I introduce today's lesson by announcing we are going shopping! This immediately engages the students, and results in much cheering and questioning. They want to know if we are going on a field trip, how much money did they have to spend, and was this for real.
I describe that we are shopping in the classroom, and will be using book order forms to practice subtraction with estimation and mental math strategies. I point out we will be using imaginary money, but I emphasize that they cannot spend more than they. Their goal is to spend all of the money.
Because the focus and the Common Core standard for this lesson is subtraction, I provide the students with a recording balance sheet to subtract along each line. This form looks similar to a checkbook register.
One of the primary “shifts” of the common core standards is the emphasis on deep conceptual understanding. The Standards for Mathematical Practice describe the habits of mind that need to be developed and supported in students.
Today’s lesson is focusing on MP 1 and MP2. Students are using concrete objects to create a representation to solve, and are checking their thinking and the thinking of their peers – “Does this make sense?”
In the application of place value strategies, students are recognizing the specific quantity of given numbers, and in response to the problem are considering more efficient ways to solve by manipulating quantities to create more easily solved equations.
I also want students to round the price of the book, so they are using mental math strategies and not subtracting $.99 (which is often a part of the price) each time.
I demonstrate how to select a book from the book order, identify the retail price, and record it on the balance sheet. Next, I have the students round the retail price to the nearest dollar amount, and then mentally subtract from the balance column.
The students use whiteboards for the subtraction to help them break apart the numbers. I taught the strategy of subtracting using place value in an earlier lesson called Break It Apart. I displayed a reference chart from the previous lesson to support this strategy. I demonstrate the strategy using three different books so the students can see how the remaining balance continues to decrease.
Each student is provided with their own copy of a book order form and a balance sheet. I encourage the students to work with a partner. However, the students do not have to choose the same books to record.
During the time the students are selecting and recording books on their sheets, I circulate through the class and observe their subtraction strategies on both the recording sheet and their whiteboards. Students are using different strategies, and I observe some students reverting back to using the standard (traditional) subtraction algorithm learned in second grade. When I saw this I asked, "How can you explain subtracting $14 from $130 to me?" If they can prove their understanding through questioning they could continue using the algorithm, but if they could only explain to borrow, cross out out, and change the ones digit to ten, I reminded the students to use the chart.
Students work at their own level, and use different strategies to get to $0 remaining. One student looks through the order form and selects the most expensive book set, explaining that it makes it easier to subtract smaller numbers. Other students try to look for books that are in multiples of $5 and $10 to make it easier to subtract. Other students simply chose books of interest to them, without considering a cost that will make the subtraction easier.
I ask the students to return to the carpet area for a discussion and to bring their recording sheets. I use observations made during the Try It Yourself section, to ask the students to share their strategies for choosing books and to do subtraction.
I ask students to share if they are able to spend all of the money, less than $5, less than $10, and less than $20 remaining. Students who successfully reach these amounts use mental math and rounding for subtraction. Those who have not reached this level state they use the subtraction with regrouping algorithm. These students also notice it took them longer to subtract with the algorithm than with the break it apart strategy.