Teaching Algebra with Manipulatives

Using Overhead Manipulatives
(Use with Algebra 1, Lesson 3-6)
Proportions
Objective Use proportions to estimate a population.
Materials
• overhead counters*
• lined paper transparency*
• 50–100 dried beans or squares of paper
• transparency pen*
• integer models transparency*
• blank transparency * available in Overhead Manipulative Resources
Demonstration
Model Estimating Using the Capture-Recapture Technique
• On lined paper transparency, prepare a chart like
the one shown at the right.
• Tell students they are going to model estimating
the population of fish in a lake using the capturerecapture
technique. Dried beans or squares of
paper will represent fish and a bowl will represent
the lake. Fill the bowl with dried beans or squares
of paper. Ask a student to grab a small handful of
beans or squares. Count the number of beans or
squares selected and record this number below the
chart. Explain that this number represents the
captured fish.
• Mark each bean or square with an X on both sides. Return them to the
bowl and mix well with the rest. Tell students that this part of the
activity is similar to tagging fish in a lake.
• Have another student take a small handful of beans or squares of paper
from the bowl. Record the number of beans or squares selected.
• Count the number of beans or squares in the handful that are marked
with an X. Tell students this represents the number of tagged fish
recaptured. Record this number in the chart.
• Return all the beans or squares to the bowl, mix, and recapture four
more times.
• Have students find the total recaptured and the total tagged. Record in
the chart. Have students use the proportion below to estimate the
number of beans or squares in the bowl.
original number captured
number in bowl
total tagged in samples
total recaptured
Number Number Tagged
Sample Recaptured in Sample
• Count all the beans or squares in the bowl. Compare to the estimate.
Answers will vary, but the estimate should be close to the actual number.
1
2
3
4
5
Total
Original number captured:
Algebra 1—Chapter 3
© Glencoe/McGraw-Hill 75 Teaching Algebra with Manipulatives