1. which explanation best describes how to solve this problem?

gloria was taking photographs at a waterfall. she deleted 18 photographs. then, during the hike from the waterfall, she took 13 more. she deleted another 9. now gloria has 22 photographs left. how many photographs did gloria have to begin with?

a.
guess and test. guess that gloria had 40 photographs to begin with. subtract the number she deleted (18) and add the number she took (13). then subtract the second amount she deleted (9). this gives 26. that is 4 more than 22. add 4 to your guess. gloria had 44 photographs to begin with.

b.
draw a diagram. draw a large circle to represent the photographs gloria had to begin with. add 22 dots, 18 dots, and 9 dots to the circle. cross out 13 dots for the ones she took during the hike. add all remaining dots to figure out that gloria started with 36 photographs.

c.
translate into an equation. 18 + 13 + 9 – 22 = b

gloria had 18 photographs to begin with.

d.
work backward. start with the number of photographs that gloria has left (22). add the photographs that were deleted (18 + 9). then add photographs that she took during the hike (13).

gloria had 62 photographs to begin with.

2. which explanation best describes how to solve this problem?

a truck travels a total of 36 miles every workday. the company doesn't count the 2 miles to and from the worksite in their mileage records.

how many miles are counted in 261 workdays?

a.
add 36 and 2. multiply the sum by 261.

b.
divide 261 by 36. subtract 2 from the quotient.

c.
subtract 36 from 261. multiply the difference by 2.

d.
subtract 2 from 36. multiply 261 by the difference.

3. which explanation best describes the answer to this problem?

the zoo sold 564 tickets to the sea lion show. each show can seat a maximum of 75 people.

how many shows does the zoo need to put on?

a.
divide 564 by 75. the answer is 7 with 39 left over. so the zoo needs to put on 8 sea lion shows.

b.
multiply 564 by 75. the answer is 41,172. so the zoo needs to put on 41,172 sea lion shows.

c.
multiply 564 by 75. the answer is 42,300. so the zoo needs to put on 42,300 sea lion shows.

d.
divide 564 by 75. the answer is 7 with 39 left over. so the zoo needs to put on 7 sea lion shows.

4. which explanation best describes how to solve this problem?

cindy rode her bike for 10 miles, ran for twice as many miles as she rode her bike, and swam for 2 miles.

how many miles did cindy cover altogether?

a.
divide 10 by 2. then add 2 and 10 to the quotient.

b.
add 10 and 2 and multiply the sum by 2.

c.
add 10 and 2 and 10 and 2.

d.
multiply 10 × 2. then add 10 and 2 to the product.