Direct Instruction: Addressing weak math writing skills.
We opened up our lesson today with a review that I hoped would help students learn how to compare in writing, exact answers against estimated answers. I had put 35 x 64 on the board earlier in the day, asking them to figure out the exact answer and the estimated answer.
I then wrote under the equation: Is your exact answer reasonable? How can you use your estimated answer to tell? Write and explain.
After we solved both problems, I turned and told them that I wanted them to answer a question like this, just like this: And I began to write...
I know that my exact answer is probably accurate because .... ( I stopped and turned to the class and asked them to finish my sentence. One girl raised her hand and continued the sentence for me).
...because both my exact and estimated answers are 2,000.
I asked them: Do you think you have said enough or can we include anything else? I did not get any response so I continued guiding the thought process with questions...
What do you notice about the exact answer compared to the estimated answer? Which is larger? Why is it larger? I called directly on a higher level student to help me out. He waited for a few minutes and I thought perhaps I had asked the wrong person because four hands had shot up. I waited because I wanted to hear what he would say after thinking about it...
He said: The estimated answer is larger because you had to round the 35 up to 40. That would mean that you were going up five more groups.
It was what I had hoped for!
So we finished the short answer: My estimated answer is larger because I had to round up, but the numbers still are reasonably close. I went back and underlined the word reasonably.
I asked students to copy the short answer and all the work to keep for notes to study for the test.
Goal: To create a visual review for the multiplication test they will be taking on Friday.
I passed out note cards to half of my students, choosing appropriate tasks (printed out and glued to cards) to match student needs. For example, one of my students was struggling with estimating double digit by double digit algorithms, so he got that card.
I asked them to line up with their cards and read them aloud to the rest of the class. Student Reading Her Card I partnered them up when each of them were done with a partner that would support their learning and guide them if they were a struggling student.
They were required to video and explanation in Educreations that would help students review the concepts that should be mastered. They were told they could be creative as possible and add visuals or what ever they thought that would help people understand their demonstration.
These were the tasks written on the cards:
1. Show how to multiply 1 digit by 2 digit algorithm using area model using place value language, the words partial products, and product in your explanation.
2. Show how to multiply 3 x 1 digit using expanded model, place value language, the words partial products and products in your explanation.
3 Show how to multiply 4 x 1 digit using expanded model or area model using place value language, the words partial products and products in your explanation.
4. Show how to estimate a 1 digit by 3 digit algorithm with one equation having a factor < 5 and one > than 5. Explain why you don't round the single digit to estimate using place value language, Associative Property and powers of 10.
5. Show how to multiply 2 x 2 digit algorithm using an area model.
6. Show how to estimate a 2 x 2 digit algorithm using place value language, basic fact, Associative Property, powers of 10 .
More advanced students write word problems for the review.
7. Write and solve a one step word problem using KWS strategy, equations with variables and correct labels. Explain your reasoning aloud. Explain why you think your answer is reasonable.
8. Write and solve a multiple step word problem using KWS strategy, equations, with variables and correct labels. Use area model to solve. Explain your reasoning aloud. Explain why you think your answer is reasonable.
9. Write and solve an estimation multi-step word problem using a KWS strategy, equations with variables, powers of 10 , the Associative Property, and correct labels. Use old homework problems for an example, or solve one you got wrong on your homework to correct it.
10. Write and solve an estimation one step word problem using a KWS strategy, equations with variables, powers of 10 , and the Associative Property
You can group your students according to your needs or make up more tasks to fit needs. This whole process discreetly but effectively meets student needs. It also challenges higher level students by making them write word problems.
They got busy working on their tasks. They were engaged, working collaboratively and were fairly quick about their work. I had set a time limit of 15 minutes to get their product done. The advanced students writing word problems worked just as quickly as everyone else. I roved the class checking work and monitoring progress.Configuring the Word Problem. In this photo we can see students working with both the iPad and their white boards. They photographed their whiteboard work. I found it interesting that even with the iPads, they love to use whiteboards. The one student typed the word problem while the other worked on the KWS chart and equations.
After the videos were all ready, ( students worked on iPad math aps of choice while waiting for everyone to finish) we started to share our movies. We started with #1 and worked through each task, discussing each video. We talked about what was left off, or forgotten. Things like labels on word problems, talking about partial products and place value language when adding of partial products was going on.
This experience of being able to talk about each video helped students see what they needed to brush up on in their work and in their thinking. We talked a lot about how labels in word problems are important in the 'K" part of the unpacking (using KWS What do I know?, What do I need to know? and How do I solve? strategy). I had to intercede and guide thinking from time to time through the process. Guiding them along in their review and discussion...
One student said that if everything wasn't labeled, you wouldn't know how to put multi-step word problems in the right order for the equations. Math Practice Standard 3 is being exercised here as we critiqued one another's work. My classroom has a well established level of trust and understanding that we are learners and we make mistakes that need attention. We have established that we learn together, no matter what level we are, we work together for understanding. This kind of classroom is conducive to mastering Common Core Standards.
Here are two samples of student videos.
Students practice IXL math to review. I assigned multiplication problems F level 1,2,3,4,5,8,9,& 11. I assigned them 2 problems from each set so they got exposure to all of the standards their multiplication would be testing. I told them that I wanted them to do their work on paper to show work. This will prepare them well for their test.