Which strategies can be used to solve this problem?
Colin invited 31 people to the picnic. He can fit 10 people at his picnic table and the rest will sit on blankets. Each blanket can hold 3 people. How many blankets does Colin need so that everyone has somewhere to sit?
Choose all answers that are correct.
A. Use logical reasoning.
Start with 31 people, subtract 10 people who will sit at the picnic table, that leaves 21 people. Keep subtracting 3 people until you get to 0. Count how many times you subtracted 3 people.
B. Work backward.
Start with 0 and keep adding 3 until you get to 30. The 1 that is left is the 1 table. The number of times you added 3 is the number of blankets.
C. Draw a diagram.
Ten people at one table, 3 people on a blanket, 3 people on a blanket, 3 people on a blanket, 3 people on a blanket, 3 people on a blanket, 3 people on a blanket, 3 people on a blanket. Count the number of blankets.
D. Translate into an equation.
31 – 10 + 3 + 3 = b
My logical thinking would go like this:
You got 31 people, so 10 will sit at the table,
leaving 21 to sit on blankets.
Each blanket will seat 3, so we need 7 blankets.
End of problem!
What's all that other nonsense ?
31 - 21 = 21 people to sat on blankets.
21people * 1blanket/3people = 21 * 1/3 = 7 blankets needed.
The correct strategies to solve this problem are A, B, C, and D.
A. Use logical reasoning: Start with the total number of people (31) and subtract the number of people who will sit at the picnic table (10). This leaves us with 21 people. Continue subtracting 3 people (the capacity of each blanket) until you reach 0. Count how many times you subtracted 3 people to determine the number of blankets needed.
B. Work backward: Start with 0 and keep adding 3 until you reach the total number of people minus 1 (30 in this case). The remaining 1 is accounted for by the picnic table, so that represents the number of tables needed. The number of times you added 3 represents the number of blankets required.
C. Draw a diagram: Draw a representation of the picnic table and blankets. Assign 10 people to the table, and then groups of 3 people on individual blankets until all the people are seated. Count the number of blankets to determine the answer.
D. Translate into an equation: Set up an equation using mathematical operations to solve for the number of blankets. In this case, the equation is 31 - 10 + 3 + 3 = b, where b represents the number of blankets.
Each of these strategies will lead to the correct answer of the number of blankets needed for everyone to have a place to sit.