Extending Partners of 10 and 100

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SWBAT use their partners of 10 to add numbers to 1,000 in partners of 100

Big Idea

Students know partners of 10. Can you believe that there are partners of 100 and 1,000 too?

Two Day Lesson

This lesson has several aspects built to support the idea of 100. It would best be used as a 2 day lesson. The first day would be the warm up and independent practice sections. 

The second day would be the 100th day activities. 

This would provide time for teaching about 100 and then a day for exploring what 100 really is. 

Warm Up/Review

20 minutes

For the warm up today I am going to divide my class into 2 groups. There are some children who had some difficulty on the recent assessment of larger numbers. There are 3 children who had a great deal of difficulty, and there are children who were very strong on the assessment as well as other class measures.

In the warm up I want my struggling students to come away with the ability to find the closest smiley face number. I am interested in them looking for the structure of the numbers and then using precision to find the closest smiley face number (MP6 and MP7) This will help them in the future when they need to know how to estimate, and how to check an answer to see if it is close to the correct answer. 

I give the strong students a problem solving task using larger numbers. challenge hto.pdfI want to extend their thinking. They will  need to think about the structure of numbers as they solve the problems (MP7)I encourage them to work with a partner to solve the problem (see challenge resource). I give them several riddles to solve that involve understanding the digits in place value. I ask them to also write their own riddles and share them with a partner. These students understand place value and smiley face numbers so this activity extends into 4 digit numbers and reinforces the terms around place value.

For the remainder of the students I begin by reviewing what a smiley face number is and how we find it. I remind them that the Smiley Face numbers have a 0 where you could draw the smiley face. We call them Smiley Face numbers because they are easy to work with and make us smile. I have students take out their journals. I say the number 47 and ask them to write the closest Smiley Face number.  I encourage them to use the number grid, or number line to move to the nearest smiley face number. I ask them to remind me where the smiley face numbers are on the number grid? (On the right) What are they counting by? (10s) I ask for a volunteer to tell me what the number is that is closest to 47.  I say the number 22 and they do the same. I repeat this process for about 5 more rounds, or until I can see that all students have an understanding of how to find a Smiley Face number. I note anyone who is still struggling. 

Next I tell students that we will try to find the Smiley Face numbers for two different numbers and then add the smileys together to get an idea of what a logical answer might be for the equation 38 + 26. I write the equation on the board and ask students to write the smiley face number closest to 38 + the smiley face number closest to 26. What did they write? (40 + 30). What is 40 + 30? (70). So our answer to 38 + 26 should be close to 30. How can we solve 38 + 26 using a tool from our math suitcase? (The suitcase is something students helped to create in a previous lesson. It includes number lines, number grids, pictures of counters, examples of column addition and subtraction, tens frames and other tools that we have introduced this year. It serves as a reminder of all the tools we can use to help us in math.)  (I take suggestions and ask students to solve the problem in their journals. We share strategies for solving the problem.) Our answer is 64. Is that close to 70? Ok then we know we have done a good job finding the answer. What if I had gotten 19 or 514? Would these be logical answers? I remind students that while we may not always get the right answer, we do want our answers to be logical. 19 is way too small. I got it by adding each digit together 3 + 8 + 2 + 6 = 19. 514 is way to big but I got it by adding 30 + 20 and 8 + 6 and then putting the answers next to each other so 514 or even 5014. The smiley faces help us to check to see if our answer is logical.

I repeat this process with several more examples. I ask students to give input at each step of the problem so they are actively engaged in the learning process. 

Counting Ones, Tens and Hundreds

10 minutes

Marking ones, tens, hundreds: 

I give students a math page with problems to solve.quick HTO page.pdf  My objective here is to help students better understand the structure of 3 digit numbers (MP7).I also give them 3 colored pencils - yellow, orange and green (light colors). I put a 3-digit number on the board and ask them, how do we know which is the ones place? (always last in line), who stands next to the ones (the tens). Who is third in line from the end? (hundreds). Ok so lets color code the ones in all of the numbers on the page. Remember, the ones are always? (last in line) I have students color all of the ones digits yellow as well as the word ones. Next I say, “Who stands next to the ones? “ (tens). “Ok, let’s color the word tens and all the tens digits green.” “Ok now who is third from the end?” (hundreds) (I don’t want to say first in line because later we will add thousands.)  “Ok, lets color the word hundred and all of the hundreds digits orange.”

Now I ask students if you want to add or subtract can you add tens to ones, or ones to hundreds? Why not? (they are not the same thing). I take out base 10 blocks and show a hundred's block and a tens rod. Can I add them together and say I have 2? I do have 2 things but would a 2 be the correct answer? Why or why not? 100 + 10 = 110 not 2 so we need to remember to add ones to ones, tens to tens, hundreds to hundreds. I repeat this demonstration with other amounts of base ten blocks to help clarify that ones, tens and hundreds are all different things.

Now you will work on your own to solve the problems on the page. Remember to match the digit’s place (the colors) as you work to solve the problems. You may use the tools in your math suitcase, except a calculator today. 

I give students time to work on their paper while I check in with the other group that is working independently on the paper without my explanation. 



100th Day Activities

45 minutes

Today is the 100th day of school. We will use this day to talk about and review partners of 100. What do we need to get to 100. Students will be working to more fluently add and subtract within 100 (2MBT5). They will also be choosing appropriate math tools (MP5) and Modeling with math when they use the base 10 block) (MP4).

 I bring all of the students together on the rug. I tell them that we will start today trying to find partners of 100. They can look for partners of 10 to help them. I put a number line marked to 100 by 2s and a 100 grid on the Smart Board for reference. 

 I have 30. What do I need to get to 100?

I have  80. What do I need to get to 100?

(I do several more of the smiley face partners.)

 Ok, those were all smiley face partners. What happens if they are not smiley face friends, can we still do it?

 I have 68 (I mark it on the number line). What do I need to get to 100?

I say, “hmmm.. maybe I can move this to a smiley face partner of ten.. ok.. how can I get to a smiley face partner of 100?” (I let children suggest ways. If someone suggests going up 2 I will build upon that. If no one does, we will explore their ways, and then I may show mine.) “Ok so I can go up 2…( I demonstrate on the number line as I count) 69, 70”. “Ok so I remember 2. Now I can find the partner of 70 that gets to 100. What would that be?” (30). (I demonstrate jumping up by tens on the number line) “Yes, 30 and my other 2 would give me what? 30 plus 1,2 = 32. 

I repeat this process with the numbers 56 and 37. 

 For the rest of math today we will look at things that we can partner to make 100. I remind students that it is the hundredth day of school so we will be looking at 100 of things. They will be moving through four centers in small groups. I will count them off into groups by 4s to visit each center. Because I have 19 children, there will be 4 or 5 children in each group. The centers require pennies, rulers, tape measures, yard sticks, math cards, base 10 blocks, connecting cubes, cups and eye droppers. I explain that there will be adults at 3 of the centers and at the last one they will work alone. I explain the water center because it will be independent.

 One job will be to predict how high 100 drops of water will come on a container. I say, you will all start with 4 drops of water in the container. I demonstrate with an eye dropper putting 4 drops in each container. How many more will you need to make 100?  You will work with a partner to decide how high you think the water will come on the cup and each place a mark with a marker. Then you will count out  how many more drops? (96). Right because 4 that I put in plus 96 more will make 100 drops.  You can repeat this by starting with a different number of drops. looking and then figuring out how many more to get to 100 and see if the second set of 100 comes to the same place as the first. 

 I break students up to visit each center. As they arrive at a center the adult explains the center as follows. (I allow just 10 minutes at each center. Each center allows for students to think about what 100 really is so the activities are quick experiences with the idea of 100.)

At the next center you will predict how high a stack of 100 pennies will be. You will measure the height of 5 pennies in centimeters. Next  you will each write your prediction in marker for how high you think 100 pennies  will be in centimeters. You will then measure a stack of 10 pennies and see how many centimeters that is. You can make enough stacks of 10 to equal 100, measure each one and then find the total. Here students need to think about bundles of 10 that equal 100 and practice measuring with a ruler. 

 At the next center you will guess how far 100 stack cubes will reach.  One of you will start with between 15 and 25 cubes. Your partner must figure out how many more you need to get to 100 and record it. Then you will both guess how far in inches 100 snap cubes will reach.  You will connect 100 cubes and then measure with the appropriate tool (ruler, tape measure or yard stick) to see how tall the tower actually is. 

 At the last center you will play Partners of 100. The first person will  draw 2 cards and make a number. The second person must take the right number of base ten blocks to make 100. You will record the number sentence (Cards + blocks = 100). Partners of 100

Each of these centers gives students a chance to visualize how big 100 really is, to think about bundles of 10 in 100 and to work with partners that add to 100. These are all practice centers and I do not expect mastery of each skill. I want to give students a chance to explore what 100 really is.