Ho Hougang gang Pr Prima mary ry Sc Scho hool ol Welc Welcom ome e to to Math Parent’s Wo Workshop rkshop 20 2018 18 Primar mary y 2 Saturday 7 April 2018
To help parents be their children’s coaches in Mathematics To help parents have a better understanding of how a Mathematical problem is solved. To explain the various types of model-drawing To show parents how students should present their solutions in different heuristics
Par arents as ents as Coac Coaches hes Be Involved -Make it Fun Be Positive in Math -Allow for Mistakes. Do not Punish. Make Math relevant -Encourage Confidence, Curiosity, Courage Teach Concepts -Provide problems according to their existing knowledge -Translate it to something they understand Reinf nfor orce cements ments - Focus on child’s progress/Mathematical ability
Why hy are our e our chi children ldren no not a t abl ble to d e to do o th the e prob oble lems ms ? Simply give up
Polya’s 4-steps problem solving approach (1) Understand the problem (2) Plan your solution (3) Carry out your plan (4) Check to ensure
Understanding the Problem Tip#1: Make Problem Numberless Tip #2: Highlight the Keywords John has 7 stickers. He buys 8 more stickers. How many stickers has he now?
Understanding the Problem Tip#3: Use guiding questions How many stickers Tip#4: Simplify, Act it out does John have at first? John has 7 stickers. He bought MORE. How many He buys 8 more stickers. more? How many stickers has he now?
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To help them visualise To enhance students ’ abstract mathematical ability in solving relationships. word problems. WHY MODEL DRAWING? To use pictorial Makes students re-read representation to the question again. solve problems.
Types of Model Drawing Part-Whole Unitary For Addition For Multiplication, & Subtraction Division, Fractions, Ratio problems, etc. Comparison When comparing 2 or more data All Levels P3 – P6
Part-Whole Model For Addition and Subtraction 1. Finding the WHOLE, given the parts A B ? 2. Finding an unknown PART, given the WHOLE A A ? ? B B
Part-Whole Model Addition 4 + 5 = ? 4 5 4 + 5 = 9
Part-Whole Model Addition [ ? ] − 11 = 8 Left Take away [ ? ] Take away Left 11 8 19 11 + 8 =
12 + 4 = [ ? ] 12 4 ? 16 12 + 4 =
14 − [ ? ] = 5 14 ? 5 14 − 5 = 9
Back to this… Tip#5: Use concrete objects John has 7 stickers. He buys 8 more stickers. How many stickers has he now?
Sample Practice 1: John has 7 stickers. He buys 8 more stickers. How many stickers has he now? 7 8 has buys ? 7 + 8 = 15 He has 15 stickers now.
Let’s Try ! Question 1 Henry had 38 pencils. He gave 20 pencils away. How many pencils has he now? ? 20 38 38 - 20 = 18 He has 18 pencils now .
Question 2: The sum of two numbers is 274. If the smaller number is 36, find the other number? 36 ? 274 274 – 36 = 238 The other number is 238.
Comparison Model For Comparison -Using two or more bars depending on the number of items involved 1. Finding unknown item, 2. Finding the Difference, given the difference Given items A ? A Given Difference B B ? 3. Finding Total, given the difference A Given Difference ? B
Comparison Model When comparing 2 or more data Sample Practice 1: There are 27 boys and 19 girls in a class. How many more boys than girls are there? 27 Boys Girls ? 19 27 – 19 = 8 There are 8 more boys than girls .
Sample Practice 2: There are 19 yellow roses. There are 5 more red roses than yellow roses. (a) How many red roses are there? (b) How many roses are there altogether? 19 Yellow 5 (b) ? Red (a) ? Red —— 19 + 5 (a) There are 24 red = 24 roses. Altogether —— 19 + 24 (b) There are 43 roses = 43 altogether.
Question 1: Janet has 180 cards. Alfred has 53 more cards than Janet. How many cards does Alfred have? ? Alfred Janet 53 180 180 + 53 = 233 Alfred has 233 cards .
Question 2: Aminah collected $500 for a donation drive. Siti collected $850 more than Aminah. (a) How much money did Siti collect? (b) How much money did they collect altogether? $500 Aminah $850 (b) ? Siti (a) ? Siti —— 500 + 850 (a) Siti collected $1350. = 1350 Altogether —— 500 + 1350 (b) They collected = 1850 $1850 altogether.
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He Heur uris istics tics The word ‘heuristic’ is taken directly from the Greek verb which means ‘to discover’. In Mathematics, there are usually different ways to go about solving problem sums. These ways or methods are known as heuristics .
Model Drawing Listing Before - After Working backwards
Heuristics Skill Make a List
Make a List Objectives Students should be able to: • carry out an investigative activity to solve a problem. • make an organised list of possible solutions.
Focused Skill: Make a List Example 1: The menu below shows the types of food sold at Café Y during tea time. How many different ways can John choose a set of sandwich and drinks? Sandwich Drinks Ham Coffee Chicken Tea Egg Milo
Focused Skill: Make a List Note: Keep one column constant . Vary the other column until all options are listed to prevent duplicate answers. Sandwich Drinks Ham Coffee Ham Tea Ham Milo Chicken Coffee Chicken Tea Chicken Milo Egg Coffee Egg Tea Egg Milo
Focused Skill: Make a List Mrs Lim wants to take a photograph of Peter, May and Lily together. They stand in a row when taking the photograph. In how many different ways can Mrs Lim line them up?
Focused Skill: Make a List Note: Keep one column constant . Vary the other column until all options are listed to prevent duplicate answers. Peter May Lily Peter Lily May May Peter Lily May Lily Peter Lily Peter May Lily May Peter There are 6 ways.
Heuristics Skill Before and After
Before and After Objectives Students should be able to: • carry out an investigative activity to solve a problem. • compare the information and relate different events together to solve the problems.
Focused Skill: Before - After Example 1: Susan, Tim and Mark have some coins. Susan has 5 coins fewer than Tim. Tim has 3 coins more than Mark. Mark has 25 coins. How many coins does Susan have ?
5 5 – 3 = 2 25 – 2 = 23 Tim ? ? Or Susan 3 25 + 3 = 28 Mark 28 – 5 = 23 25 Susan has 23 coins .
Gabriel, Freddy and Lance have some stamps. Gabriel has 8 stamps fewer than Freddy. Freddy has 6 stamps more than Lance. Lance has 36 stamps. How many stamps does Gabriel have ?
8 8 – 6 = 2 36 – 2 = 34 Freddy ? Or Gabriel 36 + 6 = 42 42 – 8 = 34 6 Lance Gary has 34 stamps. 36
Heuristics Skill Working Backwards
Working Backwards Objectives Students should be able to: • carry out an investigative activity to solve a problem. • solve a problem where the ending value is given by working backwards.
Focused Skill: Working Backwards Jerry had an empty coin bank. He started saving $2 in the coin bank every week. After some time, he had $8 in his coin bank. How many weeks did Jerry take to save $8? Let’s work backwards to find the answer!
Focused Skill: Working Backwards Jerry took one week to save $2. I shall count back by 2s … $0 $8 $6 $4 $2 $2 less $2 less $2 less $2 less Jerry took 4 weeks to save $8.
Focused Skill: Working Backwards Start: After week 1: After week 2: After week 3: After week 4: $0 $2 $4 $6 $8 $2 more $2 more $2 more $2 more When we count on by adding $2 each week, it takes 4 weeks to fill the coin bank with $8. Our answer is correct!
Focused Skill: Working Backwards Mrs Tan bought some eggs. She used 10 eggs to bake some cakes. After that, she bought another 12 eggs. In the end, she had 38 eggs. How many eggs did she buy at first? Let’s work backwards to find the answer!
Focused Skill: Working Backwards She has 38 eggs in the end. She used 10 eggs to bake a cake. She bought another 12 eggs. 38 10 12 ? at first? used bought 38 – 12 = 26 26 + 10 = 36 She has 36 eggs at first.
Doing Mathematics with your child
Relate Math to everyday activities. Let child handle money during purchases Use analog clocks and watches. Ask child to tell time. What time is it now? In how many minutes will Mr. Bean start?
Provide Manipulatives Counters: macaroni, coins, cubes Number cards, UNO cards, dice A set of different coins as play money Lego blocks o Fractions, numeracy skills
Available resources on the Internet Free Downloadable Math Apps Examples; Second Grade Kids Math Lite Math Zombies Websites http://nlvm.usu.edu/ http://nrich.maths.org/public http://www.bbc.co.uk/schools/websites/4_11/site/numeracy.shtml http://www.youtube.com/watch?v=_eFnzNw10Qc&feature=related
Our greatest natural resource is the minds of our children. Walt Disney Each day of our lives we make deposits in the memory banks of our children. Charles R. Swindoll So take time and be involved in your child’s education .
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