We Are All a Happy Fact Family

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Students will be able to identify four related number sentences, two addition and two subtraction.

Big Idea

Addition and subtraction are related! Every subtraction fact has a related addition number sentence, and every addition fact has a related subtraction number sentence.

Materials and Activator

10 minutes

I begin this lesson by having the students think about what they have learned about the part/part/whole model.  If necessary, I'll prompt the students to think about how we can use the model to show an addition problem, then a subtraction problem. 

Then I tell the students that today they will learn about how addition and subtraction problems are related.

Next, the students turn and talk about how they could use a part/part/whole model to show the problem 9 - 5.

Some students need support to connect with practices and information they've been learning.  I help them through prompts, "Do they know a part and a part", or a "whole and a part" ?

After a brief turn and talk (about 2 minutes), students share their understandings. 

Develop the Concept

20 minutes

Students now use their number cards and counters to represent the problem 5 -2 on their Part/Part/Whole Mat, using the number card to represent the whole and counters to represent the parts. 

They are instructed to solve the subtraction number sentence by placing the correct amount of chips in the missing "part".  Once students have solved the subtraction sentence, students turn and talk about what addition sentence could also be represented by that part/part/whole model. 

Students are then challenged to consider if there is another addition sentence they could write for the model. 

I explain to the students that when we have a group of number sentences, two addition and two subtraction, for a model we call it a fact family because all of the numbers are related like a family. 

To help anchor "fact families" I introduce the students to the Fact Family Song and we sing it together a few times. Singing is not only a great way to help anyone remember (adults too), it is a joyous practice that I use often with my 2nd grade students. The singing also gets the students bodies moving, and encourages deep breathing. Now my students are refreshed, and ready for our next step.

I model with students some practice problems by rolling two dice and using those numbers to help complete the Fact Family House 1/Fact Family House 2.  The two numbers on the dice will become the parts. As I work through the practice problems, I ask students to help determine the whole as well as the two addition and two subtraction sentences.


Practice the Concept

20 minutes

Once again, practicing the math is cleverly disguised as a game. I have the students work in partners to complete the One Happy Fact Family booklet.  The students roll two number cubes.  These numbers will become the two parts, as practiced all together as a class.  The partners use those numbers to determine the whole. 

Then the use the "whole" and its "parts" to create four number sentences, two addition and two subtraction sentences, to finish the fact family.

In order to create these fact families, the students have to make sense of quantities and relationships between the numbers rolled and the number created. Then they have to reason through both addition and subtraction, and create number sentences that “make sense” using these operations (MP2).

I differentiate this activity by controlling how high the number on the dice can do. I have several sets of dice, and different colors tell me the number range.  Appropriate number ranges for most of my students are x through y. I challenge some students by giving them higher numbers and/or a third die.


5 minutes

When we come back together to share, and socialize our thinking, the students are excited because the end product - the fact family homes - are a bit more creative looking than the usual math work. It doesn't take much to excite 2nd graders!

I help them to "warm up" their explanations through a shared look at each other's work in a turn and talk.  Then some of the students share their fact families, showing and explaining their fact family work. My role is to facilitate, and guide students to think about the relationship between the parts, and the whole and how they create addition and subtraction problems.