This document provides information about a grade 3 mathematics institute to be held on Wednesday. It discusses key theories in mathematics learning from Piaget, Bruner, Dienes, Vygotsky, and Skemp. The document also provides several case studies with examples of lesson plans and problems that assess different mathematical concepts like operations, fractions, problem solving, and place value.

1. BLAKEINSTITUTE2015 | Grade 3 Institute on WEDNESDAY
From Armenian (Չորեքշաբթի), Georgian (ოთხშაბათი) and Tajik (Chorshanbiyev) languages,
Wednesday literally means four (days) from Saturday.
banhar.yeap@pathlight.org.sg | www.banhar.blogspot.com
Multi-Digit Operations and Fractions
Bruner’s idea on representation (CPA Approach) classifies representations as
enactive, iconic or symbolic. Students use concrete experiences and pictorial
representations to understand abstract ideas.
Case Study A |

2. Basic Lesson Format
 Anchor Task – Explore, Structure, Journal, Reflect
 Guided Practice
 Independent Practice
Bruner’s idea on representation (CPA Approach) classifies representations as
enactive, iconic or symbolic. Students use concrete experiences and pictorial
representations to understand abstract ideas.
Skemp classified understandings in mathematics into three types – instrumental,
relational and conventional understanding.

3. Journal
Journal   June 2015
Title
Problem
__________________________________________________________________
Lesson for Practice
Case Study B |
All the five digits are different. What are they?

4. Lesson for Basic Concept and Skill Development
Case Study C |
Cheryl cuts the cake into fourths and took 2 pieces.

5. Case Study D |
Learning Outcome To divide two-digit numbers with a 1-digit number
Anchor
Task
To share  cookies among three
friends.
What if  = 36?
What if  = 51?
base ten blocks
Assessment
Runway Indicator
 if they are able to divide small
numbers
Target Indicator
 if they are able to decompose
 appropriately
Observation
Support …
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Challenge
Problem-Solving Assessment
Case Study F |
Poles are put 2m apart along a straight line that is 16m long. What is the greatest
number of poles altogether?
Poles are put 2m apart along the perimeter of a square of perimeter 16m. What is
the greatest number of poles altogether?

6. Case Study G |
In a soccer tournament, teams get:
3 points for a win
1 point for a tie
0 point for a loss
Zedland has 11 point.
What is the smallest number of games Zedland could have played?
TIMSS2011 Grade 4
Case Study H |
Helen is making a necklace using only red and white beads such that there at least
3 red beads between 2 white beads. What is the greatest number of white beads
in a 100-bead necklace?
Case Study J |
B A N H A R
Which letter is counted 99th?

8. Problem 1
Anna baked 18 cupcakes.
Ben baked 24 cupcakes.
How many cupcakes did they bake altogether?
Problem 2
Cheryl is 8 years older than David.
The sum of their ages is 24 years.
How old is Cheryl?
Problem 3
Emma has $3 more than Fiona.
Together, they have $24.
How much does Fiona have?
Problem 4
Gary has 3 times as many cookies as Holly.
Together they have 114 cookies.
How many cookies does Gary have?
Problem 5
Ian has $89 more than Jenny.
Ian has $300.
How much does Jenny have?

9. Problem 6
Kim has $89 more than Ling.
Ling has $285.
How much does Kim have?
Key Theories
1. Piaget
2. Bruner
3. Dienes
4. Vygotsky
5. Skemp