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The Guess and Check 2.0 table below shows guesses arranged to solve the question posed in this problem: Shea and Tucker area washing their father’s car.  Shea can wash it by herself in 20 minutes.  Tucker can wash it by himself in 30 minutes.  How long does it take them to wash the car if they work together? Number of minutes to wash the car Fraction of the job that Shea did Fraction of the job that Tucker did Do the fractions of the job total to 1 car washed? Thoughts 30 30/20 = 1.5 30/30 = 1 1.5 + 1

Using the interpretation of multiplication introduced in MATH 2010 where A x B represents taking A groups of size B, match each of the integer multiplication calculations with their corresponding interpretation.

You are doing a number talk with your sixth graders for

Some liquid is poured into the three containers below.  Josh says, “I know that the same amount of liquid in Container A is also in Container C.” Deandra says, “Well, I know that the amount of liquid in Container B and Container C are equal.” Jazmin excitedly adds, “Well I didn’t start out knowing anything about the amounts, but after listening to you two I know that the amount in Container A is equal to the amount in Container B.”   What property did Jazmin use to figure this out?  

Read the word problem below.  Decide which bar model best fits the problem.  State which model you chose. Write a unit solution to solve the problem using the model you chose. Derek stacked only 2/5 of the number of hay bales that Kimmy stacked. Matt stacked seven more hay bales than Derek. If altogether the three of them stacked 637 hay bales, how many hay bales did Kimmy stack? Model A long description (click to reveal) Kimmy’s bar has 5 units and is marked with a question mark.  Derek has 2 units.  Matt has 2 units and an extra 7.  The combined total is 637.   Model B long description (click to reveal) Kimmy’s bar has 5 units and is marked with a question mark.  Derek has 2 units.  Matt has 1 unit marked 7.  The combined total is 637.   Model C long description (click to reveal) Kimmy’s bar has 5 units and is marked 637.  Derek has 2 units.  Matt has 2 units and an extra 7.  The combined total is marked with a ?   Model D long description (click to reveal) Kimmy’s bar has 5 units and is marked with a question mark.  Derek has 2 units and the total is marked with a ? Matt has 1 unit and an extra 7.  The combined total is 637.  

You ask your students to multiply 22 x 22.  The student says, “I want to see the second 22 as 11 x 2.  Then I want to take that 2 and multiply it with the first 22 to get 44.  Now I have 44  x 11 but I will do that by decomposing 11 into 10 and 1 so I get 44 x 10 and 44 times 1.  Then I add 440 and 44 together to get 484.” The image below shows 8 expressions linked together in an equation string meant to highlight the properties used in the student’s solution.  Choose all of the statements true about the string.

Gill packed 3 Jaffa cakes for his road trip.  The image below shows how much remains after the first half an hour. Select the statements that correctly name the amount that remains.

If A = 5(k + 3) – 2 and B = 5k + 12, decide how A and B are related.

You ask your students to come up with lots of ways to solve 38 + 65.  One student says, “I sure would like it if that 38 was a 40 instead but I know I can’t just add 2 because then the answer will be more than it is supposed to be.  If I added 2 and also took away 2, I know there would be no affect in total; actually, that’s just like adding zero.  So that’s what I’ll do.  I’ll add 2 to 38 and take 2 away from 65.  Now I have 40 + 63.  I’ll take 60 and put it with 40 to make 100 and then tack on the other 3 at the end to get 103 in total.” 1. Show how you would record the student’s thinking at the board while the student is talking.  This should not be an equation string. 2. Show how to write the student’s thinking as an equation string that makes the properties used by the student visible.   3. Explain how your equation string makes the properties used visible.  Include mention of at least two properties used in this strategy.

Which bar model and unit solution combination show an accurate way to depict and solve the following word problem? Leanna wants her son to have a birthday cake. If she buys a cake from the bakery it will cost her $30. If she makes the cake herself, it will save her 20% of what the bakery charges her. How much money would Leanna save if she made the cake herself instead of buying it? Figure A long description (click to reveal) Homemade bar has 5 units set equal to 100%.  Bakery has 6 units set equal to 120% and 30.  Question mark is over one unit.  Teacher’s Solution reads 1 unit = 20%, 20% of 30 = 1/5 x 30 = 6.  Leanna will save $6 by making her own cake.   Figure B long description (click to reveal) Bakery bar has 5 units set equal to 30.  Homemade has 4 units set equal to 80%.  Question mark is over one unit.  Teacher’s Solution reads 5 units = 30, 1 unit = 30/6 = 6, 4 units = 4 x 6 = 24.  Leanna will save $24 by making her own cake.   Figure C long description (click to reveal) Homemade bar has 5 units set equal to 100%.  Bakery has 6 units set equal to 120% and 30.  Question mark is over one unit.  Teacher’s Solution reads 6 units = 30, 1 unit = 30/6 = 5.  Leanna will save $5 by making her own cake.   Figure D long description (click to reveal) Bakery bar has 5 units set equal to 100% and 30.  Bakery has 4 units set equal to 80%.  Question mark is over one unit.  Teacher’s Solution reads 5 unit = 30, 1 unit = 30/5 = 6.  Leanna will save $6 by making her own cake.