Grade 3: Fact Families

Warm up with a quick recall on the board. Show that three numbers make four related facts (two + and two -, or two × and two ÷) using a part-part-whole diagram or a triangle card.

A fact family is the set of related number facts you can make from the same three numbers. From 2, 3 and 5 you get 2 + 3 = 5, 3 + 2 = 5, 5 - 3 = 2 and 5 - 2 = 3. Fact families make addition and subtraction (and later multiplication and division) two sides of the same coin, so learning one fact gives you three more for free. Model the method clearly, thinking aloud:

• Use a part-part-whole frame or a triangle with the three numbers so the whole and its two parts are visible.
• Write all four facts from one family together, pointing out how the numbers stay the same and only the operation and order change.
• Show that addition and subtraction are inverses: the whole minus one part gives the other part.
• Move to multiplication and division families once times tables begin (3, 4 and 12 give 3 x 4, 4 x 3, 12 / 3, 12 / 4).
• Give students two numbers and ask for the whole family, then a missing number to find using the family.

Work this through step by step on the board, then have the class talk you through a second one.

• The family for 3, 4 and 12:
• 3 x 4 = 12
• 4 x 3 = 12
• 12 / 3 = 4
• 12 / 4 = 3

Do the first few questions of the practice worksheet together, one child explaining each step. Check for understanding before releasing the class to work alone.

Students complete the worksheet independently. Hand out the three difficulty levels below so every child works at the right stretch.

Circulate and look for these, they are the usual sticking points:

• Writing only one or two facts instead of the whole family.
• Muddling which number is the whole and which are the parts.
• Not seeing subtraction as the inverse of addition (or division as the inverse of multiplication).
• Not seeing subtraction/division as the inverse, so children re-count instead of using the known addition/multiplication fact.

Pull the class back together. Ask one child to explain fact families in their own words, pose a single check question everyone answers on a mini whiteboard, and name what you will build on next lesson.

Use the independent worksheet as the evidence. A child who can complete it accurately and explain one answer has met the objective; anyone who cannot needs the easier level and a short reteach next session.