talk number to me: mathematics practitioners christina moore christina.moore@lausd.net rafael...

Talk NUMBER to Me:

Mathematics PractitionersChristina Moore

christina.moore@lausd.netRafael Quintanilla

Rafael.Quintanilla@lausd.net

The Ratio Table

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“Our work is driven by the desire to transform classrooms into communities of mathematicians: places where children explore interesting problems and like mathematicians, engage in crafting solutions, justifications, and proofs of their own making”.

-Cathy Twomey Fosnot

Contexts for Learning Mathematics

• Familiarize ourselves with the Ratio Table and its benefits

• Practice using the Ratio Table with Number Strings and tasks within a context

Objectives

Standards• 3.OA.2

This standard focuses on two distinct models of division: partition models and quotative models.  For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

• 4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted...Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

• 5.NBT.7Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

TodaysMeet

Why do you believe students

struggle with multiplication and

anything associated with it?

Other Possible Misconceptions

Primary experiences revolved around saying and writing numbers rather than counting and cardinality, understanding magnitudes and number relationships.

NO CONTEXT; just computation, algorithms were introduced to them before they were developmentally ready.

They lack strategies.

They lack thinking tools to organize their thinking

What is a Ratio Table?

• It is similar to the input and output table but there it must begin at 0 and 0 on both sides of the table.

• Additive thinking precedes multiplicative thinking.

• Multiplication; whole number, decimals, fractions, percents

• Division to find Partial Quotients, Simplifying, Proportional Reasoning

Ratio Table: A thinking tool learners can use to organize their thinking which enables them to strategically solve problems. MP5

Number Strings

•A set of carefully crafted set of problems which enable students to build their own number relationships, big ideas and strategies.

-Fosnot

Number Strings Questions

• “Who would like to share their strategy for solving this?”

• “How did you get that?” “How do you know?”

• “Talk to your partner about this one”

• “Can anyone restate her/his strategy?”

• “Will this strategy always work?”

• “Are there helpful patterns in this number string?”

Multiplication

• Hand signals

• Talk Moves

• 8-10 Minutes

• Oral no paper pencil

Protocol

SINGLE DIGIT: DAYS IN A WEEK

YOU TRY IT

PACKS NUMBER OF WATER BOTTLES

1 6

2

4

8

10

14

18

20

24

28

PACKS NUMBER OF WATER BOTTLES

1 6

2

4

8

10

9

20

19

40

39

QR Code Links

• https://drive.google.com/file/d/0Byc3VMMSCD3sZ2ZzQ2VLVXVnemM/view?usp=sharing

DECIMALS: $1.25/Lbs

YOU TRY IT: Potatoes: $0.75/lb

Pounds Cost

1 $0.75

2

4

8

10

14

18

20

24

28

Pounds Cost

1 $0.75

2

4

8

10

9

20

19

40

39

• “Some students think their role in math classrooms is to memorize all the steps and methods. Other students think their role is to connect ideas. These different strategies link, unsurprisingly, to achievement, and the students who memorize are the lowest achieving in the world.” ― Jo Boaler

Division

Justine’s 5th grade class is going to Knott’s Berry Farm. There are 208 students. They want to get on a ride that holds 8 students per car. If there are 8 students in each car, how many cars will be used by the 208 students?

String Emcee

Context matters!

• 100 marbles, 12 in a bag. How many bag can you fill?

• 50 dollars, 8 dollars per ticket. How many tickets can you buy?

• 160 students going on a field trip, 30 per bus. How many buses should be ordered?

Fosnot Minilessons for Extending Multiplication and Division-B5

You try it-Decimals

Context-I am making tamales for Sunday Brunch.

• I purchased $6.00 worth of onions at $0.25 per pound. How many pounds did I purchase?

• I purchased $18.00 worth of masa at $0.75 per pound. How many pounds did I purchase?

Quintanilla Water Bottling Company Matthew is the new supervisor at the Quintanilla Water Packing Company. He is in charge of how to package water bottles and he also determines the price of the packages. His first assignment is to package 1,512 water bottles. He needs your help because he needs to determine whether it is best to package the 1,512 water bottles in packs 0f 12, 18, 24 or 36. So can you help him with the following situation?  

• If Matthew packages the 1,512 water in packs of 12, how many packs will he make? 

• If Matthew packages the 1,512 water in packs of 18, how many packs will he make?

• If Matthew packages the 1,512 water in packs of 24, how many packs will he make?

• If Matthew packages the 1,512 water in packs of 36, how many packs will he make?

• Additive Thinking: Distributive Property of Multiplication Over Addition and Partial Products

• Subtractive Thinking: Distributive Property od Multiplication over Subtraction and Using Friendly Numbers

• Multiplicative Thinking: Ratio and Proportional Reasoning

Developmental Progression

• How can this tool support our diverse learners? GATE, ELL’S, and SWD

• How does this tool promote the use of the mathematical practices?

• What would be some next steps for students once we have modeled the tool?

REFLECT

Learning is not about immediate perfection or mastery. It’s about learning over time: confronting a challenge and making progress.

-Carol Dweck

Thank you!

Christina.Moore@lausd.netRafael.Quintanilla@lauds.net

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