In first grade, students are expect to add and subtract within 100 (1.NBT.C4, 1.NBT.C6). This lesson is very much an extension of these standards. Students apply their understanding of different kinds of word problems, as well as their understanding of place value, to solve these problems. This lesson can be used as an extension in first grade, or as a lesson to align with 2.OA.1 in 2nd grade! Throughout this lesson, students practice making sense of problems and persevering in solving them (MP1) because students have to interpret what is happening in the problem in order to solve it.
Review Past Learning:
We have worked on so many kinds of problems this year. Today we are going to solve problems and find the unknown, then use our understanding of place value to help us solve.
Your thinking job is: What part is missing? What strategy can I use to solve for the missing part?
Present Problem: I have 54 beach toys packed for my trip. My best friend buys me more toys. Now I have 75 toys. How many toys did my friend buy for me?
Focus Question: Will I get more or less than 75 new toys? Vote!
Student Work Time:
I'll have students work on the problem for 8-10 minutes, representing how they solved. I am looking for 2-3 strategies to share.
I saw a variety of strategies during student work time. Below are a few links to student work that are great examples of student strategies.
1. Modeling with Base 10: This student showed how she used base 10 blocks to help her solve. She also has a number sentence that shows exactly what she did in numbers. First she added 20, then 1 more.
2. Ten Frame: Here is another example of base 10 understanding, but using a different tool to represent it. I often have students try using ten frames for novel problem types because they understand that the ten frame represents 10 single ones, and they can easily see all the ones!
3. Combinations: This piece of student work is so cool-it models so much thinking. It shows MP1 (Persevere in solving) and MP5 (Use appropriate tools strategically). This student tried a strategy using fingers, drew it and then abandoned it because in his words, "tens were faster". Great mathematicians know when to abandon the strategy they are using to favor a strategy that is more efficient or makes more sense to them.
This student also used combinations-he explained it in words a little, but expounded on it when he explained his work. He knew 5 and 2 made 7, so he used that to know he would have to get 2 more tens!
In the attached Student Work Example image, you'll see how one student modeled the problem exactly, but got the wrong answer. He had a typical confusion many students exhibit with base 10 change problems-he didn't know how to handle the ones. Even though he modeled adding 21 more with cubes, once he was at 75, he didn't have a way of organizing the cubes so that he could see which ones he started with and which ones he added.So he answered 25-he just grouped all of the ones with the 2 tens.
For students with this confusion, a strategy share often works out the misconception. They see how another student organized their cubes and that helps them to organize them when they tackle the independent practice problems. If a student continues to show this problem, you might use color as a scaffold in the problem. You can change the problem so that there are 54 red beach toys and your friend gives you some more blue ones. Then students can model with the color and it will help them see the missing addend.
I'll have the 2-3 students I pre-selected share their strategy for the class. I'll draw what they did as they share so students have a visual map to follow later when they solve additional problems.
I chose 2 strategies that highlight the differences in counting.
You can see both strategies here: Class Strategy Chart
After each strategy, I'll have students retell what happened in that strategy. At the end, I'll have students partner share how the 2 strategies were the same and different.
Revisit Initial Question: Did we have to get 75 more? Why not? How many more did we get?
Students solve missing part problems that are differentiated to the number set they are ready for from the packet: Beach Toy Base 10 problems. This is a time that students can either use the strategy they used before and practice it, or apply what they learned in the Student Strategy Share time and use a new strategy. I'll have the Strategy Chart posted so students can reference it.
Group A: Intervention
These students will get numbers under 50, with at least one of the numbers on the decade. This will help set these students up to practice representing the number in 10s consistently.
Example number sets: 21 + ____ = 41; 30 - ____ = 10
Group B: Right on Track
These students will get numbers under 100, similar to that of the student share problem. All numbers off the decade.
See this Student/Teacher Dialogue to hear how I discuss a story problem with a student. You'll hear the questioning I use to prompt her to solve, without ever "telling" her anything!
Also, watch this Working through the problem conversation I had with one student. He was struggling to represent what he was actually doing with his cubes on his paper-you'll see how I ask him questions to help him understand at a deeper level-you'll also see how I reinforce precise academic language (MP6) throughout the video-a key aspect of the CCSS! Side note: His answer for why he took out 2 tens is HILARIOUS!
Example number sets: 43 + ___ = 68; 52 - ____ = 33
Group C: Extension
These students will get numbers where they consistently have to compose or decompose a 10.
Example number sets: 58 + _____ = 80; 82 - _____ = 54
I'll have students share the strategy they used for the first problem with a partner in the same group (A, B or C). The focus question is: How are our strategies the same? How are they different?