## Implementaton

**Angie the Iditarod Musher - Pre-Test Analysis**

Complete the task. Score the test. Look at the rubric. How does this task assess the big ideas about understanding the operation of multiplication and division?

*Several students in this class have a basic grasp on multiplication. Creating a division problem from a word problem none of the students were able to complete.*

**Look at student work on Question 1. 23 students took the pre-test**

• How many students understood that this was a multiplication problem?

*14 students*

• How many multiplied each by 16 based on Angie starting with 16 dogs?

*One student*

What other types of errors did you notice?

•

*2 students - addition - adding all dogs four times (students F & J)*

•

*Student B - subtracted number of dogs.*

•

*Mathematical errors, adding*

•

*4 students - no attempt*

•

*Student X - counted first dog as 4, second stop - 2X4=8; third stop 3X4 then subtracted 3-12=9 dogs*

How often do students get opportunities to work with multiplication in context?

*In talking with the classroom teacher she said they do it daily.*

How does context help them develop an understanding of the operation of multiplication?

*She said they understand the operation of multiplication, especially when they realize how much faster it is than adding groups over and over again.*

**Look at student work on Question 2.**

• How many students understood that this was a multiplication problem?

*13 students*

• How many students could solve this problem correctly?

*2 students*

• What strategies did students use to solve the problem?

*19 X 60 = 1,140. Knowing that there were 19 checkpoints each with 60 pounds of food and gear multiplication mistakes were the largest factor in incorrect answers.*

*60*

__X 19__

**Look at student work on Question 3.**

• How many students understood that this was a division problem?

*None*

• How many students could solve this problem correctly?

*None*

• What strategies did students use to solve the problem?

*There was a lot of guessing*

• How many students used remainders?

*None*

• How many students understood they could use decimals to show results?

*None*

*This group of students were unable to determine that there these were division problems*.

**Look at student work on Question 4.**

• How many students understood that this was a division problem?

*None*

• How many students could solve this problem correctly?

*None*

• What strategies did students use to solve the problem?

•

*Guessing*

•

*Multiply & divide*

**: To further assess the ability of these students to multiply and divide, I created and administered a pre-test that had all the problems written in mathematical numerical form not as word problems. Pre-Test 2.**

*Note***Angie the Iditarod Musher - Pre-Test2**

**Questions were revised to numerical form and given to class to assess multiplication and division problems.**

Complete the task. How does this task assess the big ideas about understanding the operation of multiplication and division?

**Look at student work on Question 1.**

• How many students understood that this was a multiplication problem?

*17 students, five with one error.*

What types of errors did you notice?

·

*Student B – didn’t finish second problem*

·

*Student D – added numbers*

·

*Student E – transposed numbers*

·

*Students M & I – multiplication errors*

**Look at student work on Question 2.**

• How many students could solve this problem correctly?

*Three students that was an increase of one student able to complete.*

• What strategies did students use to solve the problem?

*Work not shown so unsure of strategies used.*

• What errors were made?

*Four students did not carry the zero down.*

*The remainder of the students were unable able to solve the problem.*

*There were struggles with multiplying with zero. Many were not sure what to do with the zero.*

*1 9*

__X 6 0__*One student multiplied 6 X 9 and got 54 then carried the zero down getting 540.*

*Students I & J – multiplied 6 X 9, added 10 in 19 to the 54 making 64, carried the zero resulting in 640.*

*Student M – same as I & J except did not carry the zero resulting in 64.*

*Eight students multiplied 60 by one for their answer of 60.*

**Look at student work on Question 3.**

• How many students could solve this problem correctly?

*Two students were able to solve the first problem. 998 / 9 but were unable to solve the other two division problems.*

• What strategies did students use to solve the problem?

*Just wrote answers*.

• How many students used remainders?

*None*

**Look at student work on Question 4.**

• How many students could solve this problem correctly?

*No student was able to solve this problem.*

• What strategies did students use to solve the problem?

*Just wrote an answer. Guessing*.

**Comments:**

I entered the classroom on the day the class was working on the original pre-test and the classroom teacher was working on the test with the students. She had the students reading through the problems as a class and highlighting key words. Then the students would solve the problems on their own. When working on the back side with division she told them to guess if they didn’t know.

After reviewing the results of the revised pre-test it became apparent that these students have little to no experience with division problems. I was able to review with the class how to solve these problems. This was done on a large paper they were able to take back to their classroom as an example.

Strategies in place to help students gain skills in multiplication and division:

· Daily multiplication practice with five-minute timings for facts 1-12

· Students record scores and look at changes in results.

· Daily division practice with five-minute timings.

· Students record scores and look at changes in results.

· Daily class lesson and practice over multiplication and division skills.

· Practice multiplication and division games on web. Students practice by playing a game four times. They need to choose at least two times at a level they are having difficulty with and they can choose two at the level of their choosing.

· Practice other multiplication activities through foldables and other math games.

Classroom teacher is collecting and submitting completed forms to me for evaluation.

· Multiplication timings – 60 problems – facts 1-12.

· Division timings – 17 problems – problems that align to test.

**LESSON 28 – One Fact Families -- Four Facts**

22 students - 18 - 12 correct; 2 - 11 correct; 1 - 10 correct; 1 - 9 correct

a) 9 X 3 = 27

b) 3 X 9 = 27

c) 6 X 4 = 24

d) 4 X 6 = 24 incorrect answer: 44

e) 7 X 8 = 56

f) 8 X 7 = 56 incorrect answer: 24

g) 5 X 8 = 40

h) 8 x 5 = 40 incorrect answer: 90

i) 10 X 10 = 100 incorrect answers: 20 student added 10+10, 10 student wrote down 10

j) 10 X 8 = 80

k) 11 X 9 = 99

l) 12 X 12 = 144 incorrect answer: 132

**LESSON 44 – Multiplying a two-digit number by a one-digit number.**

22 students – 12 – 6 correct; 7 – 5 correct; 1 – 4 correct; 2 – 1 correct

a) 31 X 2 = 62

b) 31 X 4 = 124

c) 42 X 4 = 168

d) 30 X 2 = 60

e) 30 X 4 = 120

f) 24 X 0 = 0

**LESSON 48 – Multiplying two digit numbers**

23 students completed - 11 - 7 correct; 8 - 6 correct; 2 - 5 correct;

2 - 1 correct

2.Student Y - looked like this student wrote down random numbers a-f

3.Student E - multiplication errors

a) 16 X 4 = 64

b) 24 X 3 = 72

c) $45 X 6 = $270

d) 53 X 7 = 371

e) 35 X 8 = 280

f) 64 X 9 = 576

g) $14 X 3 = $42

**LESSON 58 – Multiplying Three Digit Numbers**

24 students completed - 10 - 4 correct; 7 - 3 correct; 6 - 2 correct;

1 - 0 correct

4.Student Y - 0 correct, appeared to have written random numbers.

Students E, N, & M - multiplication errors

a) 234 X 3 = 702

b) $340 X 4 = $1360

c) $4.25 X 5 = $21.25

d) DO NOT DO THIS ONE

e) $2.47 X 4 = $9.98

**LESSON 49 – Word Problems About Equal Groups**

23 students completed assignment - 16 - 4 correct; 4 - 3 correct; 2 - 2 correct; 1 - 1 correct

a) 6 X 8 = 48 Student U - multiplication error

b) 9 X 6 = 54 Student P - did not finish

c) 12 X 4 = 48 Student P - set up problem incorrectly. Multiplied 4 X 4 = 16

d) 27 X 2 = 54 OR 25 X 2 = 50

Student U - 13 divided 27 X 2

Students B & H - multiplication error 27 X 2 = 64

Student O

5.multiplied 6 birds X 6 flocks = 48 then multiplied by 6 flocks 288

6.multiplied 6 people X 9 cars = 57 then multiplied by 9 cars with a total of 486

7.multiplied 12 muffins X 4 dozens = 36

Maintaining Concepts & Skills

5. $6.00 42 ÷ 7 = 6

6. 54 9 X 6 = 54

7. 2 1/2 5 ÷ 2 =2.5

8. 1/2 show an example of why 1/2 is larger than 1/346

9. Continue patterns: triangle, circle, circle; a,c,e; 32, 37, 42

10. Show 1/3 in the rectangle shape

11. Draw lines to correct story problem & write answer.

a. 108 18 X 6

b. 24 18 + 6

c. 12 18 - 6

d. 3 18 ÷ 3

9) Answers will vary

10) Answers will vary

**LESSON 46 – Relating Multiplication and Division**

23 Students completed assignment – 15 – 8 correct; 7 – 7 correct; 1 – 6 correct; 1 – 4 correct; 1 – 1 correct; 1 – 0 correct

a) 12 / 2 = 6

b) 21 / 3 = 7

c) 20 / 4 = 5

d) 30 / 5 = 6

e) 42/ 6 = 7

f) 28 / 7 = 4

g) 48 / 8 = 6

h) 36 / 9 = 4

4 correct: Student F – 21 / 3 = 7r.1; 20 / 4 = 4; 30 / 5 = 10; 42 / 6 = 7 r.1 – did not show work

1 correct: Student E – 12 / 2 = 24 multiplied to get answer; did not complete remainder of page.

0 correct: Student Y – did not attempt any problems.

**LESSON 47 – Relating Multiplication and Division**

17 students completed assignment – 9 – 8 correct; 2 – 7 correct; 2 – 6 correct; 4 – 4 correct; 1 – 0 correct

a) 49 / 7 = 7

b) 45 / 9 = 5

c) 40 / 8 = 5

d) 6 / 6 = 1

e) 32 / 8 = 4

f) 27 / 3 = 9

Use digits and three division symbols to show:

g) twenty-seven divided by nine 9)27 ; 27 ÷ 9; 27 / 9

h) twenty-eight divided by seven 7)28 ; 28 ÷ 7; 28 / 7

4 correct

Student G – c. 40 / 8 = 4; f. 23 / 7 = 8 did not complete g & h

Student M – d. 6/6 = 36 multiplied instead of divide; e. 32 / 8 = 5; g & h did not complete

Student P – a. 49 / 7 = 4; f. 27 / 3 = 7; g. did not complete

0 correct

Student L – no attempt

**LESSON 64 – Use Short Division**

21 students complete – 14 – 7 correct; 4 – 6 correct; 1 – 5 correct; 2 – 4 correct

a) 51 / 3 = 17

b) 52 / 4 = 13

c) 75 / 5 = 15

d) 72 / 3 = 24

e) 96 / 4 = 24

f) 74 / 2 = 37

5 correct

Student Y – a. 51 / 3 = 12 on side wrote 17 X 3 = 51; g. n=50

4 correct

Student G – b. 52 / 4 = 52; c. 75 / 5 = 75; d. 72 / 3 = 26

Student U – b. 52 / 4 = 1; 74 / 2 = 10

**LESSON 65 – Did not do this assignment**

a) 144 / 3 = 48

b) 144 / 4 = 36

c) 144 / 6 = 24

d) 225 / 5 = 45

e) 455 / 7 = 65

f) 200 / 8 = 25

**LESSON 68 - did not do this assignment**

a) 134 / 3 = 44 R 2

b) 240 / 7 = 34 R 2

c) 88 / 5 = 17 R 3

d) 259 / 8 = 32 R 3

e) 95 / 4 = 23 R 3

f) 325 / 6 = 54 R 1

**Angie the Iditarod Musher - Post-Test – 19 students took the test**

Complete the task. Look at the rubric. How does this task assess the big ideas about understanding the operation of multiplication and division after three weeks of practice?

**Look at student work on Question 1.**

• How many of my students understood that this was a multiplication problem?

*17 students an increase of three students from the pre-test.*

• How many multiplied each by 16 based on Angie starting with 16 dogs?

*Two students.*

• What other types of errors did you notice?

*Subtraction and multiplication errors, 16 – 3 = 13, the common mistake was 16 – 3 = 12.*

**Look at student work on Question 2.**

• How many of my students understood that this was a multiplication problem?

*13 students, no change from pre-test*

• How many students could solve this problem correctly?

*5 students an increase of three students.*

• What strategies did students use to solve the problem?

•

*Drawing arrows to show which direction to multiply, then circling the number multiplying by.*

•

*Multiply 19 X 6 then adding zero to the end.*

**Look at student work on Question 3.**

• How many of my students understood that this was a division problem?

*Seven students an increase of seven students from the pre-test.*

• How many students could solve this problem correctly?

*Three students*

• What strategies did students use to solve the problem?

*Unclear as they wrote answers without showing work.*

• How many students used remainders?

*Three students*

• How many students understood they could use decimals to show results?

*None*

**Look at student work on Question 4.**

• How many of my students understood that this was a division problem?

*Five students an increase of five students from the pre-test.*

• How many students could solve this problem correctly?

*One student*

• What strategies did students use to solve the problem?

*Most did not show any work*.

Based on teacher observation, this is what fourth graders know and are able to do

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Areas of difficulty for fourth graders:

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Strategies used by successful students:

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*:*·

*These students are able to complete basic one-digit by two-digit multiplication problems.*·

*This group of fourth grade students does not understand division.*·

*This group of students some of them know how to show their work while others do not show any work.*Areas of difficulty for fourth graders:

·

*Multiplying two-digit by two-digit numbers with a zero at the end.*·

*Division.*Strategies used by successful students:

·

*Multiplying by one digit and adding the zero to the end.*·

*Using arrows to show direction and circling number multiplying by.*·

*Showing their work*