graders...
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Assessment
Noyce Foundation

Cat Food

For Teachers 6th - 7th Standards
Determine the right mix of cans of cat food. The resource consists of an assessment task to determine the cost to feed two cats for a specific number of days and requires scholars to interpret remainders within a context. The resource...
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Assessment
Noyce Foundation

Cereal

For Teachers 6th - 7th Standards
Find the best protein-packed cereal. The short assessment task covers equivalent and comparing ratios within a context. Pupils determine the cereal with the highest ratio of protein. A rubric helps teachers with point allotments for...
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Assessment
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CCSS Math Activities

Smarter Balanced Sample Items: 7th Grade Math – Target B

For Teachers 7th Standards
Fraction and integer operations follow the same rules.  Assess the depth of understanding with operations with rational numbers using a presentation from the Grade 7 Claim 1 Slideshow series. A set of slides presents 12 question and...
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Activity
Illustrative Mathematics

Comparing Products

For Teachers 5th Standards
How can 5th graders show understanding that 30 x 225 is half of 60 x 225 without completing the computation? They can use an area model and draw it out. An array, or an open array, is an area model that allows for young learners to...

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