101 Questions
Lucky Cow
Cutting the cheese isn't a joke. Scholars observe a wedge of cheese and must determine how to cut it in half horizontally. They apply their knowledge of sectors to determine the most accurate way to slice the cheese.
101 Questions
Square Partitions
Challenge your classes while developing their problem-solving skills. A square is divided neatly into four equal triangles by its diagonals until one diagonal is moved from a vertex to the midpoint of one side. Now, scholars must devise...
Illustrative Mathematics
Voting for Two, Variation 2
John won the election, but by how much more? Your learners will calculate how many votes each candidate received in order to determine the difference. Use with other lessons provided in the series to practice different variations of this...
Illustrative Mathematics
Voting for Three, Variation 3
Get your learners to think outside the box. Young scholars require a good understanding of ratios and their relationship to fractions to complete the problem. The only quantities given in the problem are the ratio of the number of votes...
Illustrative Mathematics
Converting Decimal Representations of Rational Numbers to Fraction Representations
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...
Pie Council
National π Day
Learners can enjoy pi with pie! A collection of short activities celebrates pi day with a word search, a maze, and real-world problemsn. Using pi in formulas for area, circumference, and volume as well as exploring simple fractions is...
Illustrative Mathematics
How Many Servings of Oatmeal?
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...
Illustrative Mathematics
Comparing Products
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...
Illustrative Mathematics
Running to School
The object of this activity is to compute how far Rosa ran to school. Given in the exercise is the fractional number of miles between home and school and the fractional distance Rosa ran. The commentary shows several ways to have your...
Curated OER
Task: Grain Storage
Farming is full of mathematics, and it provides numerous real-world examples for young mathematicians to study. Here, we look at a cylinder-shaped storage silo that has one flat side. Given certain dimensions, students need to determine...
Curated OER
Finding Common Denominators to Subtract
Subtracting fractions with unlike denominators can be overwhelming, but in this task, 5th graders work systematically to break down the procedure through three questions. The first two questions ask for pictures to be drawn along with...
Illustrative Mathematics
Making S'Mores
Fifth graders will be clamoring for s'more fractions after they finish this one! Motivated by a chocolate bar used for a yummy campfire treat, learners have to decide how to add fractions without like denominators by discovering the...
Illustrative Mathematics
Mixed Numbers with Unlike Denominators
There is more than one way to add mixed numbers. This learning exercise asks 5th graders to find and record two ways. The purpose is to help pupils realize there are different ways to reach a common solution in math. The two most common...
Illustrative Mathematics
Reasoning about Multiplication
In critiquing someone else's theory, learners share insight into their own understanding of mathematical concepts. Fifth graders will explore the notion that products are always larger than their factors. While this statement is true the...
Illustrative Mathematics
Origami Stars
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...
Illustrative Mathematics
Finding Common Denominators to Add
Finding common denominators is an important strategy when adding fractions with unlike denominators. In the first two questions in this three-question task, fifth graders are asked to combine fractions and draw a picture to show their...
Illustrative Mathematics
Salad Dressing
Aunt Barb's salad dressing is a mixture of oil, vinegar, salt, herbs, and a pinch of math. Fifth graders add the fractional measurements of ingredients to find a total amount. The fractions have unlike denominators. After finding the...
Curated OER
Do These Add Up?
Common Core mathematical practices require that young mathematicians not only know how to add fractions with unlike denominators, but also to recognize when adding fractions are appropriate for the word problem. Fifth graders are given...
Curated OER
Connor and Makayla Discuss Multiplication
The commutative property of multiplication applies not only to whole numbers but to fractions as well. Connor and Makayla explore and discuss the idea that 2/3 x 3 is the same as 3 x 2/3. Your 5th grade class will connect with learning...
Curated OER
Folding strips of paper
Fifth graders need concrete experiences to introduce a unit on multiplying fractions by fractions. A strip of paper is used to create a number line and represent 5/6. It is folded first in half, and then in quarters. After unfolding,...
Illustrative Mathematics
How Much Pie?
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...
Illustrative Mathematics
Art Class, Assessment Variation
Play with paint and decide the ratio to make different shades of green. When mixing paint colors, your painters should decide which ratios make the same shade and what is needed to mix other ratios for a different shade of green. This is...
Illustrative Mathematics
Jim and Jesse's Money
Jim and Jesse started their road trip with the same amount of money. Your class must find the amount of money each one had given, the amount of money spent, and the ratio of money at the end. This is a comprehensive problem that takes...
Illustrative Mathematics
Running a Mile
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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