This document provides an overview of a Grade 5 mathematics institute that will take place on a Friday. It outlines the basic lesson format, which includes an anchor task, guided practice, and independent practice. It also references several learning theories that provide a framework for the lesson, such as Bruner's idea of concrete, iconic, and symbolic representations. The document includes several math word problems from past PSLE exams in Singapore to use for practice. It concludes with key learning theories covered and strategies for challenging advanced learners.

1. BLAKEINSTITUTE2015 | Grade 5 Institute on FRIDAY
How many months in a year have five Fridays? Is the number a constant?
banhar.yeap@pathlight.org.sg | www.banhar.blogspot.com
Problem-Solving Approach
Case Study A |

2. Case Study B |

3. Case Study C |
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.

4. Journal
Journal   June 2015
Title
Problem
__________________________________________________________________

4
1
2
1


9
8
3
1
3 
 6
3
2


4
3
3
1


5. Building Upon Prior Understanding
Case Study D |
Learning Outcome To add unlike fractions
Anchor
Task
Problem posing for sum of a half and
three fourths
square paper
Assessment
Runway Indicator
 if they are able to add like
fractions and find equivalent
fractions
Target Indicator
 if they are able to add unlike
fractions
Observation
Support …
…
…
…
…
…
…
…
…
…
Challenge

6. Bar Model

7. Newman’s Procedures
Helps teachers to identify difficulties in a mathematics word problem.
 Read - Can the student read the problem?
 Comprehend - Can the student answer basic questions? “How many boys are
there? How man coins does each girl have?”
 Knowledge of Strategies - The student knows possible strategies.
 Transform - Can the student translate the story into an appropriate
mathematical form e.g. a diagram or an equation?
 Process/Compute – Can the student perform the necessary computation?
 Encoding/Interpreting - The student can interpret the computation results to
solve the problem
Problem 1
Find the value of 12
5
4
 .
Give your answer as a fraction in the simplest form.
PSLE Singapore 2013

8. Problem 2
The total cost of a pen and a book is $32. The cost of the pen is
5
3
the cost of the
book. What is the cost of the book?
PSLE Singapore 2013
Problem 3
Kai Li spent
3
1
of her money on 5 magnets and 11 postcards.
The cost of each magnet is 3 times the cost of each postcard.
She bought some more magnets with
4
3
of her remaining money.
How many magnets did Kai Li buy altogether?
PSLE Singapore 2013
Problem 4
Mr Lim had a total of 540 long and short rulers. After selling an equal number of
both types, he had
3
1
of the long rulers left and
6
1
of the short ones left.
What was the total number of rulers left?
PSLE Singapore 2014

9. Further Practice
Problem 5
Aini and Usha each had a piece of dough of the same mass for making buns.
The same mass of dough was used for each bun. Aini made 40 buns and had 50 g
of dough left. Usha made 10 buns and had 1.1 kg of dough left.
With the remaining dough from both girls, how many more such buns can be made
at most?
Problem 6
Yulin wants to make 14 small identical stars and 20 large identical stars using wire.
She has made 12 small stars and 7 large ones using 960 cm of wire. The length of
the wire she used for 3 large stars is the same as that for 4 small stars.
What is the length of the wire she needs to make the remaining stars?
Key Theories
1. Piaget
2. Bruner
3. Dienes
4. Vygotsky
5. Skemp

10. Challenging Advanced Learners
1. Solve Using Another Method (Polya)
2. Write a Note to a Friend (21st Century Competencies)
3. Make Up Another Problem (Silver)
Traits of Advanced Learners
1. Real-World Model
2. Visual Model
3. Oral Explanation
4. Written Explanation
5. Initiative