Brian has spent too much time analyzing his leaf raking. He has created an investigation that asks students to calculate how long it would take different numbers of rakers to finish cleaning his yard of leaves. Students see the inverse relationship between number of workers and time to complete the whole job. They graph hyperbolas and consider how long the extreme condition of zero people raking might take to complete the job.
Other useful extension ideas:
In the middle of a ratio unit? Use this to see if kids apply proportional reasoning to this situation: Example: It takes 1 person 12 hours, so then it would take 2 people 24 hours?
Studying linear relationships? Use this to show that not all relationships are linear. Check out the table, rule and graph compared to linear relations.
They discover that you can’t divide by zero. With 4 people it takes 3 hours to rake my leaves, because 4×3=12 or 12/3=4. What about 6 people? 6×2=12 or 12/6=2? What about zero people? Can’t happen because nothing multiplied by zero makes 12 and you can’t divide 12 up by zero people.
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At the Toys R Us store, I saw an amazing LEGO creation. He was a life-sized LEGO fireman with a walkie-talkie, an oxygen tank and even an oxygen tank gauge. He must have taken a long time to build.
Let your students watch the short movie of the Fireman, consider what they might like to understand about him and what else they might need to know. Then, using our block measurements, encourage them to underestimate and over estimate his construction time and LEGO block quantity, and then average their class estimates. How close will they be to the actual time for construction and quantity of LEGO blocks?
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We have a number of great activities for this time of year.
Pumpkin pie … awesome - Estimation, proportional reasoning, fraction multiplication, delicious pie
Macy’s Thanksgiving Day parade - Describe, measure, calculate marching time, volumes of the giant balloons
Not enough mashed potatoes – Change fractions to decimals, generate ingredient measures for different sized Thanksgiving dinners, explain reasoning
Black Friday – Calculate savings in percents and dollars. Make a plan to save the most with limited time.
Hanukkah is way too early this year - Patterns, 19 year cycle of the Hebrew calendar, lunar and solar calendars
How much should we spend on this sale? - Percents, step graphs, linear equations, linear programming
Thanksgiving means football…
Home field advantage - reading graphic and analyzing whether there really is a home team advantage
Watson saves - Students watch one of the greatest NFL saves of all time and use the Pythagorean theorem to analyze the distances actually run.