Math games and activities can be an excellent tool to supplement and support math instruction. Using math games in your classroom allow students to practice mathematics in fun but also impactful ways. Students love games because they are engaging and exciting, and teachers love games because they help students practice what they've learned.
Grade 7 students develop their skills to reason abstractly and quantitatively and learn the importance of using representative samples for drawing inferences. They study ratios, scale drawings, rational and negative numbers, and how to graph proportional relationships. Solving real-world problems, (including objects such as triangles, quadrilaterals, and polygons) and practicing how to calculate interest and discounts are aided by activities that use a variety of models.
On the board, write 237.9036 in standard decimal form and as a sum of products.
Next, draw a number line like the one shown below. Use an arrow to represent each digit of the number written on the board. As you “build up” the number, students can see how relatively little the digit in each additional decimal place affects the size of the decimal.
Start with the first two digits: 2 3 _ . _ _ _ _
Note that even if the tens digit were 9 (the highest possible), the number would not reach 300. Write the next digit and draw its arrow: 2 3 7 . _ _ _ _
Note that even if the ones digit were 9 (the highest possible), the number would not reach 240. Continue with the next digit: 2 3 7 . 9 _ _ _
Note that even though the tenths is 9 (the highest possible), the number does not reach 238.
Discuss the fact that no matter how large each succeeding digit is, it’s arrow cannot be longer than the arrow before it.
for Dividing by Fractions
Since the fraction bar represents division, another way to think about 3⁄4 is 3 ÷ 4.
Think of multiplying by the fraction 3⁄4 as two operations with integers:
Since division is the inverse, or opposite, of multiplication, you can divide by using the opposite operations as we used for multiplying.
Think of dividing by the fraction 3⁄4 as two operations with integers:
Since multiplying by 4 and then dividing by 3 is the same as multiplying by 4⁄3, to divide by 3⁄4 , you can multiply by 4⁄3 .
Compare these models, each with a different kind of step, or slope, as shown below. Emphasize that slope is a ratio that relates the vertical change, rise, or y, to the horizontal change, run, or x. Note that the three models at the top show a positive rise from left to right, reflecting a positive change in y.
Use the same approach for models that show functions that “fall” from left to right, representing a negative slope in which the change in y is negative.
1. Start with a unit cube. Construct two other cubes, one whose edge length is twice, and another whose edge length is three times that of the original cube.
2. Disassemble each larger cube into unit squares, and stack each group to establish a bar that shows the total number of unit squares and cubes. This creates a triple-bar graph as shown below.
3. Using a different color for each, draw a line or curve through the top of the length of each edge bars, the top of the area bars, and the top of the volume bars.
for Mean and Median
for Multiplying Polynomials
Example with Numbers: Multiply 4 × 357.
Example with Polynomials: Multiply 3x (x2 + 2x − 6)
for Percent Change
Use a similar procedure to model a percent decrease of 25%.
for Perimeter-Area Relationship
1. Start with a square and construct three other, larger squares with side lengths two, three, and four times the length of the side of the original square.
2. Disassemble each larger square into unit squares and stack the unit squares to establish a bar graph.
3 Draw a line next to each stack of unit squares to show the total side length, or perimeter, of each constructed square.
4. Draw a line through the tops of the perimeter bars and a curve through the tops of the area bars.
1. Divide a rectangle into 6 equal sections to show the number of times you would expect each number on a 1–6 number cube to come up when the cube is rolled many times.
Shade the "5" section. Express the number as a fraction: 1⁄6.
2. Divide the “5” section into 6 equal subsections to show the number of times rolling a 5 will be followed by a roll of each number.
Shade the “5” subsection. Express the number as a fraction: 1⁄6 . Multiply the two fractions.
for Related Angles
Model for Angles of a Transversal
Cut out 3 strips of cardboard and assemble them with fasteners to form a transversal. Rotate the transversal as shown (the other strips remain parallel).
As the angles change in size, focus students’ attention on pairs of angles that remain congruent and pairs that remain supplementary.
Model for Angles of a Parallelogram
Use 4 strips and fasteners to form a rectangle. Rotate a pair of opposite sides as shown . . .
... to create a nonrectangular parallelogram. As the angles change in size, focus students’ attention on pairs of angles that remain supplementary and are congruent. Point out how the decrease in one angle equals the increase in another angle.
for Solving Equations
Example: Solve 3x − 5 = 7
for Solving Inequalities
Show two numbers on a number line and provide examples of adding the same amount to the two numbers.
Note that in every case, the sums are still in the same order. The red point is still to the left of the blue point.
Use a similar model to show that subtracting the same amount from the original numbers does not change the order either.
Then use the model to demonstrate what happens when two numbers are multiplied (or divided) by the same positive amount. Again the order does not change.
Finally, use the model to show that multiplying (or dividing) by a negative amount does not change the order. Note that the red and blue points switch places. The inequality sign must be reversed to keep the sentence true.
for Negative Numbers
Let one side of a coin or counter represent 1 and the other side -1.
Use the model to show the different meanings of the minus sign in a numerical expression.
Example: Simplify −|−6 − (−2)|
So, −|−6 − (−2)| = −4.
1 Fuson, Wearne, Hiebert, Murray, Human, Olivier, Carpenter, and Fennema, 1997; Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Olivier, and Human, 1997 Cited in Adding it Up