Using Grid Models

By drawing grid models, you can use the shaded regions to compare numbers. A greater shaded region means a greater number. This Gizmotm allows you to model and compare two numbers with values between 0 and 2.

  1. Use the left drop-down menu above the left grid to choose percent. Then use the other drop-down menu above the left grid to choose 100 squares = 1 unit. This setting divides each large square into 100 smaller squares. (Note that each large square, outlined in black, is one unit or one whole.) Use the left drop-down menu above the right grid to choose percent. Then use the other drop-down menu above the right grid to choose 100 squares = 1 unit. Model 14% in the left grid by typing 14 in the box below the grid and pressing ENTER. Model 140% in the right grid.
    1. Which of these numbers has the largest shaded region? Which number has the smaller shaded region?
    2. Look at the model for 14%. How many squares are shaded? Is 14% more or less than 1 whole?
    3. Look at the model for 140%. How many total squares are shaded? Is 140% more or less than 1 whole?
    4. What percent is equal to 1 whole?
    5. Use the left drop-down menu above both grids to choose decimal. What decimal is equal to 14%? What decimal is equal to 140%?
  2. Click Reset to clear the grids. Use the left drop-down menu above the left grid to choose decimal. Use the right drop-down menu above the left grid to choose 200 squares = 1 unit. Use the left drop-down menu above the right grid to choose decimal. Use the right drop-down menu above the right grid to choose 200 squares = 1 unit. Model 0.95 in the first grid by typing that value in the box below the left grid and pressing ENTER. Model 0.195 in the right grid.
    1. Which of these numbers has the larger shaded region? Which number has the smaller shaded region?
    2. Click Compare numbers to find out which number is greater. Which of these two numbers has the greater value?
    3. The number 0.195 has more digits than the number 0.95. Does the number with more digits always have a greater value? Why or why not?
    4. When comparing two decimal numbers, which digit should you look at first to make the comparison?
  3. Click Reset to clear the grids. Use the grids to model the numbers 55 over 100 and . Choose fraction from the left drop-down menu above the left grid and 100 squares = 1 unit from the right drop-down menu above the left grid. Choose fraction from the left drop-down menu above the right grid and 100 squares = 1 unit from the right drop-down menu above the right grid. Then type the numerator of each fraction in the box below the grid and press ENTER.
    1. Which of these two numbers has the greatest value? How do you know?
    2. For each of these numbers, choose simplified fraction from the drop-down menu. What is the simplest form of each of these fractions?
    3. What would you need to do with the fraction in order to model it with one of the grids in the Gizmo?
    4. Rewrite the fraction so that it can be modeled in the Gizmo. Then replace the model for 55 over 100 with a model for . Choose simplified fraction from the drop-down menu to make sure that you have modeled the correct fraction.
    5. Which of the fractions now displayed has a greater value 70 over 200 or ?
  4. Use the grids to model the numbers 0.3 and 1 over 4.
    1. Explain the steps you took to model each number.
    2. Which number has the largest shaded region? Which number has the smallest shaded region?
    3. Which of these two numbers has the greater value? Check your answer by clicking on Compare numbers.
    4. Try to write 0.3 as a fraction in simplest form and as a percent. Check your answers by modeling all three forms of 0.3 in the Gizmo. How would you know if you are correct based on the models?
    5. Try to write as a decimal and as a percent. Check your answers by modeling all three forms of in the Gizmo.
    6. This Gizmo can only model two numbers at a time. How might you use the Gizmo to help you write the numbers 0.3, , and 28% in order from least to greatest?
  5. Without using the Gizmo, try to write the following sets of numbers in order from least to greatest. Then use the Gizmo to check your answers.
    1. 19%, , 0.23 (Hint: To model , try using the denominator 200).
    2. 0.525, 53%,
    3. 15%, , 0.105