MATH WORKSHOP FOR P3-4 PARENTS FRIDAY, 12 APRIL 2019
http://www.moe.gov.sg/education/syllabuses /sciences/files/maths-primary-2013.pdf
approach … Enables students to encounter math in a meaningful way and translate mathematical concept from the concrete to the abstract .
Heuristics for Problem Solving • Model Drawing (Before and After Model) • Looking for Patterns • Guess and Check
WHY Model Drawing? • Helps students to understand the word problem in visual form • Empowers students to think systematically and master challenging problems by making multi-step and multi-concept problems easy to work on.
Model approach • Types of model – Before and After
Before and After Model
When to use ‘Before and After’ model? • This method is used in questions where there is a change resulting in a 'before' situation and an 'after' situation . • You will need to compare the two situations in order to understand the question fully and find a way to solve it. • Look out for keywords that show a change: Eg: ‘At first’, ‘In the end’, ‘After giving 50 marbles’
Chongfu Star Approach to Problem-Solving Step 1: Step 3: Step 4: Step 2: Study the Problem Think of a Plan Act on the Plan Reflect Step 1: S tudy the Gaby had 5 times as much money as Tom. problem After Gaby had spent $30, she had twice as ∙ What do I know about much money as Tom. the problem? How much money did Gaby have at first? ∙ What am I asked to find? ∙ How can I make sense of the information? ∙ Is there a Math concept I can identify with?
Chongfu Star Approach to Problem-Solving Step 1: Step 3: Step 4: Step 2: Study the Problem Think of a Plan Act on the Plan Reflect Step 1: S tudy the Gaby had 5 times as much money as Tom. problem After Gaby had spent $30, she had twice as ∙ What do I know about much money as Tom. the problem? How much money did Gaby have at first? ∙ What am I asked to find? Before ∙ How can I make sense Gaby 5 units of the information? Tom 1 unit ∙ Is there a Math concept I can identify with? After Gaby spent $30 , Gaby 2 units Tom 1 unit
Gaby had 5 times as much money as Tom. Use the manipulatives to help you construct the Before model for the word problem. BEFORE
After Gaby had spent $30, she had twice as much money as Tom. How much money did Gaby have at first? AFTER
Chongfu Star Approach to Problem-Solving Step 1: Step 3: Step 4: Step 2: Study the Act on the Plan Reflect Think of a Plan Problem Step 3: A ct Gaby had 5 times as much money as Tom. on the plan After Gaby had spent $30, she had twice as much • I will write out money as Tom. ALL the steps. How much money did Gaby have at first? • I will do my calculations accurately. • I will check 3 units $30 that each step is correct. 1 unit $30 ÷ 3 = $10 5 units $10 x 5 = $50 Gaby had $50 at first.
Bene nefits its of usi sing ng ma mani nipulat latives/model ives/model draw awin ing • Students have a visual to associate with numbers that can be abstract. • Students learn to translate the information into math concepts • Students start to see the relationship behind numerical values.
Chongfu Star Approach to Problem-Solving Step 1: Step 3: Step 4: Step 2: Study the Problem Think of a Plan Act on the Plan Reflect Step 1: S tudy the Ali and his brother shared a sum of problem money equally. After Ali gave $50 ∙ What do I know about to his brother, his brother had the problem? ∙ What am I asked to twice as much money as him. How find? much money did each of them ∙ How can I make sense of the information? receive at first? ∙ Is there a Math concept I can identify with?
Chongfu Star Approach to Problem-Solving Step 1: Step 3: Step 4: Step 2: Study the Act on the Plan Reflect Think of a Plan Problem Step 1: S tudy Ali and his brother shared a sum of money equally. After Ali gave $50 to his brother, his the problem brother had twice as much money as him. What do I know How much money did each of them receive about the at first? problem? What am I asked Before to find? How can I make Ali Same sense of the Brother (?) information? Is there a Math After concept I can Give $50 to brother, identify with? Bro 2 units Ali 1 unit
Chongfu Star Approach to Problem-Solving After S T A R
Chongfu Star Approach to Problem-Solving Step 1: Step 3: Step 4: Step 2: Study the Act on the Plan Reflect Think of a Plan Problem Ali and his brother shared a sum of money Step 2: T hink of a equally. After Ali gave $50 to his brother, his brother had twice as much money as him. plan How much money did each of them receive Have I solved at first? similar problems before? ‘At first’ and ‘after’ are hints Have I considered for us to use before and all the conditions after model to find the given in the amount of money each had at problem? first.
Chongfu Star Approach to Problem-Solving ‘At first’ and ‘after’ are hints for us to use before and after model to find the amount of After money each had at first. S T A R
Chongfu Star Approach to Problem-Solving Step 1: Step 3: Step 4: Step 2: Study the Act on the Plan Reflect Think of a Plan Problem Step 3: A ct Ali and his brother shared a sum of money equally. After Ali gave $50 to his brother, his on the plan brother had twice as much money as him. • I will write out ALL the steps. How much money did each of them receive • I will do my at first? calculations After ? accurately. Before ? • I will check A that each step A $50 is correct. B $50 $50 B 1 Unit 1 Unit
Chongfu Star Approach to Problem-Solving Step 1: Step 3: Step 4: Step 2: Study the Act on the Plan Reflect Think of a Plan Problem Step 3: A ct Ali and his brother shared a sum of money on the plan equally. After Ali gave $50 to his brother, his • I will write out brother had twice as much money as him. ALL the steps. How much money did each of them receive • I will do my at first? calculations accurately. • I will check that each step is correct. After ? 1 unit $50 + $50 = $100 A $100 + $50 = $150 B $50 $50 Each of them received $150 at first. 1 Unit 1 Unit
Chongfu Star Approach to Problem-Solving ‘At first’ and ‘after’ are hints for us to use before and after After model to find the amount of money S T each had at first. A R ? Before 1 unit $50 + $50 A $50 = $100 B $100 + $50 = $150 After ? Each of them received $150 A at first. B $50 $50 1 Unit 1 Unit
Chongfu Star Approach to Problem-Solving Step 1: Step 3: Step 4: Step 2: Study the Act on the Plan Reflect Think of a Plan Problem Ali and his brother shared a sum of money Step 4: equally. After Ali gave $50 to his brother, his R eflect brother had twice as much money as him. • Have I solved How much money did each of them receive the problem? at first? • Is my answer reasonable? Check: • How do I know that my answer is correct? Before After • Is there a better solution to the problem? Ali $150 $100 -$50 x2 Brother $150 $200 +$50
Chongfu Star Approach to Problem-Solving ‘At first’ and ‘after’ are hints for us to use before and after model to find the After amount of money each had at first. S T A R ? Before 1 unit $50 + $50 A Check: $50 = $100 B $100 + $50 = $150 After ? Each of them received $150 at first. A B $50 $50 1 Unit 1 Unit
Chongfu Star Approach to Problem-Solving Step 1: Step 3: Step 4: Step 2: Study the Problem Think of a Plan Act on the Plan Reflect Lily and James had $200 Step 1: S tudy the altogether. After giving Lily problem $20, James had as much ∙ What do I know about money as her. How much did the problem? ∙ What am I asked to Lily have at first? find? ∙ How can I make sense of the information? ∙ Is there a Math concept I can identify with?
Chongfu Star Approach to Problem-Solving Step 1: Step 3: Step 4: Step 2: Study the Problem Think of a Plan Act on the Plan Reflect Lily and James had $200 altogether. After giving Lily $20, James had as much money Step 1: S tudy the as her. How much did Lily have at first? problem • Lily + James → $200 ∙ What do I know about the problem? ∙ What am I asked to • Who has more? James find? ∙ How can I make sense • James -$20 = Lily + $20 of the information? ∙ Is there a Math concept • Lily at first → ? I can identify with? • Total unchanged (Before and After)
Chongfu Star Approach to Problem-Solving Lily + James → $200 James -$20 = Lily + $20 Lily at first → ? S T A R
Chongfu Star Approach to Problem-Solving Step 1: Step 3: Step 4: Step 2: Study the Problem Think of a Plan Act on the Plan Reflect Lily and James had $200 Step 2: T hink of a altogether. After giving Lily $20, plan James had as much money as her. ∙ Have I solved similar problems How much did Lily have at first? before? ∙ Have I considered ‘At first ’ and ‘after’ are hints all the conditions given in the for us to use before and after problem? model to find the amount of money Lily had at first.
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