Fluently Multiply with Products up to 100 Unit of Study: 13 Global Concept Guide: Strategies for multiplying by 7, 8, 9

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)

Content Development 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 the. (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 The commutative property might be one of the first strategies to teach students as it immediately cuts down the number of facts that students need to “know” in half once they understand commutativity. These facts are also called Turnaround Facts.

Day 1 The focus of Day 1 is strategies for multiplying by 9. Products of x9 facts are one group less than products of x10 facts, so our prior knowledge of multiplication of 10 can help us quickly learn to multiply by 9 (i.e., 9 x 3 equals one group of 3 less than 10 x 3 or might be thought of as 30-3). (O’Connell and SanGiovanni, 2011, p.130) Good Questions to Ask students: How are x9 facts related to x10 facts? What patterns do you notice in the multiples of 9? When multiplying by 9, do you immediately know the tens digit of the product? Why? What x9 facts do you already know? Why? Which facts will you still need to learn?

Day 1 The focus of Day 1 is strategies for multiplying by 9. Have students complete the Delicious Dot task listed in the GCG Good Questions to Ask students: How are x9 facts related to x10 facts? What patterns do you notice in the multiples of 9? When multiplying by 9, do you immediately know the tens digit of the product? Why? What x9 facts do you already know? Why? Which facts will you still need to learn?

Day 1 Reinforcing Game: Nifty Nines Directions: Materials: Deck of cards (Ace to Ten- ace represents one) or a spinner with the digits 1-10, and two color counters. Player 1 selects a card (or spins the spinner) and multiplies that amount by 9. If they correctly multiply the problem, they place a counter on the product. If they solve the problem incorrectly, Player 2 places their chip on the product. Player 2 selects a card (or spins the spinner) and multiplies that amount by 9. If they correctly multiply the problem, they place a counter on the product. If they solve the problem incorrectly, Player 1 places their chip on the product. The first player to get four in a row wins the game.

Day 2 Multiplying by 8. Explore the double, double, double concept through hands- on exploration. Ask students to select 1 counter. Ask them to double it. How many do they have now? (2) Ask them to double it again. How many do they have now? (4) Ask them to double it again. How many do they have now? (8)

Day 2 Engage: Scott was cooking hamburgers for his 4th of July BBQ. He wanted to make sure he had enough Hamburger Buns to feed his family. The hamburger buns are sold in packages of eight. Scott bought 4 packages. How many Hamburger Buns did Scott buy? Multiplication by 8 is double multiplication by 4.

Day 2 Have students apply the Double-double strategy for multiplying by eights using the task Super Starbursts listed in the GCG. Reinforce the idea by playing the game Easy Eights. Directions: Materials: Deck of cards (Ace to Ten- ace represents one) or a spinner with the digits 1-10, and two color counters. Player 1 selects a card (or spins the spinner) and multiplies that amount by 8. If they correctly multiply the problem, they place a counter on the product. If they solve the problem incorrectly, Player 2 places their chip on the product. Player 2 selects a card (or spins the spinner) and multiplies that amount by 8. If they correctly multiply the problem, they place a counter on the product. If they solve the problem incorrectly, Player 1 places their chip on the product. The first player to get four in a row wins the game.

Day 3 The focus of Day 3 is strategies and fluency for multiplying by 7. Multiplication with 7 as a factor is more challenging for students to master. If taught in this order, the only fact left to master is 7 x 7. Students can practice the strategy of multiplying by sevens using the Party Favors task that is referenced in the GCG.

Day 3 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) Play the Super Sevens game to reinforce the strategy of multiplying by sevens. Directions: Materials: Deck of cards (Ace to Ten- ace represents one) or a spinner with the digits 1-10, and two color counters. Player 1 selects a card (or spins the spinner) and multiplies that amount by 7. If they correctly multiply the problem, they place a counter on the product. If they solve the problem incorrectly, Player 2 places their chip on the product. Player 2 selects a card (or spins the spinner) and multiplies that amount by 7. If they correctly multiply the problem, they place a counter on the product. If they solve the problem incorrectly, Player 1 places their chip on the product. The first player to get four in a row wins the game.

Enrich/Reteach The games provided in the following GCG’s are Microsoft word documents rather than permanent PDF files, you can easily modify the activity page to make it simpler or more complex, personalize the tasks to motivate and engage your students, and adapt the activities to maintain your students’ interest. If students are struggling with a few specific facts, you might delete some of their known facts from a game and quickly add the ones they need to practice. If students have already mastered a set of multiplication facts, add complexity to tasks by inserting division facts or more complex multiplication equations. Some students require additional support through small-group or individualized interventions with more and different types of math fact explorations. Providing additional opportunity for some students to visualize and discuss math facts will support their path toward mastery. High anxiety might indicate the need to modify tasks by decreasing the number of facts or allowing the student additional time to complete a task. Once the student experiences success, more facts can be added or the time can be decreased.

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.