Question bank: Equality: Identical Sums and Subtractions

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.

Imagine you have some red apples and some green apples. If you counted 3 red apples and 5 green apples, and then your friend said you have 4 apples of each color, how can you explain this using identical addition and subtraction? Write the equation that shows that 3 red apples plus 5 green apples equals 4 apples of each color, and then write the equation that shows how you can find out how many green apples you need to remove to end up with 4 red apples and 4 green apples in total.

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.

Imagine you have a box of colored pencils and want to distribute these pencils fairly between you and your best friend. You decide that to be fair, each of you should have the same amount of pencils and there should be no pencils left in the box. Now, think of a number of pencils that is equally divisible between the two of you. Then, think of another different number that is also equally divisible between the two of you and that, when added or subtracted from the first number, gives the same result. Write down these two numbers and explain why you chose these numbers.