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This “Fact Family Photo Album” idea stops kids from inviting a stranger (4th number) into the family





Title – Fact Family Photo Album
By – Desiree Sumers
Primary Subject – Math
Grade Level – First


    A common misconception of my previous year’s students was the use a fourth number that was not part of the fact family. In looking for a new way to explain how the numbers move around that would help eliminate this problem, I came up with the Fact Family Photo Album.

Fact Family Concept:

    Children should think of the numbers as family members sitting at a dinner table.


When it’s just you and your favorite cousin eating dinner at Grandma’s house, you might argue about who gets to sit next to whom. Your grandmother, being a smart woman, would come up with a plan to take turns sitting in various seats.

Grandma is G , you are Y , and your cousin is C .

First meal, the seating might be you, your cousin and your grandmother. That would be Y + C = G

      I would then change the seats for the student and cousin and write

C + Y = G

      Point out that Grandma (G) is always the biggest number. When Grandma lets the children sit first (addition problems), she is always last (biggest number is always last when we add).
      Then I would say, “

Now, Grandma wants to sit in the first chair! So now we have Grandma, you and your cousin. G – Y = C.

      Next switch, I list

G – C = Y

      Point out that when Grandma chooses first (subtraction problems), she goes first (whenever we subtract, the largest number must go first).
      Now, we would look at the problems as I listed them. I would now replace each person with a number.


Y + C = G C + Y = G G – Y = C G – C = Y


      We would end up with the following:


2 + 3 = 5 3 + 2 = 5 5 – 2 = 3 5 – 3 = 2


      The students might try 5 + 2 = 3 once, but we test it out using pictures and find that this is not a true sentence, so we know we didn’t put it in the right order.)
      Then I would ask them “

Would Grandma let some stranger off the street just walk in and join them for dinner.

      ” “



So, should we let the number “8” join this dinner party?

      ” “


    We would create more seating arrangements using numbers only and then they would each be given their own Fact Family Photo Album to work on.

Fact Family Photo Album:

  • Make the books by putting two pieces of paper together, folding them in half and stapling them in the middle, like a book.
  • On the outside cover of each book, write three numbers.
  • Each pair of students would get four different photo albums to create.
  • They would then open the book, and on the first two facing pages they would write the addition sentences for those two numbers and on the last two facing pages, they would write the two subtraction problems.


    Using this lesson entirely eliminated the use of a fourth number in fact families in my classroom!

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