Singapore Math Computation Strategies
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Singapore Math Computation
StrategiesJune 2012
“Understanding is a measure of the quality and quantity of connections that an idea has with existing ideas.” (VandeWalle, Pg.
23)
Mathematical proficiency has 5 strands:
1. Conceptual understanding2. Procedural fluency3. Strategic competence4. Adaptive reasoning5. Productive disposition
Source: Common Core (Pg. 6)
Number SenseDefinition:Number sense is a “good intuition about numbers and their relationships. It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms.” (Van de Walle, Pg. 119)
According to a 2007 Trends in International Mathematics and Science Study, Singapore students are among the best in the world in math achievement.
The Singapore model drawing approach bridges the gap between the concrete and abstract models we tend to jump to in the US.
Model drawing reinforces students’ visualization and understanding of math processes.
Model drawing can be used effectively to solve 80 percent of problems in all texts.
Why Singapore Math?
Computation is about students comprehending what they are doing, not following a set of rules.
Students need to understand both what to do and why.
Students will have a variety of strategies to solve problems.
Changes students attitudes toward math and problem solving.
Language based learning- think alouds and math talks Can be used as a supplement to an adopted
curriculum Singapore Math Video
Why Singapore Math? Cont.
Instruction begins at the concrete level with manipulatives to build understanding of basic concepts and skills. (begin with proportional manipulatives)
Then students are introduced to the pictorial stage: model drawing.
Students are not introduced to formulaic or algorithmic procedures, the abstract, until they have mastered model-drawing.
C-P-A Concrete, Pictorial, Abstract
How do you know when manipulatives are and are not needed?
Discuss.Catch thinking on chart paper.Write a summary paragraph.
1) Teacher modeling and thinking aloud about the strategy
2) Students practice with the teacher3) Students practice in small groups4) Students practice in partners5) Independent practice
I Do, We Do, We Do, We Do, You Do
Purpose: Modeling, communicating, promoting a more efficient strategy, promoting reasoning, moving to a more sophisticated level of thinking.
“I’m thinking…” “I’m wondering…” “What are you thinking?” “How did you figure that out?” “Is there another way?” “Why did you choose this way?” “How do you know this answer is correct?” “What would happen if?”
Model clear, explicit language about concepts Mathematical thinking and language promote
more understanding than memorization or rules
Math Talk-Teacher Think Alouds
346+475= First, I’m going to add the hundreds. That
means 300+400=700. Now I will add the tens, four tens (40) plus seven tens (70) equals eleven tens. I can make 110. So now I have 700+100+10. Now I will add the ones and 6+5 makes 11. This is one ten and one 1 so I have 700+100+10+10+1. My answer is 821.
Place Value Talk is critical!
Teacher Think Aloud Example
Math Talk – Ask a Math QuestionPurpose: “Unstick” someone, get help, clarify, promote deeper thinking, make connections
Math Talk – Partner PromptsPurpose: Promote productive math conversations
Example: Practicing questions in multiple-choice format Step 1: Solve individually. Write down your
answer. Step 2: Compare. Same or different? Step 3: Explain why you chose that answer.
Math Talk – Expand the Use of VocabularyPurpose: Use words that proficient mathematicians would use, make connections
Example: End of Year Jeopardy Review Game. 500 point question: What is addition?
Trying to Help Someone? Look at their work.
Do the model, the picture, and the equation match the question and each other?
Read or listen to their explanation. Ask a math question. Seek professional help – Ask a student
expert, the teacher, or other adult.
Place Value Strips Place Value Disks Place Value Chart Number-bond cards Part-whole cards Decimal Tiles Decimal Strips Gratiot Isabella ISD Maniplatives Link
Instructional Materials
Begin with no regrouping Sequence1. Number bonds2. Decomposing numbers3. Left-to-right addition4. Place value disks and charts5. Vertical addition6. Traditional addition
Addition
A Collection of Number Relationships- Relationships Among Numbers 1 Through 10 Spatial Relationships
pattered arrangements One and Two More, One and Two Less
counting on and counting back7 is 1 more than 6 and it is 2 less than 9
Anchoring Numbers to 5 and 10using 5 and 10 to build on and break from is
foundational for working with facts Part-Part-Whole Relationships
understand that a number is can be made of 2 or more parts
A Collection of Number Relationships - Relationships for Numbers 10 to 20
A Pre-Place Value Relationship with 1011 through 20, think 10 and some more
Extending More and Less Relationshipsi.e. 17 is one less than 18 like 7 is one less than
8
Double and Near-Double Relationshipsspecial cases of the part-part-whole constructuse pictures
Number Sense and the Real World Estimation and Measurement
More or less than _______? Closer to _____ or _____?About _______.
More ConnectionsAdd a Unit to Your NumberIs It Reasonable?
GraphsMake bar graphs and pictographs
Basic FactsBig Ideas:1. Number relationships provide the foundation
for strategies that help children remember the basic facts. (i.e. relate to 5, 10, and doubles…)
2. “Think addition” is the most powerful way to think of subtraction facts.
3. All of the facts are conceptually related. You can figure out new or unknown facts from those you already know.
4. What is mastery? 3 seconds or less
33+56= Decompose each number by place value. Put the tens together and one ones
together. (30+50) + (3+6)
(30+50) + (3+6) 80 + 9 = 89
Left-to-Right Addition
30 50 63
Begin with no regrouping Sequence1. Number Bonds2. Place Value Disks and Charts3. Traditional Subtraction
Subtraction
Before “memorizing” multiplication facts, students must first understand the concept of multiplication----they must know it is repeated addition with special attention to place value
Stages1. Number bonds2. Place value disks and charts3. The distributive property4. Area model5. Traditional multiplication
Multiplication
Begin by introducing division as repeated subtraction
Use number bonds to demonstrate the inverse relationship of multiplication and division
Sequence for teaching1. Number bonds2. Place value disks and charts3. The distributive property4. Partial quotient division5. Traditional long division6. Short division
Division
64÷5 Step 2: The divisor tells us how many groups
we need: Draw 5 rows 1
2 3 4 5
Place Value Disks and Charts
10 1010101010 1 1 1 1
64÷5 Step 3: Begin with the tens. Do we have enough
tens to put one in every row? Yes
1
2 3 4 5
Place Value Disks and Charts
10
10
10
10
10
10
1 1 1 1
64÷5 Step 4: If there are any large disks left, trade
them for an equivalent value of smaller disks
1
2 3 4 5
Place Value Disks and Charts
10
10
10
10
10
10
1 1 1 1
1 1 1 1 1
1 1 1 1 1
64÷5 Step 5:Divide the ones equally among the groups
1
2 3 4 5
1 2 10+2=12 64÷5=12 r 4
Place Value Disks and Charts
10
10
10
10
10
1 1 1 1
1
1
1
1
1
1
1
1 1
1
345÷3= 345=300+40+5 unfriendly345=300+30+15(300÷3) + (30÷3) + (15÷3)= 100 + 10 + 5 = 115
The Distributive Property
Drawing simple visual models to represent word problems.
Steps1. Read the entire problem.2. Rewrite the question in sentence form, leaving a space
for the answer.3. Determine who and/or what is involved in the problem.4. Draw unit bar(s).5. Chunk the problem, adjust the unit bars, and fill in the
question marks.6. Correctly compute and solve the problem.7. Write the answer in the sentence, and make sure the
answer makes sense.
Model Drawing
Janet picked 3 daisies and 2 sunflowers from her garden. How many total flowers did Janet pick from her garden?
Work problem on your Part-Part Whole Model Handout
Part-Part Whole Model: Addition and Subtraction
Scrooge had 17 pennies in his piggy bank. He also had 8 dimes. How many total coins did Scrooge have in his piggy bank?
Work problem on your Part-Part Whole Model Handout
Part-Part Whole Model: Addition and Subtraction
Liz earned $500 as her weekly pay. She paid $413 to cover her bills for the week. How much money did she have left to spend?
Work problem on your Part-Part Whole Model Handout
Part-Part Whole Model: Addition and Subtraction
A movie theater has 1,250 seats. If 756 people attended today’s matinee, how many seats will there be left in the movie theater?
Work problem on your Part-Part Whole Model Handout
Part-Part Whole Model: Addition and Subtraction
Joe has $45. Tom has $28. How much more money does Joe have than Tom?
Work problem on your Comparison Model Handout
Comparison Model: Addition and Subtraction
Thomas makes $35 more dollars a week than Bobby. Bobby makes $82 dollars a week. How much money does Thomas make?
Work problem on your Comparison Model Handout
Comparison Model: Addition and Subtraction
When planting her flower garden, Tanya placed her flowers in 3 rows. She put 8 flowers in each row. How many flowers did she plant in her garden?
Work problem on your Part-Part Whole Model Handout
Part-Part Whole Model: Multiplication and Division
Ann saved $45 dollars in nine weeks. She saved the same amount each week. How much did she save each week?
Work problem on your Part-Part Whole Model Handout
Part-Part Whole Model: Multiplication and Division
The movie theater has 12 rows of chairs with 36 chairs in each row. How many chairs are in the movie theater? If there are 250 kids in our school, can we all go to the movie at the same time?
Work problem on blank piece of paper.
Part-Part Whole Model: Multiplication and Division
There are 8 white flowers. There are 3 times as many red flowers. How many red flowers are there?
Work problem on your Comparison Model Handout
Comparison Model: Multiplication and Division
There are 36 red flowers. There are 4 times as many red flowers as white flowers. How many white flowers are there?
Work problem on your Comparison Model Handout
Comparison Model: Multiplication and Division
Joe buys 27 toys. 2/3 of them are trucks. How many of them are not trucks.
Solve on a scrap sheet of paper.
Fraction Models
Susie spent 2/5 of her money of a purse. The purse cost $15. How much money did she have before she bought the purse?
Solve on a scrap sheet of paper.
Fraction Models
From a 5th grade Singapore text. Mrs. Chen made some tarts. She sold 3/5 of
them in the morning and ¼ of the remainder in the afternoon. Is she sold 200 more tarts in the morning than in the afternoon, how many tarts did she make?
Solve on a scrap sheet of paper.
Fraction Models
In a class of 35 students, the ratio of girls to boys is 3:4. How many more boys than girls are there?
Solve on scrap paper.
Ratio Models
There are 30 dogs, cats, and hamsters altogether at a pet store. The ratio of dogs to cats to hamsters is 5:3:2. How many dogs and cats are there at the pet store?
Solve on scrap paper.
Ratio Models
There are 30 dogs, cats, and hamsters altogether at a pet store. The ratio of dogs to cats to hamsters is 5:3:2. How many dogs and cats are there at the pet store?
Solve on scrap paper.
Ratio Models
There were 250 people at a concert. Of these, 40% were children and the rest were adults. How many adults were at the concert?
Solve on scrap paper.
Percent Models
Of the 60 students in the third grade, we know that 60% are girls. We also know that 50% of the girls have blue eyes and 25% of the boys have blue eyes. How many of the students in third grade have blue eyes?
Solve on scrap paper.
Percent Models
We know that ¾ of a sum of money is $72. What is the sum of money?
Solve on scrap paper.
Algebra Models
Susie bought 26 treats for her 2 cats, Joe and Moe. She gave Joe 4 more treats than Moe. How many treats did each cat receive?
Solve on scrap paper.
Algebra Models
Build, Draw, WritePurpose: Concept development, communicating ideasActivity: Work with a partner or in a small group. Choose one of the problems that we wrapped a story around.1- Build a Model 2- Draw a Picture 3- Write an Equation 4- Write your answer in a complete sentence. 5- Explain.
Wrap a Story around ItPurpose: Provide context, aid concept development, make real-world connections
Activity:
Article: Round-Robin Story Telling
Title: Round-Robin Story Problems Author(s): Joseph Martinez and Nancy Martinez Source: Instructor (1990). 109.6 (Mar. 2000): p70.
Round-robin storytelling works well as a math activity with
elementary-school students. Provide each small group with a story beginning such as: Jon and Michelle make paper hats. Their standard hat is paper with a tissue tassel. It costs $.30 to make and sells for $1.25. Within each group, students add to the story For example: They also make a fancy hat that sells for $2.50. The last student in the group wraps up the story and poses the problem: Jon and Michelle sell 60 standard hats, and 40 fancy hats. How much profit will they make? Each group works to solve its problem. The groups then swap stories.
Why Before How: Singapore Math Computation Strategies: Jana Hazekamp
Building Number Sense: Catherine Jones Kuhns The Singapore Model Method for Learning
Mathematics: Mastery of Education Singapore The Parent Connection for Singapore Math:
Sandra Chen 8-Step Model Drawing: Singapore’s Best
Problem-Solving MATH Strategies: Bob Hogan & Char Forsten
Step-by-Step Model Drawing: Char Forsten
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