Math Instructors Notes with Math Supplement.Pdf
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Instructor Notes Lesson: Math using common manipulatives in the ABE & GED classroom. Why use manipulatives to teach math? There is a link between seeing math and understanding math. Building with manipulatives incorporates the visual, kinesthetic, figurative, and tactile; Saying taps into the auditory and semantic; Writing teaches the symbolism of math and bridges the concrete and the abstract. The result? When a student sees the numbers on paper (abstract) he or she is able to visualize the concept. Objectives: In this lesson, the participants will: Use common items (many are provided in this kit) in an effort to give students a concrete example of math principles. Utilize various critical thinking skills related to learning about math. Understand the importance of good math skills in everyday life as well as in workplace settings. Reduce stress often associated with learning math concepts by making the lessons interactive and fun. Subjects: math, workplace skills, reading, writing, social studies, and critical thinking Procedure: 1. Humans – the always accessible manipulative! Use the students in class to make bar graphs, walk number lines, or demonstrate commutative and associative properties. Students will remember these concepts when they have fun and move around. 2. Fractions can be difficult to comprehend so some ideas are included in this kit. Use the egg cartons and measuring cups to start the fractions lesson. If you really need a reinforcement activity, splurge on some candy bars! Four sets of laminated make-your-own fraction circles are also included for students to use. 3. Popsicle sticks are a great, inexpensive way to teach place value, carrying, and borrowing. A game with Popsicle sticks is included as well. 4. Building a brick wall uses critical problem solving skills as well as math. Enjoy allowing your students to use dominoes to create a wall and to think strategically. 5. ―Make Fifteen‖ and ―24‖ are two games using number cubes to reinforce basic number facts and order of operations. This game is a real winner because it can be altered slightly to make it easier or more difficult depending on the needs of your students. 6. Convincing students to focus on math facts can be difficult. Use the ―Fact Family Houses‖ to reinforce addition or multiplication facts. This activity works especially well when an independent learning activity is needed. 7. As a hands-on activity to help students visualize what is happening in the ―Fact Family Houses‖, try the ―Math on a Plate‖ activity. 8. Even more reinforcement and ideas for integer rules can be found on the ―Developing Integer Rules‖ worksheet. Some students will enjoy learning a short history on the subject. Use the chips to let students have a hands-on approach to this lesson. 9. Positive and negative numbers were introduced in the first activity with the number line. If your students are ready to move on and practice their knowledge in this area, use the deck of cards and instructions included in activity # 9 to have fun with this concept that is sometimes confusing. 10. Pentominoes are shapes that use five square blocks joined edge to edge to form various combinations. Pentominoes allow the introduction of important mathematical concepts and skills in a fun way. Some of those concepts include: measurement, geometry, and multiples. 11. Probability can be a difficult, abstract notion. Use the probability lesson and let students actually try it out to let the idea make some sense. It will also give practice with graphing. 12. The ―Math Readiness Activities‖ sheet includes ideas for those working with ABE students. All of the ideas are concrete examples to illustrate basic math concepts. 13. A list of more advanced math ideas is included for those teaching GED students. These are all practical life or work skills activities that utilize these specific math applications. Activity # 1 (Page 1 of 1) Tactile Math – Using Humans – the Always Accessible Manipulative Use humans for bar graphing. Have the students physically move and make rows for: gender, hair color, favorite subject, number of children, or any other topic. Ask students to actually walk through a number line of positive and negative integers. Place the numbers on the floor on pieces of paper writing positive in black and negative in red (accounting). Let students walk up and down the number line to act out addition or subtraction problems using positive and negative numbers. Demonstrate commutative and associative properties in math using humans. Have several students go to the front of the room and then switch places or switch groupings to illustrate these properties. For example: addition is associative if you can group numbers in any way without changing the answer. It doesn’t matter how you combine them, the answer will always be the same. Addition and multiplication are both associative. Use your human manipulatives to show the following: 1+(2+3)=(1+2)+3 1+(5)=(3)+3 6=6 An operative is commutative if you can change the order of the numbers involved without changing the result. Addition and multiplication are both commutative. Subtraction is not commutative: 2-1 is not equal to 1-2. Activity # 2 (Page 1 of 1) Fractions 1. Use different color egg cartons to demonstrate fractions. Use 4 egg cartons to find one-half, one-third, and one-fourth of twelve. Show 2 cartons, one white and one blue. Have the student cut the blue carton in 1/2. Place the 2 equal parts (halves) in a white carton. With student watching, remove one part and ask, “How much of a whole carton is this?” (1/2) Place the 2 halves back into the carton and ask, “How many eggs will a carton hold?” How many eggs will ½ of a carton hold? How much is ½ of 12? Write the following and ask the student to complete: ½ of 12 = ____ Display a pink carton and cut it in thirds. Do the same as above and then offer this equation: 1/3 of 12 = ____ Do the same with a yellow egg carton to show fourths. ¼ of 12 = _____ 2. Fill a ½-cup measuring cup and empty it into a 1-cup measuring cup. Talk with the student about how much is filled. Repeat and talk about how many ½-cup measuring cups it takes to fill the 1-cup. 3. Use Kit-Kat or Hershey bars for this activity. Discuss how many parts make up a whole candy bar. Break off pieces and discuss what fraction of the candy is broken off and what fraction is remaining. Activity # 3 (Page 1 of 1) Popsicle Stick Activities 1. Use Popsicle sticks bundled in sets of ten and some individual sticks. Write a number from 10-99 and ask the students to model the number using the sticks. 2. Show nine Popsicle stick bundles of ten sticks and nine ones. Ask the student to count the number of 10s and ones and record the number. Place one more stick with the 9 ones and ask how many sticks there are. Observe to see if the student bundles the 10 ones to make 1 ten. If not, ask: “What do we do when we have 10 ones?” (make a ten). Then ask how many 10s do we have now? (10) We have 10 tens. What do we do when we have 10? (We bundle them) So we will bundle the 10 tens and we have? (100) One bundle of tens is 100. Make certain to have rubber bands on the table for this activity. 3. Follow up by having the student do problems to practice carrying/borrowing using the Popsicle sticks. NIM Place 20 Popsicle sticks in a row. Each of 2 players will alternately pick up 1, 2, or 3 Popsicle sticks until they are all picked up. The player who picks up the last Popsicle stick wins the game. Develop a strategy!! Activity # 5 (Page 1 of 2) Make Fifteen Game for 2 players that provides practice for building and solving equations. In turn, each player throws 3 dice and uses the number showing on top to form equations naming numbers 1 to 15 in that order. The number on each die must be used once, and only once, in an equation. When a player is unable to form an equation that names the next number, the play passes to the next player. Example: First player throws 2, 4, and 6 and forms the equations below. (2 +4) ÷ 6 = 1 (2 x 4) – 6 = 2 (2 x 6) ÷ 4 = 3 (6 + 2) – 4 = 4 (6 + 4) ÷ 2 = 5 The player is unable to name 6, so the dice are passed to the next player. Player number one will begin naming numbers at 6 on the next round of play. The first player to name all numbers to 15 is the winner; however, if both players reach 15 in the same round, extend the goal to 21. Activity # 4 (Page 1 of 7) Building a Brick Wall As you consider the different ways to make a wall with a certain number of bricks, look for a pattern or a system to predict what will happen with any number of bricks. Brick wall made with one brick Since the wall must be 2 units high, there is only one possibility. Brick wall made with two bricks There are two possibilities if the wall can be made with 2 bricks. A height of 2 units can be made either using two horizontal bricks or two vertical bricks. Brick wall made with three bricks There are three possibilities if the wall can be made with 3 bricks. Now the Activity # 4 (Page 2 of 7) pattern begins.