Next, I invite 7 students to stand in a line at the front of the room. "How many children are standing in the front of the room?"
I ask 3 of the students to return to their seats. How can we find out how many children sat down?How do we know how many students are standing?
I model this on the board: 8 - 5 = ___.
Do you think you can complete this problem using connecting cubes and a part part whole mat?
Have the students discuss an addition sentence that could help them solve the subtraction sentence 8 - 5 = ____.
After I give students time to talk, I ask them to work independently, using their white boards to write the related addition facts that could be represented on the part/part whole mat (5 + 3 = 8, 3 + 5 = 8).
Give the students at least 10 two-color counters. Have the students put 7 counters in a row, yellow side up. Then have them flip over the first 4 counters.
"Is there an addition sentence you could make based on how you've changed these counters?"
If necessary, have the students think about how many red counters there are, and then how many yellow counters. Give them time to grapple with thinking through the problem. Struggle (productive struggle) is an important part of the thinking process.
After students have spent time working through how to represent their counters, it is time to explain that the model should show 7 as two parts, 4 and 3. Check your students for understanding at this point. "Which color counters are represented by the 4 - where does the 4 come from? Can you point to where the 3 is using your counters?"
"If you take away the 3 counters, how many counters would you be left with?"
"So, if I have 3 counters, and I add 4 more counters - my number sentence would be...(3 + 4 = 7)."
"Now think carefully about this addition sentence. Can it help you to solve 7 - 4 = ___?"
Have the students practice this method with the following problems:
Students should set up the whole first with two-sided counters, and then flip over the second digit. After students have had time to use their part/part/whole thinking to solve subtraction problems, it is time to discuss as a class which addition sentence the model shows for each problem. The focus is on how addition can help students to solve subtraction. Discuss each problem individually before moving to the next one. Scan/check for understanding to determine who is not seeing the connection between addition and subtraction.
Have the students complete the Thinking About Related Facts to 10 Practice. They should continue to build the model with two-color counters, the same as they did in the "Develop the Concept" section.
This is where it is helpful to have been assessing your students as you go along. Those students who seem to be struggling with the idea will continue to need support, and it may be helpful to group them (small group) to continue to monitor their progress.
Have the students come back together as a class to share their answers. Often time this is a great time for self reflection for the students. Often times the students learn more from one another's thinking than they learn from the teacher. Have the students discuss how they could use this strategy to help them quickly and accurately recall their subtraction facts. The CCSS expects the students to be able to fluently recall their basic math facts. It is important for the students to understand the need for this, and how learning this strategy can help them in learning these facts.