First I set the context for this lesson by explaining to the students that people don’t always have paper and pencil and time to write down numbers and subtract to find out the difference between numbers. We have to use what we know about adding and place value to help us subtract.
I ask the students to talk to a partner or their group to discuss the following questions:
What are some instances when we would need to subtract in our head?
Why do you think this is something we need to learn in third grade?
What did you learn about subtraction in second grade?
3.NBT.1 states that by the end of third grade, students will be able to add and subtract fluently within 1000 using strategies and algorithms. This lesson provides an opportunity for students to apply a place value strategy of using friendly numbers in subtraction with regrouping.
Using unifix or interlocking cubes, I demonstrate a subtraction problem because I know this is a new strategy for the students to grasp, and having a visual will provide them with a reference to this strategy.
First, I select a number with tens and ones, such as 45. I ask the students how I would build that number with the unifix cubes. My students are able to explain that I need four groups of ten and a five individual cubes. Through discussion I may say these cubes represent pencils or cookies, and that I need to share some of these with another person or class.
Next, I explain that the class next door needs 18, and we will be sharing. I ask the students to think about how I will be able to give away 18.
This leads to the idea of having to break apart a 10. When they reach this point, I ask the students to consider that even though I'm breaking apart a group of 10 cubes, I still have the same number at this point.
I demonstrate how breaking apart the 18 into a group of 15 and 3 ones will help us to subtract easily by matching the ones digit in the whole amount. It is important to call attention to the ones digit, and I underline it for visual learners.
The number sentences are listed here for clarity:
45 - 18 = _____
(45 - 15) - 3 = _____
30 - 3 = 27
This would also work using 5 and 13 to break apart 18. The number sentences would look like this:
45 - 18= _____
(45 - 5) - 13 = _____
40 - 13= ______
(40 - 10) - 3 = _____
30 -3 = _____
In this example, there is a second breaking apart of 13 into 10 and 3. It's one extra step, but one may happen as students focus on only matching the ones digit without keeping the tens digit in the first subtrahend.
In this section you will create an anchor chart, titled "Break It Apart", with the students to demonstrate the process of breaking apart (decomposing) a number. To relate this concept to a concrete idea, I take an old wooden pencil and actually break it into two pieces. (Note: I use a pencil that never seems to sharpen well for this.)
I share with students that it's still a pencil. I could tape it back together and it would still work as a pencil.
I use the same number sentence from the demonstration with the connecting cubes to write out the chart.
45 - 18 = _____
I focus on breaking apart the number by matching the ones digit from the whole amount to allow for mental math subtraction. In this example using the five in the ones digit as the guide, and breaking apart 18 as 15 and 3, or 5 and 13. I use color coding to focus students on this important step. Color coding is also an ELL strategy useful for may visual learners.
This strategy is based on the Common Core Math Practice 2, Reasoning Abstractly and Quantitatively, because it supports the students with decomposing the subtrahend to create an easier, friendlier number to subtract.
I have students use individual whiteboards to practice this process of breaking apart numbers. Also, I create word problems from these numbers to provide context.
First, I demonstrate to the students how to underline the ones digit. This helps them to identify which number to break apart (decompose).
I model each step and number sentence for several problems, pausing and ask students to identify the ones digit, to identify the numbers to use in this strategy, to ask for the next steps, etc.
It can also be written this way:
I ask students which one has more steps, and we discuss why. Some students realize that taking away a larger amount at the start saves steps. Other students focus on only using exact matches to the ones digit in the subtrahend, without considering the tens digit. Right now, both approaches are OK, so long as students understand what we are doing.
We are going to use a foldable to recreate the structure of steps that we are taking in decomposing to mentally subtract. I demonstrate each fold, and students follow.
I fold the paper into thirds along the vertical. (If using 8.5 x 11. If using square paper, which side folds makes no difference.) Some may know this as a "hotdog fold" (Dinah Zike). Using the idea of creating a long, thinner shape like a hotdog bun may help some students follow along. Next, I show students how to turn their paper sideways, and fold the long shape into halves. When it is opened, there are six boxes, defined by folds. A printable example is attached in the resource section.
Next, I have students use their math journal to rewrite the problem, broken down, in the first square on their paper. Then, I write and display on the document camera five additional problems, one to be placed into each square, to be solved by using the modeled mental math strategy.
The students work with their shoulder partner at their desk, or in a group of three when necessary. My goal is to see if they can apply the decomposing strategy, working through each step to subtract mentally.
I have the students tell me the steps to solve a new subtraction problem. I connect the review of this process of mental math subtraction by using addition to check some of the problems used during the Try It Yourself section.
45 - 18 = 27
(27 + 3) + 15 = _____
30 + 15 = 45