Saturday, February 14, 2015

Solving Word Problems Part 2

This week in math we finished up our unit on the 4 operations. Again, we focused on word problems. We looked at some specific types of word problems that they will encounter.

We had a short week this week in math because we spent a couple of days on benchmark testing for the district.

Day 1
Monday we looked at interpreting remainders. This was a skill I noticed they needed from our work last week with different word problems. I used an anchor chart that I found on Pinterest to help me create one with my kids. Unfortunately, I haven't been able to find the source of the chart.

Here's what mine looked like:

We talked about 3 different types of remainder problems. Times when we ignore the remainder, times when we have to round up our answer to account for the remainder and times when the remainder is our answer.

Once we'd looked at these types of problems. We worked out some problems together, using the CUBES problem solving strategy, and discussed which type of problem it was.

Then I had the students work in pairs on some remainder word problems from our textbook. They were pretty challenging problems. Once they'd had time to work them out together, we went over them as a class.

Day 2
Tuesday, I explained to the kids that so far we'd been looking at a lot of 1-step problems where the main focus was on deciding the correct operation. However, in 4th grade, they're not going to see too many 1-step problems. So for today we were going to sort problems into 3 different categories: problems with extra information, one-step problems, and multi-step problems.

Together we looked at 6 different word problems and sorted them. We talked through how to solve each problem, but the main emphasis was on deciding which category the problem would fit in. (I tried to pick problems that clearly fit into one of the categories)

Then the kids got in pairs and had their own 6 problems to sort (You can see their directions in my picture above). Once most groups were done sorting, I had them choose 1 problem from each category to work through our problem solving paper on. They had to use the CUBES strategy, solve the problem, write their answer in a complete sentence, and justify their answer.

I had several groups who realized they had sorted a problem incorrectly once they began solving it. This just further reinforced the idea that using a problem solving strategy helps the kids read more critically.

Day 3
Wednesday was our last day of lessons for the week since we were benchmark testing Thursday & Friday. I was also out half the day for curriculum meetings so I needed something that could easily be taught by a substitute.

We completed a frayer model on estimation. I forgot to take a picture of mine at work, but you can find a great example at Math Workshop Adventures' blog.

Then the kids worked in pairs to complete some word problem task cards. I tried to choose a variety of word problems (1-step, multi-step, extra info, different operations, remainders, estimation, etc). I also did a mix of problems that gave answer choices & problems that didn't.

I used a lot of partner work and group work during our lessons on problem solving. I think that it is critical for kids to talk out the problems.

I haven't gotten the results of our benchmark yet, but I loved seeing their strategies on their papers. I even had a couple of students raise their hand to share with me that they noticed some important key words in the problems. Yay! : )

Sunday, February 8, 2015

Solving Word Problems

This year we changed the pacing of our instruction a little bit. We spent a chunk of time teaching the 4 operations, with heavy emphasis on the skills. Once the students had learned all 4 of the operations, we set aside 2 weeks to focus on problem solving using all of the operations.

In the past we would teach a skill and then look at word problems using that skill. I noticed that I wasn't spending a lot of time explicitly teaching kids how to determine which operation to use. I also realized a lot of kids would catch on to the fact that the word problems were over the skill we were practicing. They didn't have to do a lot of analysis to figure that out.

So this week we spent all week looking at simple word problems. I wanted to spend time explicitly teaching kids strategies to help them solve different types of word problems.

Day 1:
On Monday we looked at example word problems for each operation. We did the same activity 3 different times. First I modeled it whole group, then they worked in small groups of 4, and finally they did it again on their own.

We took 4 problems (1 for each operation) and looked for key words that helped us decide on the operation. We highlighted those words. Then we wrote a sentence explaining how we knew which operation to use. Finally, we wrote a number sentence showing the solution to the problem.

Day 2:
On Tuesday, I wanted the kids to really focus on some of the big concepts for each operation. Looking back, I think it would have been better to flip the activities for Day 1 & Day 2. 

I wrote some simple 1-step word problems for each operation. I passed out different math manipulatives to each table. I displayed one problem at a time and had the students "act out" the problem with the manipulatives. Then we worked together to write a number sentence and discuss what words in the problem helped us know what to do. 

After about 15-20 minutes of acting out different word problems, I collected the manipulatives and passed out a recording sheet. The sheet had 4 sections with an operation symbol at the top of each section. We had a class discussion about the things we noticed for the different operations and recording these observations on the sheet. Some of the big things we talked about were that addition and multiplication give us a larger number and subtraction and division give us a smaller number. We also talked about the fact that multiplication and division have equal groups, while addition and subtraction don't need equal groups. 

Day 3:

 Wednesday, I introduced the kids to a problem solving strategy that I have used in the past. The acronym is CUBES:

Circle the numbers
Underline key words
[Bracket the question]
Eliminate extra info.
Solve the problem 

I explained that this strategy helps them focus in on the important parts of a problem. This will become more important when we start looking at more complex problems. 

Like Monday, we did the same activity 3 different times. I modeled the steps, they worked it out in pairs, and then did it individually. 

I had copied different word problems on a recording sheet. Their first step was to do CUBES to the problem. Then they had to write a number sentence showing how to solve the problem. Once they had the answer, they had to write the answer in a complete sentence (this was harder than you would think!). Finally, they had to justify their answer. We referred back to our chart from Tuesday to help us explain why our answer was reasonable. 

Day 4:

This year our math curriculum specifies that students need to be able to use strip diagrams to represent problems involving the 4 operations. I wanted to spend a day looking at different strip diagrams. The kids had seen these diagrams on our spiral review warm-ups and a lot of them had a difficult time with strip diagrams modeling multiplication or division.

There's a great website and app called Thinking Blocks. We used this to help the kids practice with different diagrams. I don't have a smart board in my room, but we have a "smart pen" that turns the regular board into an interactive board. We used that to practice some different diagrams together.

Then I let the kids spend time in pairs, or independently, playing on the app. We used the addition/subtraction and multiplication/division apps. They were begging for more!

Day 5:

Friday is our assessment day. I gave the kids 8 one-step word problems. They had to use the CUBES problem solving strategy and show their work for each problem. They did a great job! While, I still have some kids who are struggling with the skills, every student knew which operation to do on the different problems. Woohoo!!

Next week we are looking at interpreting remainders and multi-step problems (including problems with extra info.)