Illustrative Mathematics
Drinking Juice, Variation 2
An excellent activity using word problems where pupils interpret and compute quotients of fractions. The commentary includes using a fraction bar model and equations to represent the problem. In this variation of the resource, the...
Illustrative Mathematics
Base and Height
It is easy to find the area of a triangle where the base and the height are given. But in this resource, it is up to your geometers to identify the base and height of the triangle. In fact, your pupils will learn that there are three...
Illustrative Mathematics
Christo’s Building
Hook your charges on how to solve a real-world art problem with mathematics by showing works of Christo. You can find eye-catching images on the Christo and Jeanne Claude webpage. Here, math learners help Jean Claude and Christo prepare...
Illustrative Mathematics
Banana Bread
Show your future bakers how to choose the right baking pan by calculating the volume of a pan. The resource compares two pans, one with decimal edge lengths and is too small for the recipe and one that may work. Your number crunchers are...
Illustrative Mathematics
Explaining Fraction Equivalence with Picture
Visual models are a great tool for demonstrating the concept of equivalent fractions. Given two pictures, young mathematicians first identify each fraction and then write an explanation for why they are equivalent. Use as a guided...
Illustrative Mathematics
How Many Marbles?
Don't lose your marbles! This simple story problem helps make teaching division with fractions much easier. Work on this problem along with the instructional activity titled, How Many Servings of Oatmeal? to highlight the...
Illustrative Mathematics
Numbers in a Multiplication Table
Identifying patterns is a crucial skill for all mathematicians, young and old. Explore the multiplication table with your class, using patterns and symmetry to teach about square numbers, prime numbers, and the commutative and identity...
Illustrative Mathematics
Money in the Piggy Bank
It's time to crack open that piggy bank and see what's inside. First, count up the pennies, nickels, dimes, and quarters, identifying what fraction of them are dimes. Then calculate the total value of the coins, writing another fraction...
Illustrative Mathematics
Dimes and Pennies
Help your fourth graders make cents out of fractions and decimals with this short word problem. After learning that dimes are one-tenth and pennies one-hundredth of a dollar, young scholars write a fraction and decimal for a given...
Illustrative Mathematics
Lines of Symmetry for Quadrilaterals
Explore how lines of symmetry help define different categories of quadrilaterals. Looking at a square, rectangle, trapezoid, and parallelogram, young mathematicians discover that each shape has its own, unique symmetry. Encourage your...
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 young scholars to discuss their...
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
Ratio of Boys to Girls
How many boys are in the class? Here is an introductory exercise describing ratios. The commentary shows different ways learners can approach the problem, using a tape diagram of boys to girls and using a table. The activity includes...
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...
Illustrative Mathematics
Overlapping Squares
The objective of this activity is to find the percent of the area of a two squares overlapping. Mathematicians find the ratio of area for the part that overlaps to the rectangle formed. The final answer is a percent as a rate per 100....
Illustrative Mathematics
Voting for Three, Variation 1
This is an opportunity for young mathematicians to apply reasoning to solve real-world problems with ratios. Even though there are three candidates for class president, students will only consider two at a time, making the first problem...