Illustrative Mathematics
Finding an Unknown Angle
Teach your class how to apply their knowledge of geometry as they explore the unknown. In order to find an unknown angle, students must understand that rectangles have four interior right angles, that right angles have 90 degrees, and...
Illustrative Mathematics
Plastic Building Blocks
Let's build a castle! Dennis and Cody have big plans, but do they have enough blocks between the two of them to accomplish their goal? A great context that requires students to add and compare mixed numbers. Encourage the use of pictures...
Illustrative Mathematics
Using Benchmarks to Compare Fractions
Introduce a new strategy for comparing fractions by analyzing Melissa's use of benchmarks. Walk the class through her process, calling on students to explain their understanding of each step she took. Then practice this method on two...
Illustrative Mathematics
Lines of Symmetry for Triangles
What can symmetry tell us about triangles? After looking at four examples, learners will come to realize that lines of symmetry are different for equilateral, isosceles, and scalene triangles. Use this guided practice activity as an...
Illustrative Mathematics
Ordering 4-digit Numbers
Place value is a concept that sets a foundation for mathematical understanding. Ordering these sets of three- and four-digit numbers will help to strengthen that foundation. A great independent practice worksheet or short assessment to...
Illustrative Mathematics
Doubling Numerators and Denominators
Understanding the meaning of fractions is a challenge for many young learners. These two questions examine what happens when the numerator and denominator of a fraction are doubled. Consider allowing students to discuss their ideas in...
Illustrative Mathematics
Margie Buys Apples
One of the most common, everyday applications of math is dealing with money. This single problem calculating how much change Margie receives is more involved than it appears at first glance. An understanding of how fractions and decimals...
Illustrative Mathematics
Comparing Two Different Pizzas
What better way to learn about fractions than with a couple pizzas? Help Jessica figure out how much of the pizza she has eaten, while teaching your class that fractions refer to a specific whole amount. This problem will be challenging...
Illustrative Mathematics
Two Interpretations of Division
Division can be seen in two ways; as splitting a whole into a certain number of pieces, or splitting it into pieces of a certain size. Help your class reach this understanding with these two simple word problems. Encourage the use of...
Illustrative Mathematics
Are These Right?
Is that a right triangle or a wrong triangle? Young mathematicians look at eleven different shapes and use a measuring tool of their choice to determine which triangles have right angles. Consider cutting out sets of the shapes to...
Illustrative Mathematics
What Shape Am I?
Sharpen your pencil and grab a ruler, it's time to draw some quadrilaterals! Given the definition of a parallelogram, rectangle, and rhombus, learners draw examples and nonexamples of each figure. The three definitions are then used to...
Illustrative Mathematics
Half of a Recipe
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....
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
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
Patterns in the Multiplication Table
Explore patterns in the multiplication table in order to deepen your third graders' understanding of this essential skill. Implement this activity as a whole-class lesson, allowing students to work in pairs or small groups to support...
Curated OER
Which is Closer to 1?
A seemingly simple question that reveals a lot about a student's understanding of fractions. In finding an answer, learners compare fractions with different denominators that are both greater and less than one. No number line is...
Curated OER
Locating Fractions Greater than One on the Number Line
Supplement your lesson on improper fractions with this simple resource. Working on number lines labeled with whole numbers between 0 and 5, young mathematicians represent basic improper fractions with halves and thirds. The fractions...
Curated OER
Jon and Charlie's Run
Let's use math to solve an argument. Jon and Charlie are debating about who can run farther, but who is right? That's what your class will figure out as they apply their understanding of fractions to this real-life situation. A simple,...
Curated OER
Find 2/3
This short problem with representing fractions on a number line is more than meets the eye. Labeled only with the numbers zero and 1/4, a number line is used to locate the fraction 2/3. A solution can be found in multiple ways, but young...
Curated OER
Find 1
Extend your class's ability to represent unit fractions on a number line with this challenging worksheet. Given two number lines, one labeled with zero and 1/4, the other with zero and 5/3, students must accurately locate the number one...
Curated OER
Comparing Fractions with the Same Numerators, Assessment Variation
Have your class demonstrate their ability to compare fractions with this short multiple-choice assessment. Using the fractions 9/8 and 9/4, the students first make comparisons using both words and the greater than/less than signs. Next,...
Curated OER
Comparing Fractions with the Same Denominator, Assessment Variation
A short, multiple choice assessment that determines your 3rd graders' ability to correctly compare fractions with like denominators. This quiz asks learners to compare two fractions using words, the greater than/less than symbols, and...
Curated OER
Closest to 1/2
Using a number line, pupils are asked to identify which of four fractions is closest to one half. Includes a single problem that can serve as a practice problem or formative assessment for 3rd or 4th graders learning to partition number...
Curated OER
Comparing Fractions
Learners compare three sets of fractions using the greater than, less than, and equal signs. To justify their answers, a drawing is also required that illustrates their reasoning. Including fractions with like and unlike denominators, as...