EL Support Lesson

Fact Family Triangles

This hands-on lesson will get students thinking and talking about how the numbers in fact families are related. Use alone or with the lesson plan **Fact Family Trees.**
This lesson can be used as a pre-lesson for the Fact Family Trees lesson plan.
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This lesson can be used as a pre-lesson for the Fact Family Trees lesson plan.

Students will be able to write related addition and subtraction facts within 20.


Students will be able to describe how the numbers in a fact family are related with content-specific vocabulary using visual and partner support.

(3 minutes)
  • Draw a triangle on the board, and ask students what shape it is.
  • Write the numbers 15, 7 and 8 inside the corners of the triangle, with 15 in the top corner.
  • Ask students to turn and talk to a partner about what they notice about the numbers. Provide the sentence frame, “I notice ____.”
(5 minutes)
  • Choose a few students to share observations about the numbers, and record ideas on the board.
  • Think aloud, “I see 7 and 8 in the bottom corners.” Point to the numbers. Say, “I know that 7 + 8 = 15. This is an addition fact. Seven and eight are the parts, and 15 is the total of the two numbers.” Write the equation on the board, and have students repeat after you, “Seven plus eight equals fifteen.”
  • Ask students if there is another addition fact that can be made using the three numbers. Say, “That’s right, 8 + 7 = 15. This is sometimes called the turn around fact because it has the same parts in a different order.” Write the equation and have students read it aloud.
  • Think aloud, “I know the total of the two number is 15. This can help me solve two subtraction facts, 15 - 8 = 7, and 15 - 7 = 8." Add these equations to the list of related facts. Notice, "Subtraction is the inverse, or opposite, of addition!"
  • Say, “These three numbers 7, 8 and 15 are part of the same fact family. A fact family is a group of math facts that uses the same numbers." Remind students that they have read facts, or true information in non-fiction books. Here, the equations or number sentences are true, so they are also called "facts."
  • Ask students to think about thier own family, and turn and talk to a partner to name a few relatives (e.g. sister, brother, aunt) using the sentence frame, "My ____ is in my family." Tell students that just like we are related to people in our own families, the numbers in the fact family are also related, or connected.
  • Use the Vocabulary Cards to review key words.
(10 minutes)
  • Distribute two different colored cubes or other counting manipulative to students, and tell them that they will use the cubes to show the four related facts in a fact family.
  • Begin with facts within ten. Instruct students to follow along with their cubes as you write numbers in the triangle.
  • Write the numbers 4 and 6 in the bottom corners. Ask students to build a train with four red cubes and six blue cubes.
  • Tell students to tell their partner which number is missing in the fact family. Provide the sentence frame, “I think the number is ____ because ____ .” Students should share an addition fact that helped them solve for the missing number. Encourage students to agree or disagree with their partner. Provide the sentence frames, “I agree with my partner because ____” and “I disagree with my partner because ____.”
  • Provide a few more examples with students solving for an unknown total. As students show mastery, introduce sums to 20.
  • Next, challenge students to solve for the missing part. Write the number 8 in the upper corner and 6 in the left corner. As students how many cubes they need to show total.
  • Students should build a train with six red cubes, and add two blue cubes to show eight total. Think aloud, “Yes I know that the missing number is 2. I know that 6 + 2 = 8 and 8 - 6 = 2. I can solve for the missing part using addition or subtraction. Addition and subtraction are opposite, or inverse, operations.”
  • Provide more opportunity to students to solve for a missing part in a fact family. Allow students time to compare and justify their answer to a partner using a number sentence.
(20 minutes)
  • Tell students that they will now create their own fact family triangles. Distribute the Blank Fact Family Triangle worksheet to each student, along with two different color blocks or other counting manipulatives.
  • Instruct students to write three numbers that are part of a fact family in the corners of the triangles. As students build the facts, they should model the fact using the cubes. Show an example, writing 4, 5 and 9 in the corners. Build a train with four red cubes and five blue cubes, and say aloud the four related facts in the fact family. Tell students to take their time, and think about how the numbers are related, or connected. They should be prepared to justify how they know that the numbers are in the same fact family.
  • As students finish, they should cut out their triangles. Students can cover one corner, and challenge a partner to name the missing number. Students should ask how their partner why they choose that number.


  • Work with students in a teacher-led small group to create the fact family triangles. Guide students to explain how the facts are related using blocks to help them visualize the amounts and relationships between the numbers.
  • Allow students to say the related facts in their home language (L1). If possible, pair students who speak the same L1 during the partner activity.


  • Instruct students to explain the steps to write a fact family in their own words.
  • Ask students to explain how knowing that 7 + 8 = 15 could help them solve 15 - 8.
  • Circulate as students write the three numbers in the fact family triangles. Ask students to show you with blocks how they know that the three numbers in the fact family are related.
  • Prompt students to say the four equations in each fact family.
  • Assess whether students are able to identify the unknown number in a fact family, and whether they are able to justify their answer.
(2 minutes)
  • Remind students that knowing addition facts can help them solve related subtraction facts.
  • Provide a plastic baggie, and tell students to keep the fact family triangles in their desk. Students can practice the facts, and add more triangles as part of a small group center activity. Or, have students take the triangles home and challenge a family member to name a hidden number.

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