Fluently Multiply with Products up to 100Unit of Study: 13Global Concept Guide: Strategies for multiplying by 3,4 and 6

Content Development•The goal in today’s math classrooms has shifted from memorizing facts and procedures to increased understanding of math skills and concepts. (O’Connell and SanGiovanni, 2011, p.)

•Developing fluency requires a balance and connection between conceptual understanding and computational proficiency. (NCTM 2000, p. 35)

•Do not subject any student to fact drills unless the student has developed an efficient strategy for the facts included in the drill. (Van de Walle, 2006, p.94)

•Drill can strengthen strategies with which students feel comfortable- ones they “own”- and will help to make these increasingly automatic (Van de Walle, 2006, p.94)

•By creating a large number of drill activities promoting different strategies and addressing different collections of facts, it is not at all unreasonable to direct students to activities that are most useful for them. (Van de Walle, 2006, p.94)

•Automaticity means the quick and effortless recall of math facts. No need to count every object. No need to think about related facts. No need to extend patterns. The answer is automatically known. Although automaticity is a goal for our students, alone it is not enough. Students must first understand the facts that they are being asked to memorize. (O’Connell and SanGiovanni, 2011, p. 3)

Thinking Strategies for

Multiplication Facts: Commutativity Primary strategy for helping children learn the facts The power of the commutative property…

There are only 55 facts to learn if students use the commutative property first.

2 x 6= 12 6 x = 12

These facts are also called Turnaround Facts.

Day 1 The focus of Day 1 is strategies for multiplying by 3.

Multiplying by 3 can be thought of as multiplying by 2 and then adding one more group, or as tripling a number. (O’Connell and SanGiovanni, 2011, p.10)

Good Questions to Ask students: What patterns do you notice in the products? Does the order of the factors affect the product? Give examples to

justify your thinking. What does it mean to triple a number? How is it different from

doubling a number? How do the x3 facts compare to the X2 facts? How are the x1, x2, x3 facts alike? How are they different?

Day 1 Sample Engage: Use this

task to explore the relationship between multiplying by 2 and 3.

Students should have access to manipulatives during this activity if needed.

Day 1Reinforcing Game: x3 Memory

1. Memory is a card game designed for 2 people. 2. The object of the game is to match more pairs of cards than the

opposing player. 3. To Begin: Lay the x3 product cards and the x3 expression cards face

down on a flat surface, forming a grid. 4. Players take turns flipping pairs of cards over. If a pair makes a

match, those cards are kept. If they do not, they are placed back on the grid where they came from.

5. One point is scored for each matched pair, and the player with the highest score after all cards have been matched wins.

Day 2

The focus of Day 2 is strategies and fluency for multiplying by 4.

Multiplying by 4 is simply doubling the product of the x 2 fact.

Noticing that multiples of 4 are always even numbers or realizing that multiples of four are also multiples of 2 leads to interesting conversations.

Day 2

• Take turns pulling x4 fact cards and model the fact on grid paper.

• Take turns until you cant fit any more models on your grid. • The player with the most models on their grid win.

• Explore patterns by having students chart multiples of 2 and 4 on a 100 Chart.

• First have students chart multiples of 2 circling each one.

• Next have students place an X on all multiples of 4.

Click here for the chart

Click here for Quilt Cover Up

Day 2 Game

Click here for game

x4 Go Fish

Day 3

The focus of Day 3 is strategies and fluency for multiplying by 6.

A strategic way to explore multiplication with 6 as a factor is to build on students’ previous mastery of x5 facts and explore the connection between x5 and x6. (The products of a x6 fact is 1 set more than the product of the related x5 fact.)

Students can also explore multiplication with 6 as a factor by building on previous mastery of x3 facts and exploring the connection between x3 and x6.

Students have already explored doubling x2 and x4 facts and should see the connection between x3 and x6 facts. They may also notice the tripling connection as they observe x2 and x6 facts.

Day 3 Engage activity: Ask the students to answer the following

questions in their journals. What do you notice about the products of 5 and 6? How could knowing the products of 5 help you figure out the

products of 6?

x6 Arrays Provide students with a set of x6 fact cards and a dot

paper recording sheet. Have students select a fact card and represent the fact by

circling the matching array.

Day 3 GameRIO 12 18 30

24 6 60

36 24 18

42 48 54

•Each player takes 5 chips of the same color •Player 1 rolls the decahedra •If a 3 comes up, for example, he or she puts a chip on the tile marked “18” for 6 x 3. •Player 2 then rolls the number cube, and if an 4 comes up, he or she puts a chip on 24 for 6 x 4. •If the 3rd player rolls a 3, the tile marked “18” already has a chip on it, so the player must take it. The third player now has six chips and the first player has four. Play continues until one person has been able to “play” all of his or her chips. The winner is the first person to get rid of all of their chips.

Enrich/Reteach It is unreasonable to expect every student in your class to

develop and be comfortable with the same strategies…There are multiple paths to most facts. Different students will bring different number tools to the task and will develop strategies at different rates. This means that there are few drills that are likely to be efficient for a full class at any given time. (Van de Walle, 2006 p.94)

Therefore, you need a variety of games and other activities available for students to practice basic facts.

Literature for your Classroom Library