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Math Lesson for Beginning ABE Learners (Grade Equivalent 1-3)Written by Karen GulyaLesson Target: to multiply whole numbersMaterials: 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 recallWhere we will use multiplication in our livesMultiplying by one digit with no re-groupingMultiplying by one digit with re-groupingMultiplying by two or more digits with no re-groupingMultiplying 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 AWarm-upThis 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.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.Appendix BMath FactsThe 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.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.Appendix CMultiplication of Whole Numbers LessonThe 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.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 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 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.Appendix DAuthentic Word ProblemsAfter 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 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.Appendix EScavenger Hunt Game and HomeworkThe 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 GameName(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 # 59 x 6 =12 x 4 =59 x 7 =15 + 3 x 8 =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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