Question bank: Equality: Identical Sums and Subtractions

In the school library, teacher Ana arranged books on shelves. She put 7 storybooks and 5 science books on each shelf. Then, teacher Renata did differently: she put 4 storybooks and some more science books, totaling 8 books on each shelf. Write two different equations showing how many science books teacher Renata put on each shelf. Remember that the total amount of books on both science shelves must be the same.

In a school project, the 3rd-grade students decided to plant flowers in a rectangular flowerbed. They noticed that they could arrange the flowers in 4 different ways to cover the same area. The first configuration was with 8 flowers aligned in 2 rows, the second with 6 flowers in 3 rows, the third with 4 flowers in 4 rows, and the last one with 2 flowers in 8 rows. Considering that each flower occupies the same area, how could they mathematically justify that these 4 configurations are all equivalent in terms of the area covered by flowers? Write an addition or subtraction sentence that expresses this equivalence of different arrangements.

Imagine you have a piggy bank and every day you save some coins in it. Today, you saved 7 coins of 1 real. If tomorrow you want to save the coins from today along with some more coins to add up to a total of 9 coins of 1 real in the piggy bank, how many coins will you need to save tomorrow? Write two different operations that show how you can reach the same answer by adding the coins. Remember that, even using different sums, the total number of coins in the piggy bank has to be the same.

João and Maria are playing a game in which they need to balance the scale. They found out they can use sandbags to make both sides of the scale have the same weight. If João puts 7 sandbags on one side and 9 on the other, the scale is balanced. But if he puts 8 sandbags on one side, then Maria needs to put 3 fewer sandbags on the other side to balance it. It can be done differently: if he puts 6 sandbags on one side, Maria needs to put 3 fewer on the other side. Think of a number that, when added to 6, gives the same result as adding 8 with 3. Write in two different ways how João and Maria can place the sandbags to balance the scale.

Imagine you have a bag with 8 apples. In a different way, you can distribute these apples into two baskets, where the number of apples in each basket is the same. How many apples would you put in each basket? Now, you can think of another way to distribute the same 8 apples into two baskets, but this time the baskets do not have the same number of apples. How many apples would you put in each basket? Write both situations in the form of an addition or subtraction.