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...
Illustrative Mathematics
To Multiply or not to multiply?
When do you multiply a fraction by a fraction? Here, fifth graders are given 10 different word problems and asked to decide if multiplying 2/5 x 1/8 is appropriate. Many times, real-world word problems sound similar although the required...
Illustrative Mathematics
Bowling for Numbers
When do teams want a strike? When they are playing this fun math game modeled after bowling. First, class teams roll four dice to generate the numbers they will use in that round, called a frame, of the game. Next, pins numbered 1...
Illustrative Mathematics
Video Game Scores
Eric and Leila's video game scores are the inspiration for writing equations with parenthesis. The numbers are purposefully large to deter the class from calculating them: rather this activity meets the standard that asks 5th graders to...
Illustrative Mathematics
Rainfall
Ideal for use as an introduction to the idea of inverse functions, this activity investigates rainfall as a function of time. Learners use the data displayed in a table of values to analyze the function and its inverse, including why the...
Illustrative Mathematics
Medieval Archer
This activity presents a problem about a computer game which uses functions to simulate the path of an arrow fired by an archer. Learners use the given function to determine where the archer must stand in order to fire an arrow that will...
Illustrative Mathematics
Temperatures in degrees Fahrenheit and Celsius
Learners investigate the relationship between the Fahrenheit and Celsius temperature scales. Given two data points, they construct a linear function to describe the relationship, find the inverse of the function, and make observations...
Illustrative Mathematics
Seeing is Believing
How many visual models can be used to show multiplication? Three basic kinds of models can be used to represent and explain the equation 4 x (9 + 2). The commentary section provides description and graphics to explain the set...
Illustrative Mathematics
Identifying Rational Numbers
Eight different numbers are listed for mathematics masters to analyze. They simply tell if each number is rational or irrational. They can also explain their reasoning. A simple and straightforward worksheet that is a handy tool for...
Illustrative Mathematics
Converse of the Pythagorean Theorem
Use the given tasks and detailed teacher's commentary to introduce your 8th graders to the Pythagorean theorem and its converse. Embedded links to information about Egyptian geometry make your presentation interesting. Consider...
Illustrative Mathematics
Toll Bridge Puzzle
Here is a great problem-solving activity for young mathematicians. Intended solely for instructional purposes, the activity is appropriate for learners to add four numbers together. Not only must they add four numbers together,...
Illustrative Mathematics
Building toward fluency
Here is a great learning task that focuses on the development of areas in computational fluency including strategies in mental math. Young learners are guided through a list of addition expressions that help them visually understand the...
Illustrative Mathematics
Rounding to 50 or 500
In a six-problem learning activity, children are guided to solve word problems that involve rounding to the nearest ten and nearest hundred. A commentary and answer key provide different approaches that learners may take in solving the...
Illustrative Mathematics
Naming the Whole for a Fraction
How many different ways can you represent a whole? In a picture that represents six parts (two of which are shaded), learners are asked to label the parts appropriately to show how three different mathematical interpretations can be...
Illustrative Mathematics
The Stamp Collection
By using language like "half of the stamps," children are exposed to patterns in arithmetic that requires solving a two-step word problem. This type of language opens a new door for transitioning learners toward understanding fractions...
Illustrative Mathematics
Identifying Multiples
Administer an activity that fosters a child's understanding of multiples. Young mathematicians are guided to complete three tasks on a multiplication chart. Once they color the boxes with multiples of two, three, and four, learners...
Illustrative Mathematics
The Locker Game
Here is a learning activity that incorporates a classic puzzle in mathematics. Young mathematicians are guided through a series of statements that describe rounds of pupils opening and closing lockers. The first person opens all 20...
Illustrative Mathematics
Runners' World
Learners must investigate the validity of a claim made in a running magazine. They must identify and look up unprovided information, make appropriate estimations, and be able to convert units. Might be best used as a group or whole-class...
Illustrative Mathematics
Checking a calculation of a decimal exponent
In a writing prompt, learners are asked to check the calculation of a decimal exponent without a calculator. Use as an opener or assessment after studying fractional exponents. Requires a strong understanding of exponents and roots to...
Illustrative Mathematics
Calculating the square root of 2
Does a calculator give you the exact value of the square root of 2? Here, learners must decide if 1.414236 is equal to the square root of 2. They must also explain why the square root of 2 could never be equal to a terminating decimal....
Illustrative Mathematics
Traffic Jam
How many cars would be involved in a traffic jam 12 miles long? A slightly ambiguous writing prompt gives learners the opportunity to practice making reasonable assumptions to tackle a real-life problem. Few details are given, so they...
Illustrative Mathematics
Ice Cream Van
In an open-ended problem, learners calculate costs involved in driving an ice cream van. Is it better to park in one place or drive through different neighborhoods? Learners look at these and other factors and must make reasonable...
Illustrative Mathematics
Harvesting the Fields
This problem involving rates may look simple at first, but it is actually quite challenging. Two different sized fields are harvested by a team of workers and learners must use different rates to calculate the number of workers on the...
Illustrative Mathematics
Rational or Irrational?
Is 4 plus the square root of 2 rational or irrational? After your class has gained a basic grasp of rational and irrational numbers, use this instructional activity to push them a little further in their understanding. Learners must...