To activate prior knowledge, I present students with the partners of tens rhyme: Partners to ten rhyme. I ask them to recite the rhyme. I ask how this helps us to add? Students offer suggestions for how this helps them. I am hoping that they will recognize the partners of ten structure (MP7) and that if they know the partners of ten, they can then count on or back from ten to the new number, so if they know 2 + 8 = 10 and have 3 + 8 it will equal 11.
Now I ask what happens if you wanted to add 90 + 10? How could partners of ten help us? Students should recognize the use of the partners of ten to help them. If they are not sure, I say and write "9 +1 =" below the 90 + 10 and ask them what they notice that is similar? (that the 9 + 1 is the same as the 90 + 10 except for the zero. They may also use adding 10 to a number to help them. Both of these are strategies that have been introduced in prior lessons and will help to scaffold new learning.
We use a number grid to practice adding partners of 100, (20+80, 30+70, 40+60, 50+50). What pattern do students notice? (It is the same as 2+8 with a 0 on the end. It is 2 tens plus 8 tens instead of 2 ones plus 8 ones). I reinforce the concept of place value for tens and ones.
Next I tell the students I have some smiley face friends I want them to meet. Can they guess which numbers remind me of smiley faces? The ones with zeros.. and I add a smile to the numbers on the number grid.
Can anyone guess why these numbers make me smile? (Because they are partners of 100 and I can add them easily.)
We practice looking at a two-digit number (43) and thinking about 3s partner that will get me to the smiley 50. Now it is a number I can add easily. I call out 2-digit numbers and ask students to think of the partner of 10 that gets me to the smiley face.
** I want students to see that they can often locate partners of 10 within an equation to help them add the ones, and partners of 100 to add the hundreds such as in 85 + 25 I ask them what is the partner of 10 set in the ones place? (5 +5). "Right, so now we have 10, so lets look at the tens place. Are there any partners of 100 here? (80 + 20) Ok so 80 + 20 is ? (100) and we already had ten so now we have 110.
Next I ask what would happen if I wanted to add 22 +58? Could use the partners of 10 or 100 here? (Right, I see partners of 10. Do we have partners of 100 too? Right, not this time but we checked to see. So how could I use my partners of ten to help me solve this problem? I ask students to write in their journals how they would solve the problem.
We discuss the solutions students have. I want them to make sense of the problem (MP1) by looking for partners of either 10 or 100, or the problems close to those partners that can help me more easily solve a problem.
I want students to begin to rely on using the partners of 10 and 100, and to be using place value – adding tens and then ones to solve problems with larger numbers. This is helping students to notice and use the structure of problems to aid in finding solutions (MP7)
Some students are already proficient in this area. They will be given some problems to work on independently. They will be reminded to show their work. Their problems will be centered around a hypothetical recycling project where students gather newspapers and have to bundle them into packages of 100 papers.
For the remainder of the students, who do not do this automatically, we will discuss using bundles of ten to add larger numbers. We will talk about looking for partners of one hundred in our bundles, and then looking for partners of 10 in our ones digits and then combining our amounts to get a final solution so students might start with 52 and I will have them add 8. They look for partners of ten so 8 + 2 = 10, and then add that bundle of ten to the 5 bundles to have an answer of 60. If the number had been 53 + 18 they could say 8 + 2 is 10 so I make 1 bundle of ten and have 1 left over for the ones place. Now I add 5 bundles of ten plus 1 bundle of ten plus the bundle I just made to give me 71. I explain that there will be two groups working during independent practice today and then everyone will return to their seats to do a practice page.
These students will pretend that they are part of a group to recycle newspapers. They will collect the imaginary papers, count them and bundle them into groups of 100. The students will work with finding partners of 10 and then partners of 100 to complete the task. The students will be able to work with ones, tens and hundreds in this project. The imaginary papers are already in amounts. Students are looking for ways to combine those pile amounts into groups of 100 (for the tens place) and 10 (for the ones place). The idea is to use the structure of tens and hundreds(MP7) to make this task easier.
As an extension, students will be told that they will earn 28 cents for each bundle of 100 that they collect. They will add up the money they have earned. Students must work together here to reason quantitatively and abstractly (MP2)about the papers collected and the money earned. They must also find a way to model with math as they solve the problem (MP4).
The students who need help will gather with the teacher and work with manipulatives to practice combining tens and ones and looking for partners of 10 and 100.
Students will use bundles of ten popsicle sticks. They will also have single sticks to show the ones. I will write 2 numbers on the board and ask students to build each number by taking bundles of ten and then single ones. My first problem is 36 + 74 which gives me both partners of ten and partners of 100 Together we each bring our bundles of 10 together and count to see if we have one hundred by counting by tens (7 bundles + 3 bundles so we count 10,20,30, 40, 50, 60 ,70. 80, 90, 100 as we point to the bundles and remember that each one has 10 things in it.. Next we count all our ones and see if there are enough to make another bundle of ten (in this case there is with none left over). If so we add it to our count to know how many tens and how many ones in all. I will encourage students to see if they can make a new bundle of 10, count the tens and then add on with the ones.
I use some examples that have both partners of 10 and 100, and some that have only one of the two.
We also refer to the hundreds chart as we work each problem to give students another way to make sense of the problems as they try to solve them (MP1). Here we find 74 (the bigger number) count up 3 bundles of 10 to get to 104 and then count on 6 more. At the end I hand each child a number grid and a smiley face to put above the zeros numbers. I tell them they can use the chart for their work today.
This group will be adjusted to meet the needs of the learners.
It would be possible to make the struggling group more similar to the enrichment group by using amounts of newspapers rather than just numbers that the students add to get to 100. That way everyone would have similar experiences, but the struggling group would work together to add the piles, build them with popsicle stick bundles and get a total.
Each group will work for about 15 minutes.
Students will return to their desks. They will complete a practice page that encourages finding partners of ten and adding on the ones. This paper will be word problems for students to solve. I remind students to look for partners of 10 and partners of 100 as they try to solve the problems. I am hoping that they make use of the structure of things that add to 10 in order to solve the problems using place value tens and hundreds strategies.