Day Two Training

Taking Time to Self- Reflect Fact Selection StrategyPracticeKnowledge How do I select which facts for students to learn? What strategies do I use to help students understand these facts? How do I get students to learn these facts once they understand them? How do I get students to use the basic facts they know? Adapted from Basic Facts Knowledge: A Staff Tutorial. http.nzmaths.com, 2010.

A Look Back at Day One

What to expect from today. Examine alternative strategies for multiplication and division. Relate the concepts of multiplication & division. Assess student work and identify their misconceptions.

Fact Selection Multiplication and Division-Grade 3-Unit 2. Georgia Department of Education p. 26.

Mastering Math Facts The problem with rote work comes when it is used exclusively for teaching math facts. Research shows that overemphasizing memorization and frequently administering timed tests is actually counter-productive, (National Research Council, 2001). Van de Walle, J.A., & Lovin, L.H. (2006) Teaching Student Centered Mathematics Volume II (3-5), Boston: Pearson.

Let’s get rockin’ with SALUTE Materials: a deck of ten frame cards with wild cards removed. three participants for each group Student CAPTAIN

How my students think!

A muffin recipe requires 2/3 of a cup of milk. Each recipe makes 12 muffins. How many muffins can be made using 6 cups of milk? Adapted from Multiplicative Thinking. Workshop 1. Properties of Multiplication and Division. http.nzmaths.com, 2010.

The Additive Thinker A muffin recipe requires 2/3 of a cup of milk. Each recipe makes 12 muffins. How many muffins can be made using 6 cups of milk?

Each rectangle represents a third of a cup of milk.

A muffin recipe requires 2/3 of a cup of milk. Each recipe makes 12 muffins. How many muffins can be made using 6 cups of milk?

The Multiplicative Thinker Works with a variety of numbers such as larger whole numbers, decimals, common fractions, etc. Can solve a range of problems involving multiplication and division Can communicate math findings in a variety of ways including words, diagrams, symbolic expressions and written algorithms.

Multiplicative Thinking-Workshop 1. Properties of Multiplication and Division. http.nzmaths.com, 2010.

A family has $96.00 to spend at the Wally World adventure park. Each ride at the park costs $4.00 per person. How many rides will the family be able to enjoy while there?

Time for a Break Additive MultiplicativeBoth

Learning How Students Think

Why encourage multiplicative strategies if additive strategies can be used? “The Jones family has $ to spend at the Wally World adventure park. Rides cost $4.00. How many rides will the family be able to enjoy?”

Writing about what you have seen. Reflection Time

Why is math vocabulary so difficult? Students must be provided adequate opportunities to learn this vocabulary in meaningful ways. Learners need experiences with constructing meaning from context as well as from direct teaching.

Reflection Time

Let’s Make Use the die to generate a number. Spin the spinner to get the multiplier. The person closest to 100 after 5 spins is the winner. 2.You have the option of “staying” after 3 spins. 3.Any number greater than 100 is a bust.

Reflection Time

Multiplication in KCAS

Multiplication 23 x

Errors or Misconceptions? Ashlock, Robert. Error Patterns in Computation: Using Error Patterns to Help Each Student Learn-Tenth Edition, Covenant College p.15.

If you use it, you must understand why it works and be able to explain it. John Van De Walle What About Alternative Strategies?

Partial Products x 19 x x x x x x x x x

Partial Products (Area Model) 62 x

= x 37 =

(2x + 5) (x + 6) x6 5 2x 5x 2x 30 12x

Lattice Method x

46 ×

× 37 =

x 8x times times

CHINESE METHOD OF MULTIPLICATION

CHINESE METHOD OF MULTIPLICATION 23 x 24 =

31 x 43=

Reflection Time

Lies my teacher told me… To multiply by ten just add a zero to the end of the whole number. The product is always larger. 5 x 10 =3245 x 10=10 x 2 =.5 x 10=3.245 x 10=10 x.02=

So What About Division? How many of our students understand dividing a number by 3 is the same as multiplying the number by 1/3?

To begin thinking about division, solve this problem using a strategy other than the conventional division algorithm. You may use symbols, diagrams, words, etc. Be prepared to show your strategy 169 ÷ 14 = Hedges, Huinker and Steinmeyer. Unpacking Division to Build Teachers’ Mathematical Knowledge, Teaching Children Mathematics, November 2004, p. 4-8.

KCAS CONNECTION

Primary Resources: Maths: Multiplication and Division.

The Confusion of Division 24 ÷ 6 = How many times can 6 be subtracted from 24? 24 divided into 6 equal groups. 24 divided into equal groups of size 6. What number times 6 gives the product of 24?

24 ÷ 6 24/ The symbolism of division 6

Division Vocabulary Quotient Divisor Dividend

THE PARTITIVE PROBLEM

Partitive

Example 1: Write a word problem to represent this model of division?

THE MEASUREMENT PROBLEM

Measurement

Example 2: Write a word problem to represent this model of division?

Multiplicative Thinking-Workshop 2. Properties of Multiplication and Division. http.nzmaths.com, 2010.

The standard algorithm

Reflection Time

Forgiveness Method

Issic Leung, Departing from the Traditional Long Division Algorithm: An Experimental Study. Hong Kong Institute of Education, 2006.

Change it UP!!!! 1. Deal each player five cards. The remaining cards are placed face down on the center of the table. 2. Player one places a card face up on the table reads the division problem and provides the quotient. The next player must place a card with the same quotient on the first card. If the player cannot match, he/she may place a “Math Wizard” card on top and then a card with a different quotient. 3. If the player in unable to make either move, he/she must draw from the deck until a match is made. 4. The first player to use all of his/her cards is the winner.

Lies my teacher told me… Division is about “fair sharing”. 35 ÷ 8 =

The Remainder Can be discarded. The remainder can “force the answer to the next highest whole number. The answer is rounded to the nearest whole number for an approximate result.

1.Landon bought 80 piece bag of bubble gum to share with his five person soccer team. How many pieces did each player receive? 2.Brittany is making 7 foot jump ropes for the school team. She has a 25 foot piece of rope. How many can she make? 3.The ferry can hold 8 cars. How many trips will it need to make to carry 25 cars across the river?

Near Facts… Find the largest factor without going over the target number

Partial Quotients 18 R

The Remainder Game 1. To begin the game, both players place their token on START. 2. Player one spins the spinner and divides the number beneath his/her marker by the number on the spinner. If there is a remainder, he/she is allowed to move his/her token as many spaces as the remainder indicates. If the division does not result in a remainder, he/she must leave his/her marker where it is. 3. The play alternates between the two players (a new spin must occur each time) until some reaches HOME.

Lies my teacher told me… Any number divided by zero is zero! 6 ÷ 0 = How many times can 0 be subtracted from 6? How many 0 equal groups are there in six? What does six divided into equal groups of 0 look like? What number times 0 gives you 6?

Reflection Time