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 asects of the task and its potential use. Here are the first few lines of the commentary for this task: One day, Frog and Toad were sitting together on a lily pad. Some lily pads were in a line across the pond. In the morning, Frog hopped three lily pads ...

Both of the questions in this task are solved by the division problem 12Ö3 but what happens to the ribbon is different in each case.

When students plot irrational numbers on the number line, it helps reinforce the idea that they fit into a number system that includes the more familiar integer and rational numbers.

This task suggests methods of introducing and continuing choral counting in the classroom.

Students work in pairs to measure length by lining up cubes along the longest side of an item. They count and record length by counting the number of cubes.

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.

In this activity, students explore the effect of chemical erosion on statues and monuments. They use chalk to see what happens when limestone is placed in liquids with different pH values. They also learn several things that engineers are doing to reduce the effects of acid rain.

In this video from Cyberchase, the CyberSquad searches for a kidnapper using their only clues: a footprint and a handprint. ***Access to Teacher's Domain content now requires free login to PBS Learning Media.

Students create patterns using pattern blocks. Then they pose a question to their peers like, öWhat fraction of my shape is red?’– Students describe their answers geometrically, verbally, and in writing.

In this video segment from Cyberchase, Digit and the CyberSquad learn that equations are balanced when the same number is on each side. ***Access to Teacher's Domain content now requires free login to PBS Learning Media.

In this activity students become familiar with the math vocabulary more/less/same and most/least as they count and compare small groups.

In this scavenger hunt games students are given the task of finding and identifying real-world shapes in their environment.

The first of these word problems is a multiplication problem involving equal-sized groups. The next two reflect the two related division problems, namely, "How many groups?" and "How many in each group?"

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 asects of the task and its potential use. Here are the first few lines of the commentary for this task: Materials * Class white board and one marker * Paper and pencil for students * Materials such as counters or linker cubes * Number lines that go from 0...

Students find the volume and surface area of a rectangular box (e.g., a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original. As they construct the new, cube-shaped box from the original box material, students discover that the cubical box has less surface area than the original, and thus, a cube is a more efficient way to package things. Students then consider why consumer goods generally aren't packaged in cube-shaped boxes, even though they would require less material to produce and ultimately, less waste to discard. To display their findings, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved. The activities involved provide valuable experience in problem solving with spatial-visual relationships.

One common mistake students make when dividing fractions using visuals is the confusion between remainder and the fractional part of a mixed number answer.

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).

The goal of this task is to provide examples for comparing two fractions by finding a benchmark fraction which lies in between the two.

This task is meant to address a common error that students make, namely, that they represent fractions with different wholes when they need to compare them. This task is meant to generate classroom discussion related to comparing fractions. Particularly important is that students understand that when you compare fractions, you implicitly always have the same whole.