Mary Ellen Kanthack BROOKWOOD MIDDLE, GENOA CITY, WI
4th Grade Math : Unit #13 - Multiplication Unit : Lesson #18

Estimation Scenarios: Writing Estimation story problems.

Objective: SWBAT create a logical and solvable word problem using estimation.
Standards: 4.NBT.A.3 4.NBT.B.5 MP1 MP3 MP6
Subject(s): Math Enrichment
60 minutes
1 Warm UP: Estimation of numbers 1x4 digit. - 5 minutes

Enrichment Warm Up: Slap Happy Estimation. I wrote 20 (1x4 & 1x 5 digit) multiplication equations on note cards. I shuffled them and gave the stack to my above grade level achieving students. I asked them to turn one over from the top of the stack and solve it by estimation. Whoever calculates first slaps the card and says the estimated product. One person used a calculator to quickly figure out the estimated product.  If the person who slapped the card was right, they won the card.  I explained that they could use mental math only. I heard a lot of excited whoops and ughs! It was funny to hear them be so intense. Happy Group: This photo shows the simple cards I made for this lesson. They like note cards to work with...and it makes it easy for me because I simply store them in my file for this lesson to use again. They are the same note cards used in the next sections.

This can be modified for lower level mental math and for all operations. It's a great little mental math estimation tool!

2 A Multplication and Estimation Task at hand for the higher lever thinker.... - 30 minutes

Purpose: This engaging lesson is intended for higher level thinkers in my class. I wanted to challenge their minds because they master word problems quickly in their homework. They need something more! This opportunity extends their thinking on a different level. They have the opportunity to make sense of and solve problems they have created for each other. ( MP 1.) As they create their problem, they attend to precision of language, order, accuracy in calculations, and logic (MP 6) and then, as they solve each other's work, they are critiquing one another (MP 3.) It also strengthens writing skills and makes them understand the importance of clarity when they are writing.

 

We begin: I asked my above grade level achieving students to pick two cards from a deck of note cards where  I had written 4 x 1 digit multiplication expressions. I did this because it would give them two choices to work with and make it interesting.

I asked them to think about this as an estimated equation put it into a real world as an exaggerated situation. Could it be the cost of something special? Could it be a population or some data from research? What in life could fit into the number? Or, could it be turned into something crazy that would make a tall tale. I gave them suggestions like these because the group is mixed brains: two have very serious scientific minds, and three are creative and sort of quirky with goofy jokes and wild stories. I like to try to fit my student's personalities with assignments and give them choices. They all liked the exaggerated story idea. This clip shows my conference with a student as I help him figure out what he needs to do and reason his choices. Phillip's Choice

I asked them to create an estimation problem using one or both of their equations. They could work in pairs, but each of them were to have a card and their own story problem. Each problem had to be different. I told them that if they wanted to be challenged, they could create a two step problem. They could choose any topic, but they shouldn't be afraid to equate it to something they had read lately, or the season, or anything interesting that is going on.

I expected that everything had to be spelled well and written neatly so that others could read it. They had to create a KWS chart to organize their word problem and see if it made sense. Then, they had to create equations with variables and solve their own work to make sure everything was correct. As they worked, I roved and checked progress. This student needs to extend herself further and I encouraged her to write a two step problem in this clip. This supports CCSS design for us to promote rigor for the student. Realizing its a one step.

When they were done, they were told to work on IXL math online or another math ap on their iPads until everyone in their group was finished.

 When everyone was finished, they switched word problems and solved them on a separate sheet of paper. Then, after they solved it, if there was time, they switched again and solved another one. After solving three, they needed to compare their answers and equations to check each other.

3 Time to Switch! - 20 minutes

When everyone was finished, they switched word problems and solved them on a separate sheet of paper. I moved them to the hallway where they could conference with one another. Cooperative Learning Word Problem Writing . It was my hope at this point in the lesson, that they could see the value of clear writing, accurate language, and creativity in math. I wanted them to see each other's wonderful thinking and appreciate the challenge they mastered.

After they solved the problem they received, they met with the author of the word problem and compared answers and solutions. This takes a little while, so enough time needs to be allowed. It will vary with students because some students may be challenged.

 As I checked on this group, I could hear the laughter and relevant discussion that was going on between the five of them. They were very engaged and interested in their work.  They hadn't written terribly far fetched problems, but from the sounds of their discussion, they were having a great time solving each others work. They met with me when they were confused about the problem. I helped this student try to make sense of this problem because this author has not quite mastered the idea of clarity. Solving Multi-step word problems checking.

As we talked together to close the lesson, it was revealed that they could see how they mastered something new and different. They expressed how much they enjoyed this work.

 

 

The Challenge of Challenging My Students
Rigor

This was a challenging assignment for my above grade level achieving students because they had to work at writing very clearly. One of my students who is very capable of writing a two step problem wrote a one step problem. I challenged her and pushed her to add to it and edit it so that it was a two step problem. I had to guide a few students to write about appropriate topics.

Questions in the problems were very accurately written. They all had the right question for the situation. I was concerned about this because I hadn't really done any instruction on direction of questions. But it seems these students have this thought process well mastered. I need to adjust my practice  in the future for my lower and mid grade level achieving students on making sure the question fits the problem when I teach them to write two step problems. I know this from past experience. I was lucky this time..and very pleased!