Math Lesson Plan for Remediation of Regrouping

Lesson Topic: Multiplication 2 digit X 1 digit; regrouping (with remediation), based on results of Math Multiplication Diagnostic Test

Grade/Subject: 4^th Grade Mathematics

Rationale: Florida Sunshine State Standard:

Standard 2: The student understands number systems.

Benchmark (MA.A.2.2) 1. Uses place value concepts of grouping based on powers of ten (thousandths, hundredths, tenths, ones, tens, hundreds, thousands) within the number system.

Standard 3: The student understands the effects of operations on numbers and the relationships among these operations, selects appropriate operations, and computes for problem solving.

Benchmark (MA.A.3.2) 2. selects the appropriate operation to solve specific problems involving addition, subtraction ,and multiplication of whole numbers, decimals and fractions, and division of whole numbers.

Real Life Application: Students will need a very strong basic sense of place value and grouping in order to compute any and all everyday computations in real life situations. In order to balance a checking account, budget their income and expenses, calculate how many of various items they can purchase, and the differences in cost and income variances.

Objective: For the fourth grade mathematics students to demonstrate their comprehension of place value in numbers, and regrouping strategies, so that when given multiplication problems of 2-digit X 1-digit, as well as addition and subtraction problems requiring regrouping, they will use counting and place value strategies previously learned, to solve with 80% accuracy.

Prior Knowledge: The children have been working with the concept of regrouping since almost the beginning of the year, and have had significant practice in this concept. However, many of the students in this class have exceptional learning abilities, and based on the results of a recent diagnostic test measuring their ability to accurately solve multiplication problems as listed above, we are revisiting teaching regrouping to reinforce skills.

Content:

§ Review place value: ones, tens, hundreds, and thousands

§ Review the math “cue words” that children should look for to know whether to add, subtract, or multiply.

§ Do a sample addition problem with regrouping on the board together.

Source: http://www.firn.edu/doe/curric/prek12/pdf/math3.pdf

Material:

“Safari” math worksheet with addition and subtraction word problems requiring regrouping.
“Factors” math worksheet with multiplication word problems requiring regrouping.
Place value boards for each group
Plastic baggies of counters for each group
Stickers

Procedure:

Hook: First I will tell the children a story about my friends the Johnson’s, that went on a safari last year for their summer vacation. During their trip, they ran into a lot of wildlife and had a lot of adventures. I will ask the children if they know what a safari is. I will tell them that I turned the story of the Johnson’s trip into a worksheet, and each day of their trip has been made into a word problem. If we solve all the problems that the Johnson’s ran into during their safari, we will be amazed at how much math the Johnson’s had to do on their trip, and they didn’t even know it!..

I will have passed out the place value boards (sample attached) and baggies of counters in advance.
Next, I will pass out the safari worksheet. I will point out the “math cue words” at the bottom of the page in the word bank, for them to use.
We will do the first problem together: “The first day, the Johnson’s photographed 89 zebras and 13 elephants. How many animals did they photograph in all?”
I will explain to the children that the first thing they are to do is search the problem for a “cue word” that will tell them what type of computation to use. (The cue word in this problem is AND.) They are to underline, or highlight the cue word.
Next, I will ask them what the 2 numbers are that they need to compute (89 and 13).
Next, I will explain that they have 3 sets of chips in their baggies: each set is a different color. They are to choose one color to use to represent hundreds, one for tens, and one for ones.
I will ask the following questions:

High End Questions: “In the first number, 89, do we see any numbers in the hundred’s place?

“What place, on our place value chart, is the first place we see a number in 89?”

“What number is left after the 8 (80)? Where does that number go?”

“You said that the first place value in 89 is the tens, so how many tens did we say we have in 89?”

“Take out your colored chips that you are going to use for your tens’ place.”

“How many will go in the ten’s place?” Place them there.

“Now, the number you said was left is 9, right? What place does the 9 go in? Take out the colored chips you are going to use for your ones’ place. How many chips (ones) are you going to put in your ones’ place?

Now we will work on the second number we are computing.

Low-Order Questions:

“What did we say we were going to do to compute this problem: add, subtract or multiply?”

“What is the second number in the problem?” (13)

“What is the first place value in 13?” (10)

“How many tens in 13?” (1)

“Where will you put your 10?”

“And how many one’s are left?” (3)

“use your colored chips for ones and place 3 ones in your one’s place.”

Next, I will start walking them through the computation using the chips they have placed on their boards.
How many ones can you have in the ones’ place before you have to start moving them to the tens’ place? (Answer 9)
How many ones do you have on your place value board right now? (12)
Now, if we look at the number 12, do we see any hundreds? (no), tens? (yes) How many? (1). So what are we going to do with those ones? (trade them for a ten and move it over to the tens place.) Now how many ones do we have? (2)
How many tens do we have on our boards now? 10. Ten tens is the same as how many hundreds? (1), so what are we going to do with our ten tens? (Trade them for one hundred and move it to the hundreds place.)
Now how many hundreds, tens and ones do we have? What number is that? So how many animals did they photograph in all? Any questions????
Then we look at the second worksheet, which is called “factors.” This worksheet specifically deals with word problems requiring multiplication with regrouping. I read them the directions and the sample problem, and we talk about what the 2 factors in the problem are, and the product. I reiterate, as we do the problem together that when we “carry” our ones over to the ten’s place, we leave them there for a moment, as we multiply the next 2 numbers, and then we ADD them to that number. We do NOT multiply again. We ADD them, even though the main problem is multiplying!!
Ok, now the children will begin working in pairs, as I work with the two children who need special accommodations.
[P.D.P. Human Development]: Prior to teaching this lesson, I have spoken with my D.T. about mathematics skills that can be diagnosed (ie: addition, subtraction, multiplication, and division) by using the EPA (Error Patterns Analysis) software available to me at UNF. We decided to diagnose the children’s aptitude with multiplying 2-digit by 1-digit numbers. A copy of the results of the diagnostic test administered is attached. The error pattern that 85% of the class results showed, was regrouping difficulty. In speaking with the teacher, we also suggested that possibly because the computation was multiplication, the children had forgotten that they could add when “carrying” numbers to the next place value. The other 15% (2 students) of the class are E.S.E. children, and had difficulty with basic multiplication facts as well as regrouping, according to the results of the test. For this reason, I decided to work individually with them. With these two children, I plan to only do the first worksheet today, dealing with addition and subtraction with regrouping, and will also have a second addition/subtraction worksheet (*remediation) for them to start with me in class, and take home and finish, and bring back to me the next day. I will work with them in 2 separate settings on multiplication with regrouping. I want them to have a strong foundation in regrouping with addition before we move on to the multiplication with regrouping.

Closure / Review:

§ After the groups have completed both sheets, we will go over a few problems and solutions from each sheet. I will draw the place value “boards” on the white board in the front of the room and choose children from each group to come forward and show us how they solved the problems.

§ I will answer any questions, and discuss whether anyone got any “different” solutions than the ones we have found.

§ During this time, we will clarify any misconceptions and correct any errors. I will also have a few spare worksheets, of the same I am giving to my 2 remedial students, that can be sent home with anyone else who seems to still be having difficulty, as we go over our papers.

§ Finally, all children will receive a metallic sticker for working hard.

Modifications: Two of the students are struggling with reading and math, and are the same two children who will be working in a group with me on this lesson. I will read the problems to them, slowly and clearly, and we will break the problem down in steps, so that I am sure that they understand what we are computing, and finding the “cue words” they should be looking for to tell them which computation to use. I will allow them to use their hundreds charts, and any other counters or manipulatives they wish to use, in addition to the counters I have supplied for them.

Remediation: [P.D.P. Human Development] : As explained above, I will be working to remediate two of the children in their regrouping mathematics skills and place value skills during this lesson. (Detailed explanation above.)

Accomodation: In this particular class, all of the children are able to compute 2 digit numbers in addition and subtraction, and need more work with regrouping. However, if there were a child that could not yet move on to the double-digits and regrouping, I would have a separate worksheet for them to work on, at the same table with me that the other 2 children are working on, only with basic multiplication ( and addition ) problems.

ESOL Accomodation: For any ESOL child in the class, our place value board would have pictures above each place, representing one, ten and hundred, and I would scaffold their group throughout the lesson, whenever they needed help. I would make sure that the partner they were working with was letting them do some of the solving, as well. Since all of the children in our class can count to ten in Spanish, and also know the Spanish word for 100, I would place those words next to the pictures on their boards, and ask the partner to help them by counting the ones in Spanish for them, and then let them see them trading ones for tens, tens for hundreds, as well.