This activity shows how reading a mathematics problem three times, with a different focus question each time, can help students make sense of a problem.

## 3D Figures/Isometric Dot Paper

Draw three-dimensional figures on two-dimensional isometric dot paper. Try holding the cubes in different orientations so you can see the possibilities in both the three-dimensional "real world" and the two-dimensional representations on paper.

## Accuracy vs. Precision

Measure the length of the notepad and desk in millimeters and centimeters and their mass in kilograms and grams. Notice how the precision and accuracy differ for each measuring device.

## Area and Perimeter

Create several rectangles with areas of 16 square units and calculate the perimeter. Predict how the length and width of the rectangle affects the perimeter.

## Area Model for Multiplication

Area models offer a visual representation of mathematical operations. Here you will use area models to multiply and reduce fractions.

## The Area Model

Use area models to find either the greatest common factor or the least common multiple of two numbers.

## Arm Span and Height Measurements

Measure your arm span and height. See how your measurements compare to others when your data is added to a data table and corresponding scatter plot.

## Arrays and Fractions

What opportunities for learning are offered by having students work on a problem using both arrays and fractions? Decide whether or not using an array is the best way to solve a problem.

## Balancing Excesses and Deficits

Create a line plot [with dots] to represent stacks of coins. Then rearrange the dots to form different line plots and watch what happens to the mean.

## British and Metric Conversions

Learn to convert measurements from metric to English and vice versa, by learning the symbols used in both systems for properties such as mass, length, volume, and temperature.

## Building From Directions

Use blocks to build a design from a written description. Try various descriptions to achieve the correct design. View non-Flash version.

## Building the Number Line

Classify the different types of numbers we use, and learn how numbers and operations relate to one another. Start with counting numbers and then add integers, rationals, algebraic, and, finally, real numbers to the line.

## Chairs, Stools, and Tennis Balls

Find out how many different combinations of four-legged chairs and three-legged stools you can have after covering each leg with one of 30 tennis balls to silence the chairs whenever they're moved.

## Comparing Figurate Numbers

Investigate, make conjectures, and develop proofs about triangular and square numbers. Compare numbers whose corresponding figures have similar base lengths.

## Comparing Fractions: Bubble Gum Blowing Contest

Explore equivalent fractions, and decide which of two classrooms is better at blowing bubble gum.

## Comparing Representations

Statistical analysis allows us to organize data in different ways to draw out potential patterns in the variation. Review and compare data represented in a bar graph and accompanying tables depicting relative and cumulative frequency.

## Comparing Slopes

Control the slope of lines passing through the origin (0, 0). Keep track of what changes when the slope becomes positive or negative, and when slope is larger or smaller than 1.

## Congruent Shapes

Find shapes that are congruent. Verify that they are congruent by making rotations, slides, and reflections.

## Constant Area

Do figures with the same area have the same perimeter? Arrange and rearrange 12 square tiles on a grid, and then measure the perimeter of each shape you create.