Math Lesson for Beginning ABE Learners (Grade Equivalent 1-3)Written by Karen Gulya

Lesson Target: to multiply whole numbers

Materials: warm-up problems on a PowerPoint slide or on an overhead slide; math facts test

sheets; multiplication facts sheets for students who need them; 2-3 TI-30SX Multiview

calculators; large flattened beads to be used as math manipulatives; individual whiteboards with

markers and erasers; individual multiplication practice worksheets; authentic word problems

using multiplication of whole numbers on PowerPoint slide or on an overhead slide; word

problem practice sheets; scavenger hunt sheets and scavenger hunt items; homework worksheets

or textbook problems.

Lesson Plan:

1. Warm-up: addition involving re-grouping and checking of homework. (10 minutes –

Appendix A)

2. Individual flashcard practice (5 minutes – Appendix B)

3. Paired flashcard practice (5 minutes – Appendix B)

4. Math facts timed tests (5 minutes – Appendix B)

5. Whole group discussion and lesson with guided practice on all types of multiplication

except basic facts. (30 minutes – Appendix C)

Why do we need to memorize multiplication facts with quick recall

Where we will use multiplication in our lives

Multiplying by one digit with no re-grouping

Multiplying by one digit with re-grouping

Multiplying by two or more digits with no re-grouping

Multiplying by two or more digits with re-grouping

6. Class Break (10 minutes)

7. Individual practice worksheet on multiplication of whole numbers (15 minutes –

Appendix C)

8. Whole group quick lesson on reading word problems involving multiplication and

solving them. (5 minutes – Appendix D)

9. Collaborative group learning with word problems involving multiplication. (10 minutes

– Appendix D)

10. Presentation of one word problem from each group and its solution with any necessary

discussion. (10 minutes – Appendix D)

11. Multiplication Scavenger Hunt Game (10 minutes – Appendix E)

12. Hand out and go over homework assignments (5 minutes – Appendix E)

Appendix A

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Warm-up

This warm-up activity will review prior learning involving adding whole numbers with

re-grouping. The purpose of this review is to review place value, lining up whole numbers with

right-justification, and carrying digits over to the next column (re-grouping). The concepts being

reviewed will be utilized in much the same way when we multiply whole numbers. The learners

will write these problems and their work in their math notebooks, which will hopefully be graph

paper spiral notebooks. They will be encouraged to correct any errors in their work when we go

over the problems (and even write the problem with correct solutions if the work is beyond them

at this point.)

After we go over the warm-up, we will check the homework from last class. Students

will check their own work and be able to circle the problems they did not understand. This can

also serve as reinforcement that the students are progressing adequately.

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A second activity that will take place during warm-up time is that the students will sign-

in and turn in their homework from the last class they attended. A table will be set up near the

door of the classroom where students can pause to take care of these administrative activities.

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Appendix B

Math Facts

The next three learning activities involve memorizing math facts. Unless the standards

have changed, students moving on from the GE 1-3 class should know their addition,

subtraction, and multiplication facts 0-9. In addition to knowing these facts, they should be able

to recall the answers fairly quickly (roughly 2 second retrieval time per fact).

In my experience, the best way to learn these facts is consistently over time. Therefore,

the GE 1-3 class will always have a fifteen minute block devoted to them, and the learners will

be encouraged to practice with their flashcards between classes as well. Each group of facts will

be broken down as follows: 0-1, 2, 3, 4, 5, 6, 7, 8, 9, and mixed practice; and each math fact test

will contain 100 problems which will need to be completed with 90% or better accuracy in 3

minutes or less. Accommodations will be made for students with disabilities who may find

writing difficult or who may need other accommodations.

In order to pass each group (addition, subtraction, and multiplication), the learner will

progress through all the levels and end with the mixed practice test for each. The beginning

point for each student will be flexible, depending on the entry level of the student. The math

flashcards will be handled in much the same way as the Dolch Sight Word flashcards for

reading, where the learners start with one level and then trade it in for the next level when they

are ready to move on. If a student has successfully completed all levels but is not ready to

advance to the next class, he or she will rotate through the mixed practice to maintain his or her

skills.

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Knowing the addition and subtraction facts gives the learners a nice advantage by cutting

down the time needed to do a problem. In a pinch, however, the learners could just count to

figure out the answers. Knowing the multiplication facts is critical, though, and this one should

not be overlooked if we want our students to continue to be successful with their math. Knowing

the multiplication facts and being able to retrieve this knowledge quickly is a must because

fractions are completely based on multiplication and division, as is percent. If the learners do not

have a firm grasp on the multiplication facts, they will have difficulty understanding fractions

and percent, as well as some of the higher level concepts like exponents and roots.

The learners will be able to progress through the facts at their own paces. One of the

formative assessments kept will be a chart where success at each level of the math facts has been

noted with a date as to when the success occurred. The dates, combined with attendance history,

can help the student and I identify possible learning disabilities.

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Appendix C

Multiplication of Whole Numbers Lesson

The next part of the class deals with the actual lesson on multiplying whole numbers. To

begin this activity, the students will get some beads and their individual whiteboards, markers,

and erasers; and they will also keep their notebooks and writing utensils nearby. In addition,

learners who have not yet begun working on their multiplication facts will be given complete

multiplication charts (0 – 9) and students who have not yet completed the multiplication facts

will be given partially completed multiplication charts (6 – 9) to aid them with this learning.

Even though these students do not have sufficient knowledge of the math facts, they should still

be able to grasp the underlying principles of multiplication. In addition, the two or three students

who are most proficient with multiplication will be given TI-30SX Multiview Calculators for the

learning activity.

After all necessary materials have been distributed, we will take a few minutes

understand the concept of multiplication using manipulatives and to discuss the relevancy of this

lesson to the students’ lives. I will once again re-iterate why the learners have to learn the facts

with quick recall and then we will discuss where these students will use multiplication of whole

numbers in their lives. Some examples that our class may generate include purchasing multiple

quantities of an item at a store, finding how many square feet of carpet to purchase in a

rectangular room, figuring out gross pay based on hourly wage, or comparing different service

contracts with different base charges and hourly rates to find the better deal. If there are any

relevant multiplication examples in the newspaper or a current magazine, I will show them to the

class as well.

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With the basic facts already addressed, we will move on to the other levels of whole

number multiplication indicated on the TABE profiles. These levels include one digit

multiplication with no re-grouping, one digit multiplication with re-grouping, two or more digit

multiplication with no re-grouping, or two or more digit multiplication with re-grouping. We will

begin with one digit, no-regrouping problems. I will demonstrate the common way to do this

with several examples. Each time, I will talk about what I am doing while I am showing it on the

board. After I work several problems, we will stop so the students can try one or two on their

own. They will record their worked problems on their white boards so I can check them for

accuracy. Next, we will look at one digit multiplication with re-grouping. With re-grouping, the

students may wonder if they need to add the re-grouped digit or if they should multiply it. This

may come from the rule for addition, where it is added just like the addition problem itself. To

solve this problem, we will have the students with calculators work the first problem we do on a

calculator so the class can figure out if we are adding or multiplying. As we look at the correct

answer and compare it with the problem we are doing, the class will discover that we need to add

the re-grouped digit after we multiply the next two numbers. After this issue is resolved, we will

complete the rest of the lesson in the same pattern, with me working a few problems and then

having the students try several of the same type of problems on their whiteboards. When we

move to two or more digit multiplication, the learners will need to see how place value works in

this. Once again, the calculators can be used to help understand how this works.

After the break, the students will work individually on a multiplication worksheet. There

will be four levels to these worksheets depending on skill levels, and the worksheets will be

color coded for ease of distribution and evaluation. The pink worksheets will be for students

who are not yet working on their multiplication facts and will contain mostly one digit

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multiplication with no-regrouping but will also have a few one digit with re-grouping problems.

The yellow worksheets will be for students who are at the early levels of the multiplication facts

(0 – 5). These worksheets will have an equal amount of one digit multiplication problems, but

they will also have some two-digit multiplication problems of both kinds. The green worksheets

will be for the students who are learning the final levels of multiplication facts (6 – mixed).

These worksheets will have an equal amount of each type of multiplication learned, but they will

also have one or two problems that have more than two digit multiplication. The blue

worksheets will be for those students who have completed their multiplication facts. These

worksheets will have one multiplication problem of each type as well as one three digit

multiplication problem. In addition, these students will have enrichment problems of the

following type:

Fact families. Example: Give the multiplication/division fact family for 2, 6, and 12.

Answer: 2 x 6 = 12, 6 x 2 = 12, 12 ÷ 2 = 6, 12 ÷ 6 = 2. Note: this skill will aid the

students when they learn division of whole numbers.

Factor pairs. Example: Find the four ways we can multiply two whole numbers to get

24. Answer: 1 x 24, 2 x 12, 3 x 8, 4 x 6. Note: this skill will aid the students with many

other subsequent skills, like changing fractions or factoring polynomials.

Beginning order of operations. Example: In the order of operations, we multiply before

we add or subtract, even if the multiplication comes second. So, if we have 3 x 4 – 2, this

is 12 – 2 which is 10. Also, if we have 5 + 3 x 7, we have 5 + 21 which is 26. Using this

procedure, find the value of the following problems. 14 – 2 x 3. Answer: 14 – 2 x 3 is 14

– 6 which is 8. Note: The students will be given several of these problems. Order of

operations is one of the most essential math skills and also one of the hardest for students

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to master, so early and continuing practice as the problems become more complicated is a

plus.

After the students finish their individual work, they will be able to check their answers

with me so we can assess if the learning is taking place. In addition, I will walk around

during this activity to catch and correct any errors I see.

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Appendix D

Authentic Word Problems

After the students complete their individual worksheets, we will look at authentic word

problems involving multiplication of whole numbers as a class. Just like with math facts,

authentic word problems will be a part of every class. It is important for students to learn how to

read word problems of all kinds and solve them. The Adult Basic Education students who began

as English Language Learners may need to use a bilingual dictionary here to understand

vocabulary. If any of those students do not understand a word, we will stop to define it and will

allow them to write the word and its definition in their notebooks.

The next activity involves the students breaking up into ability groups and working

together on three authentic word problems utilizing multiplication of whole numbers. There will

be four different groups, although some of those groups may need to be split up so that each

group has about three to four students in it. Just like with the individual problems, our class will

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have a beginning level (pink), an elementary level (yellow), an intermediate level (green), and an

advanced level (blue). After the students complete their word problems by hand, they will check

their answers by using the TI-30XS Multiview calculator. Each student in the class will need to

check at least one answer so they all will get practice using this calculator. This skill will help to

prepare them for the GED test. Each group will choose one problem to present, and they will

write their solution on an overhead sheet or on a large piece of paper. When their turn comes,

someone will read the problem and then the group will discuss how they solved the problem.

We will discuss the problems as needed or desired. This will be another opportunity for me to

use formative assessment, both for the process of the collaborative learning and for the finished

product.

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Appendix E

Scavenger Hunt Game and Homework

The last two activities of the class involve a scavenger hunt game and homework

assignments with instructions. The Multiplication Scavenger Hunt Game can be played

individually or in pairs and it involves moving around the room to find scavenger hunt problems

that to with the answers on the scavenger hunt sheet. It will be a multi-level game again, using

the same four colors we have used throughout the class. Each student will receive a colored

sheet of paper with ten answers on it. Here is an example of the pink sheet:

Multiplication Scavenger Hunt Game Name(s):

18 matches clue # __________ 15 matches clue # __________

49 matches clue # __________ 54 matches clue # __________

0 matches clue # __________ 28 matches clue # __________

16 matches clue # __________ 6 matches clue # __________

56 matches clue # __________ 40 matches clue # __________

Here is an example of the multi-level clue sheets that will be placed around the room:

Clue # 5

9 x 6 =

12 x 4 =

59 x 7 =

15 + 3 x 8 =

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Note: The pink and yellow groups will be able to use complete multiplication charts and the

green group will be able to use partially complete multiplication charts. When the individuals or

pairs complete the game, they will turn in their game sheets and sit back down for the homework

discussion. I will check the answers either in class or after so I can assess if the students are on

track with their learning.

When everyone is done with the game, we will discuss homework for the day. I will

remind the students to study their facts flashcards before the next class, but each student will also

either be given a color coded worksheet or assigned problems from a textbook or workbook.

Before we leave for the day, I will emphasize again why it is important to do some outside self-

study for the class.

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