Imagine that you are a young student in Kindergarten or first grade. If you had blocks or other objects, how would you solve the following problems? What are the differences and similarities between them?
(a)
Johnny has 7 apples and Susie has 5 apples. How many apples are there altogether?
(b)
Johnny has 7 apples. Susie gives him 5 apples. How many apples does Johnny have now?
(c)
Johnny has some apples. He gives 7 of the apples away to Susie and now has 5 apples. How many apples did Johnny start with?
(d)
Johnny has 7 more apples than Susie. If Susie has 5 apples, how many apples does Johnny have?
(e)
How would these problems change if the numbers 7 and 5 were replaced with 7264 and 567?
What does it mean to “add” two numbers? What action or actions are we taking when we add? How do we recognize addition?
Thinking about how you would use the blocks to solve the following problems, what are the differences and similarities between them?
(a)
Altogether Johnny and Susie have 12 apples. If Johnny has 7 apples, how many apples does Susie have?
(b)
Johnny has 7 apples. Susie gives him some apples and Johnny now has 12 apples. How many apples did Susie give Johnny?
(c)
Johnny has 12 apples. He gives 7 of the apples away to Susie. How many apples does Johnny have now?
(d)
Johnny has 12 apples and Susie has 7 apples. How many more apples does Johnny have than Susie?
What does it mean to “subtract” two numbers? What action or actions are we taking when we subtract? How do we recognize subtraction?
There are three different types of addition and subtraction problems. The three types are:
  • Put together/take apart problems (two sets are joined or separated)
  • Change over time problems (the actions happen over time)
  • Comparison problems (the action of the problem is primarily comparing two sets)
(a)
Classify each of the problems above. Which type are they, and why?
(b)
Write your own example of each of the three types. How do you know your answers are correct?
2026-07-17 02:43:11