Objectives To review and provide practice with the lattice method for multiplication.

Transcription

1 Objectives To review and provide practice with the lattice method for multiplication. Teaching the Lesson materials Key Activities Students review the lattice method for multiplication with - and -digit multipliers. They practice using this multiplication algorithm. Key Concepts and Skills Add single-digit numbers. [Operations and Computation Goal ] Solve basic multiplication facts. [Operations and Computation Goal ] Use the lattice method to solve multiplication problems with - and -digit multipliers. [Operations and Computation Goal ] Key Vocabulary lattice lattice method (for multiplication) Math Journal, p. Study Link Teaching Aid Master (Math Masters, p. ) Transparency (Math Masters, p. ; optional) º, / Fact Triangles index cards (optional) dictionary (optional) Ongoing Learning & Practice materials Students play Multiplication Top-It to practice basic multiplication facts. Students practice and maintain skills through Math Boxes and Study Link activities. Ongoing Assessment: Recognizing Student Achievement Use Math Masters, page. [Operations and Computation Goal ] Differentiation Options Math Journal, p. Student Reference Book, p. Study Link Master (Math Masters, p. ) Game Master (Math Masters, p. ) per partnership: each of number cards (from the Everything Math Deck, if available) materials READINESS Students explore patterns in the Fact Lattice. ENRICHMENT Students investigate Napier s Rods, a seventeenth-century multiplication method. ELL SUPPORT Students make posters to display multiplication algorithms. Teaching Masters (Math Masters, pp. ) Teaching Aid Master (Math Masters, p. ) Multiplication/Division Facts Table scissors; chart paper colored pencils and markers Technology Assessment Management System Math Masters, page See the itlg. Lesson

2 Getting Started Mental Math and Reflexes Students use their Multiplication/Division Fact Triangles to practice the facts in the Try Again pile. They transfer appropriate triangles to the OK pile and color the OK facts in the table on journal page, fasten their new piles with paper clips, and store them. Math Message What do you think the missing digits are Study Link Follow-Up Ask volunteers to write solutions on the board. Students indicate thumbs-up if they agree with the solution. Challenge students to find a way to solve mentally. Sample answer: Multiply by. The answer is half of this product, or,. Teaching the Lesson Math Message Follow-Up WHOLE-CLASS DISCUSSION Students share answers. The pair of digits in each cell names the product of two digits outside the lattice one above the cell of the lattice and the other to the right of the cell of the lattice. Thus, the missing digits in the first lattice form the product of and (). The missing digits in the second lattice form the product of and (). Teaching Aid Master Lattice Multiplication Computation Grids Tell students that in this lesson they will review the lattice method for multiplication. Introduced in Third Grade Everyday Mathematics, this algorithm relies almost entirely on the recall of basic multiplication facts. If students do not yet have a favorite multiplication algorithm, the lattice method is a good one to suggest. Demonstrating the Lattice Method for -Digit Multipliers (Math Masters, p. ) WHOLE-CLASS Math Masters, p. Demonstrate the lattice method using the following examples. Students should show their work using the computation grids on Math Masters, page. Unit Big Numbers, Estimation, and Computation

3 Example: Use the lattice method to multiply. A lattice ususally consists of two or more cells with diagonals. Write and above the cells of the lattice. Write on the right side. Multiply. Write the answer as shown. NOTE The lattice method is a very efficient algorithm, no matter how many digits are in the factors. For problems with - and -digit multipliers, the lattice method takes about the same amount of time as the partial-products algorithm or the traditional multiplication algorithm. For problems with three or more digits in the factors, the lattice method is much faster and much more likely to yield a correct answer. Multiply. Write the answer as shown. Starting at the right, add the numbers inside the lattice along each diagonal. Read the answer starting on the left side of the lattice and continuing across the bottom.. Adjusting the Activity Have students look up the term lattice in the dictionary and think of places where they might see lattices, such as a gate, a window, or a patio. Have students discuss why this word is used to describe the multiplication algorithm. ELL The sum of the numbers along a diagonal may be a -digit number. When this happens, write the ones digit in the answer space and the tens digit at the top of the next diagonal. AUDITORY KINESTHETIC TACTILE VISUAL Example: Use the lattice method to multiply. The sum of the numbers in the middle diagonal is. Write in the answer space and at the top of the next diagonal. Then add the numbers in that diagonal. Read the answer:. Practicing the Lattice Method for -Digit Multipliers (Math Journal, p. ) Students complete Problems independently. Partners check each other s work. Date LESSON Time Lattice Multiplication Use the lattice method to find the products.,..., Student Page..,..,.., Math Journal, p. Lesson

4 Demonstrating the Lattice Method for -Digit Multipliers (Math Masters, p. ) WHOLE-CLASS Adjusting the Activity Consider these suggestions for students who need help with the lattice method. Demonstrate the lattice method for -digit multipliers using the example below. Use a transparency of Math Masters, page or copy the lattices onto the board. Students should show their work on the lattice grids. Example: Use the lattice method to multiply. Use an index card to mark the place when adding along each diagonal. Write above the lattice. Write on the right side. Cross out the factors of the problem before adding so those numbers are not accidentally added with the numbers within the grid. Multiply. Then multiply. Multiply. Then multiply. Write the answers as shown. Extend the diagonal lines through the lattice as shown. AUDITORY KINESTHETIC TACTILE VISUAL Starting at the right, add the numbers inside the lattice along each diagonal. The sum of the numbers along the second diagonal is. Write in the answer space and at the top of the next diagonal. Read the answer:. The lattice method of multiplication may seem like a trick. It is not, of course, and place value is evident within the lattice. thousands tens hundreds ones Practicing the Lattice Method with -Digit Multipliers (Math Journal, p. ) Students complete Problems independently. Partners check each other s work. Unit Big Numbers, Estimation, and Computation

5 Ongoing Learning & Practice Playing Multiplication Top-It (Student Reference Book, p. ; Math Masters, p. ) Students play Multiplication Top-It to develop automaticity with multiplication facts. See Lesson - for additional information. Ongoing Assessment: Recognizing Student Achievement Math Masters Page Use Math Masters, page to assess students automaticity with basic multiplication facts. Students are making adequate progress if they can name the product of the factors generated by the two cards. Some students may play a variation of the game and demonstrate the ability to mentally solve -digit by -digit multiplication problems. [Operations and Computation Goal ] Date LESSON Math Boxes Time. This is a circle graph of what Seema does on a typical day. a. What does she spend the least amount of time doing Soccer practice b. She spends about the same amount of time at school and doing homework as she does sleeping. c. About what fraction of the day does she spend doing chores, eating, and relaxing. Estimate the sum. Write a number model to show how you estimated. a., Number model: Sample answers:,, b.,,. Write each number using digits. a. twenty-six million, nineteen thousand, eighteen,, b. three hundred fifty-two million, eight hundred thousand, two hundred,, Student Page Number model:,,, Math Journal, p.. Complete. Rule:. Look at the grid below. a. In which column is the triangle located B b. In which row is the triangle located Seema s -Hour Day in sleep chores eating relaxing soccer practice school and homework out,,,,, A B C Math Boxes (Math Journal, p. ) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson -. The skill in Problem previews Unit content. Study Link (Math Masters, p. ) INDEPENDENT Home Connection Students use the lattice method to solve multiplication problems. Students are asked to solve Problem by using both the lattice method and the partial-products method. Study Link Master STUDY LINK Lattice Multiplication Use the lattice method to find the following products.,,,. º. º. º. º. º. º. Use the lattice method and the partial-products method to find the product. º, Practice Math Masters, p. Lesson

6 LESSON Teaching Master Fact Lattice Patterns. Look at a Multiplication/Division Facts Table. Find the shaded diagonal showing the doubles facts.. Find the doubles facts on the Fact Lattice on Math Masters, page. Shade the doubles facts lightly with a colored pencil.. Compare the two fact tables. Sample answers: a. List things the tables have in common. Both show multiplication and division facts for the factors ; both are a square shape; both show the square products along a diagonal; both show the factors along the top and one side. Differentiation Options READINESS Exploring Fact Lattice Patterns (Math Masters, pp. and ) Min b. List things that are different on the Fact Lattice. Lists factors in reverse; shows factors from, not ; shows zeros in s place for numbers ; has diagonal lines between the s and s place for products; shows factors on the right; and does not shade square products.. Describe patterns that you see on the Fact Lattice. Sample answers: a. Not counting zero as a factor, in the s columns and rows, the digit of the s place goes up by while the digit for the s place goes down by. b. The bottom (s) digits in the s column and rows repeat a pattern on,,,,.. Which of your Fact Lattice patterns is also in the Multiplication/Division Facts Table in your journal Sample answer: The s pattern is in the fact table. Math Masters, p. To explore the use of the lattice grid for multiplication, have students find patterns in the Fact Lattice (Math Masters, page ) ENRICHMENT Investigating Napier s Rods (Math Masters, pp. ) To apply students understanding of lattice multiplication, have them use Napier s Rods to solve problems. Discuss students responses to Problem. Students may note that when solving a problem with as a digit in one of the factors, a space is left between the rods where the rod would be. INDEPENDENT Min Teaching Master ELL SUPPORT Creating Visuals for Multiplication Algorithms SMALL-GROUP Min LESSON Napier s Rods Scottish mathematician John Napier ( ) devised a multiplication method using rods made of bone, wood, or heavy paper. These rods were used to solve multiplication and division problems. Example : Example : º º,, To provide language support for multiplication, have students make posters to illustrate the multiplication algorithms they have learned. Display the posters for students to refer to during the rest of the unit. Planning Ahead For use in Part and the optional Enrichment activity in Part of Lesson -, borrow a ream of copy paper and an empty carton used to pack reams of paper. Cut out the rods on Math Masters, page. Use the rods and the board on Math Masters, page to solve the following problems and some of your own. Use another method to check your answers.,. º. º,. º. º, Try This. Show a friend how you would use Napier s Rods to solve º or º,. Math Masters, p. Unit Big Numbers, Estimation, and Computation