10 Less: An Exploration

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SWBAT explain why the ones place stays constant when subtracting 10 repeatedly.

Big Idea

The CCSS asks students to mentally find 10 more and 10 less, without having to count! This lesson helps students develop a conceptual understanding of +/- 10, which will give them the foundation they need to mentally calculate 10 more/10 less!

Objective & Hook

5 minutes

CCSS Context:

1.NBT.C.5 calls for students to mentally find 10 more and 10 less. Not only are students expected to do this without counting, they have to be able to explain the reasoning used-which means they can't just memorize it! This lesson build the conceptual understanding necessary for students to understand what is happening when they add 10 repeatedly, and to notice the pattern that will help them solve these problems mentally. 

Review Past Learning:

We made a booklet for adding 10 yesterday. Today we are going to make another booklet that explores how numbers change as we repeatedly subtract 10.

Connect to the Real World:

In 2nd and 3rd grades, you are going to have to figure out 10 less, 100 less and even 1000 less! The practice you do today thinking about 10 less will help you with these big numbers!


Your thinking job: Why doesn't the ones place change when we repeatedly take away 10?

Opening Discussion

15 minutes

Present Task: We are going to make a 10 Less Book today. In your book, you will show how you take away 10 over and over from your number. We will focus specifically on how the number in the tens place changes and how the number in the ones place changes. 

Because we used a similar style of book to add 10 in this lesson, it might be tricky for kids at first to use the same tool to do the opposite operation. We will make a 10 less book whole group at first so they understand the book. I'll use an enlarged version of what their booklets look like (see next section for the template).

I'll have one student use a base 10 model in front of the class to model the process of subtracting 10. I'll model recording in the book. What is tricky is that students have to take the number from the previous page and subtract 10 from it. This is most difficult when they have to turn the page-this is a 6 year old's quantum mechanics! Modeling how I transfer the number to each new page will help students easily use the booklet.

My Start number: 95

Focus Question as we subtract 10:

  • How is the number of 10s and 1s changing? Do you notice a pattern? This question primes students for MP8, Look for and express regularity in repeated reasoning. We will revisit this in the student debrief.


Independent Practice

15 minutes

Students each create a 10 Less Book. They start with a number (decided and written in by the teacher) and repeatedly subtract 10. Students record their strategy in the picture frame (most likely the base 10 model) and record how many tens and ones are in the answer. Then they think about why the ones place remained constant!

  • Group A: Intervention - Students in this group have fewer pages in their booklet, and start with a number in the 50s. In some cases, it may be best for these students to start on the decade, particularly if they are still developing their understanding of counting by 10s.
  • Group B: Right on Track - Students start with a number in the 90s, repeatedly subtracting 10 until they get to the last page, a number under 10. These students have base 10 models, and will most likely use them throughout the activity. They need the concrete model support right now to think about this concept.
  • Group C: Extension - Students start at a number in the 150's. These students are thinking about how the number changes when it is above 100. This leads to understandings of where the tens place is in 3 digit numbers, what the hundreds place tells us, and mental subtraction above 100.


20 minutes

Class Debrief: 

I'll bring students back together, and show one number set that a student in Group B had. I'll have the start number and all of the 10 less numbers listed on a piece of chart paper.

Focus Question: Why didn't the ones place change? 

  • First, confirm that the ones place in fact did not change with the class. I'll underline the ones place in each group so we can discuss how it stayed constant.
  • Scaffold questions: 
    • What do you notice about the tens place? 
    • Why did the tens place count backwards like 9, 8, 7, 6 etc?

I will have base ten models available on the carpet when we discuss this-students will probably want the concrete model to help them explain that the number of ones didn't change when you take a ten away.

Student Writing: After we discuss, I'll have students go write why the ones place didn't change on the cover of their 10 less book. This is aligned to the CCSS shift to writing across the curriculum, and it provides a great summarizer of the day's learning. Students sum up all of their learning for the day in this response.


6 minutes

To close out this lesson, I'll give students a chance to apply their understanding of subtracting 10 to a novel problem. Students will get the attached exit ticket and show 2 strategies to solve the same problem.