This task is intended for instruction, providing the students with a chance to experiment with physical models of triangles, gaining spatial intuition by executing reflections.
Material Type: Activity/Lab
This is a challenging fraction comparison problem. The fractions for this task have been carefully chosen to encourage and reward different methods of comparison.
Material Type: Activity/Lab
This task requires students to represent fractions on a number line.
Material Type: Activity/Lab
In this number line task students must treat the interval from 0 to 1 as a whole, partition the whole into the appropriate number of equal sized parts, and then locate the fraction(s).
Material Type: Activity/Lab
The purpose of this task is for students to compare two options for a prize where the value of one is given $2 at a time, giving them an opportunity to "work with equal groups of objects to gain foundations for multiplication." This context also provides students with an introduction to the concept of delayed gratification, or resisting an immediate reward and waiting for a later reward, while working with money.
Material Type: Activity/Lab
This instructional task gives students a hands-on experience with composing and decomposing geometric figures.
Material Type: Activity/Lab
This task is for students who know how to use base 10 blocks.
Material Type: Activity/Lab
This task is a straightforward task related to adding fractions with the same denominator. The main purpose is to emphasize that there are many ways to decompose a fraction as a sum of fractions, similar to decompositions of whole numbers that students should have seen in earlier grades.
Material Type: Activity/Lab
This tasks lends itself very well to multiple solution methods. Students may learn a lot by comparing different methods. Students who are already comfortable with fraction multiplication can go straight to the numeric solutions given below. Students who are still unsure of the meanings of these operations can draw pictures or diagrams.
Material Type: Activity/Lab
The purpose of this instructional task is to motivate a discussion about adding fractions and the meaning of the common denominator. The different parts of the task have students moving back and forth between the abstract representation of the fractions and the meaning of the fractions in the context.
Material Type: Activity/Lab
This task requires students to study the make-a-ten strategy that they should already know and use intuitively. In this strategy, knowledge of which sums make a ten, together with some of the properties of addition and subtraction, are used to evaluate sums which are larger than 10.
Material Type: Activity/Lab
This task is to introduce students to the concept of reading an analog clock.
Material Type: Activity/Lab
Making a 10 provides a technique to help students master single digit addition. The task is designed to help students visualize where the 10's are on a single digit addition table and explain why this is so. This knowledge can then be used to help them learn the addition table.
Material Type: Activity/Lab
This task provides three types of comparison problems: Those with an unknown difference and two known numbers; those with a known difference and a bigger unknown number; and those with a known difference and smaller unknown number. Students may solve each type using addition or subtraction, although the language in specific problems tends to favor one approach over another.
Material Type: Activity/Lab
The purpose of the task is for students to solve a multi-step multiplication problem in a context that involves area. In addition, the numbers were chosen to determine if students have a common misconception related to multiplication.
Material Type: Activity/Lab
The purpose of this task is to help students realize there are different ways to add mixed numbers and is most appropriate for use in an instructional setting.
Material Type: Activity/Lab
This task is designed to help students focus on the whole that a fraction refers to. It helps students to realize that two different fractions can describe the same situation depending on what you choose to be the whole.
Material Type: Activity/Lab
This counting activity is done in pairs and helps reinforce the concepts of greater than, less than, and equal to.
Material Type: Activity/Lab
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
Material Type: Activity/Lab
The goal of this task is to show that when the whole is not specified, which fraction is being represented is left ambiguous.
Material Type: Activity/Lab
