Subtracting with Partners of 100

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SWBAT apply their knowledge of partners of 100 to solve difference problems with whole numbers using base-ten notation.

Big Idea

When subtracting ten from a 2 digit number, students should be able to compute the answer as fluently and comfortably as do when they add ten to a 2 digit number.

Warm Up

10 minutes

Today I begin by having students practice automaticity with subtraction facts to 10. Fluency and automaticity are different but are often interchanged.  Fluency means using an efficient strategy to compute accurately in the context of mental strategies. Automaticity means “by memory”. Students develop fluent strategies based on PV and properties of operations so that by the end of the year they know these facts by memory.This is not just memorization of number facts, but understanding how the number facts work so they can be used in more complex operations as children get older. The students are looking for the structure of how numbers work and applying that to their ability to solve problems quickly (MP7) 

I state the problem (e.g., 10 - 4) and students should be able to respond with the solution. We do several problems out loud. Next, I call out several problems for students to respond by writing the answer in their math journals. I give them only 5 seconds to write the answer to promote automaticity with number facts. 

Next I remind them that we have learned the doubles facts. I ask them if they can subtract the doubles. I give several doubles subtraction facts for students to record in their journals. I walk around to assess how students are doing with the facts. We check our work together.

I ask students for a thumbs up if they think they are good at subtraction, a sideways thumb if they think they are ok with subtraction, and a thumbs down if they think they can't subtract. 

I respond to what I see by encouraging them that because they can add, they can subtract. I show them walking forward on the blank number line is adding, but if I take the same steps backwards I am subtracting. I say 6 (and take 6 steps forward), plus 6 (take another 6 steps forward) is .... (I let kids call out 12). Now I say I am on 12 so if I step back 6(as I walk backwards 6 steps) where do I end up? (6).

I ask for a volunteer to do the walking. I say 8 (they walk forward 8) plus 5(they walk forward 5) equals.. (13). Now start at the 13 and walk back 5 (they step back 5) where are they? (8). 

I ask if students notice anything? (They have talked about fact families in the past so they may notice that these are fact families.) 

I tell students that subtracting is just going backwards with the fact families and that today we will talk about adding and subtracting using partners of 10 and 100 (which are bigger fact families).

Teaching the lesson

10 minutes

We start the lesson today by writing the partners of one hundred (as addition sentences) that we know on large sentence strips. I assign a different fact to each student to write. We post the fact sheets at the front of the room. The strips include 10 + 90, 90 + 10, 80 + 20, 20 + 80, 70 + 30, 30 + 70 etc.  Students will take more ownership of the process of converting to subtraction from addition if they write the strips themselves. I want students to make the connection so even though I could have had ready made strips for the students, by taking the time to have them write the strips, they will be able to make more sense of the related subtraction process. 

I tell students that these sheets can help them to subtract. I point to 20 + 80 = 100 and say what would 100 - 80 be? The students raise their hands to give the answer. I ask how the number strip helped them? (It is the same numbers, it is backwards, it is the opposite of addition).

Before moving into group work, we practice several other subtraction facts together using the number strips the students have created. Then I tell students that they will be working with subtraction today in several ways as they rotate through 3 centers. 

After I explain the 3 math centers, I assign the students to heterogeneous groups. This way those who already understand subtraction can help those who are struggling. As this is an introduction to subtracting with partners of ten, I do not feel that I need to provide more challenging numbers for the proficient students. Instead I want them to explain their thinking to their peers. Being able to explain one's thinking is an advanced skill that is important to applying understanding to later learning. Students are looking for and even more importantly expressing regularity in reasoning. (MP2)

Small Group Practice

45 minutes

Students rotate through 3 math centers today.

Center 1: In this activity students begin by drawing a single digit card. They will interpret that number on their paper as identifying the number of groups of ten (i.e., a 3 represents 3 groups of 10 - 30). Next, students make a subtraction sentence using 100 as the minuend by writing 100 - 30 = and go on to solve the equation. Their partner will do the same with his/her own number card. The two compare answers and the lowest answer gets a tally mark. At the end of the game, the partner with the most tally marks wins.Subtracting Partners of 100 Students are making sense of the problems they create and then solving them to see who has the lowest number (MP1)

Center 2: In this activity partners will begin by rolling a ten sided dice and a 6 sided dice. They will subtract the smaller number from the larger number, using the difference to determine how many place to move their game piece on the board. (Materials: a 6 and a 10 sided dice for each group, a game board and 2 colored chips).

Center 3: Students solve and create subtraction word problems,smiley face problems.docx subtracting smiley face numbers (10s numbers) from 100. This activity is a warm up for a later lesson. Students must remember to write a problem in words, posing a problem that uses subtraction, as well as give the answer to their word problem. Students are making sense of a smiley faced problem and then solving it. (MP1)


5 minutes

To close today's lesson, I ask students to clean up their area and return to their seats. As they are returning to their seats, I do a quick review and choose one word problem created today. I look for a problem that starts with 100 of something, a multiple of 10 is taken away (flies away, goes away, etc) and there is a question such as how many are left? A sample might be " I have 100 cards in my collection. I give away 30. How many are left.  I want to see if students were able to make sense of a subtraction problem with 100 and a multiple of 10 (MP1). I also want to see if they are using partners of 100 to solve the problem. I hope that they did not need to use tally marks or count by ones to solve the problem today, but instead they were using the powers of 10 and 100 to solve their problems. Students take out their math journals, and I read the word problem for them to solve independently in their journal.  I check their work for understanding.