PROVEN TO BE THE WORLD’S BEST PRACTICE
A world-class program based on top-performing Singapore,
Republic of Korea and Hong Kong, in collaboration
with the Ministry of Education in Singapore.
Proven to be the World’s Most
Effective Teaching and Learning
Practices in Mathematics
Singapore, Republic of Korea, and Hong Kong have consistently topped the
Trends in International Mathematics Study (TIMMS) from 1995 to 2011. More
than 600,000 students in 63 countries and 14 benchmarking entities participated
in the most recent TIMSS. Education systems worldwide are looking for different
pedagogies with proven results to improve students’ achievement.
TIMSS Grade 4 Trends in Mathematics Achievement
Mathematics combines the best practice pedagogy from Singapore,
Republic of Korea, and Hong Kong. It has been adapted from the highly
acclaimed and widely proven Primary Mathematics Project developed by the
Ministry of Education in Singapore. The result is a comprehensive and proven
approach to teaching and learning mathematics that works!
TM
2
www.scholastic.com/primemathematics
Why
TM
Mathematics Works
Explicit problem solving emphasizes both processes and strategies
including the bar model to prepare students for success in the STEM
topics of science, technology, engineering, and mathematics (page 4)
Students learn through consistent pedagogy and a concrete-pictorialabstract approach leading to deep conceptual understanding (page 5)
Students develop metalanguage and metacognitive
thinking through various instructional devices (page 6)
The program is measurable and diagnostic. It
contains features that enable a teacher to assess
students’ understanding at every stage of concept
development and learning (page 7)
Comparing Numbers
1.
Comprehensive teacher support and professional
development in Coursebooks and prescriptive
Teacher’s Guides empower teachers to build
effective mathematics classrooms (back cover)
Interactive Whiteboard versions of Coursebook and
Practice Book allow teachers to use technology to
teach, engage, and interact with the class (back
cover)
Lesson 1
A
B
Set A has more.
Set B has less.
Comparing Numbers
You will learn to…
• use‘morethan’and‘lessthan’
• find1moreor1lessthanagivennumber
Comparing sets
Practice 1
C
3
D
1. Arethesentencestrueorfalse?
Set
has more.
a)
Set
has less.
5
22
b)
Therearemoreapplesthanplates.
There are moregiftsthanchildren.
3
4
1. Aretheremorewormsthanbirds?
Therearemoredollsthanairplanes.
2. a) Whatnumberis1morethan9?
b) Whatnumberis1lessthan4?
c) Whatnumberis1morethan3?
d) Whatnumberis1lessthan7?
23
26
27
www.scholastic.com/primemathematics
3
Focus on Problem Solving to
Develop Higher-Order Thinking
teaches mathematics via problem solving through the systematic development of
problem sets. It focuses on both aspects of problem solving:
TM
The method: the concepts and strategies students use to solve word problems.
The process: understanding the problem, identifying the variables and unknowns,
determining the best method to use, and checking one’s answer.
Students view concepts
through real world
problems, making
mathematics relevant
to everyday life.
Bar model method helps
students solve word
problems through visual
representation.
Four-step problem solving
process builds good
habits for approaching
mathematical problems of
all levels of difficulty:
1.Understand the problem
2.Plan what to do
3.Work out the answer
4.Check one’s answer
4
www.scholastic.com/primemathematics
Consistent Structure and Visual
Representations Build Deep
Conceptual Understanding
Students learn through activities using concrete manipulatives, followed by pictorial
Lesson 4 representations.
Subtracting Fractions
representations and finally, abstract mathematical
Students then have
the opportunity for guided practice.
You will learn to…
• subtract fractions
Subtracting fractions with the same denominator
Concrete: Hands-on activities
with everyday materials like
cubes, ice cream sticks, or
pasta shapes build conceptual
understanding.
7
a) David had 9 of a pizza.
2
He ate 9 of the pizza.
What fraction of the pizza was left?
Pictorial: Pictures represent
physical objects previously
used to help students
construct mental images.
7
9
2
9
7 2
5
– =
9 9
9
5
of the pizza was left.
9
Abstract: Math concepts are
modeled using only numbers
and mathematical symbols
so students can relate physical
and picture representations to
this final stage.
98
5
9
99
Dividing by 6
Let’s Learn introduces
and develops the
concept. Let’s Do then
provides guided practice.
Subtracting 2 ninths
from 7 ninths gives
5 ninths.
We can use related multiplication facts when we divide.
a)
b)
7 × 6 = 42
5 × 6 = 30
30 ÷ 6 = 5
= 42
6×
6 × 5 = 30
1.
Fill in the blanks.
a)
× 6 = 48
6×
= 48
b)
48 ÷ 6 =
× 6 = 54
6×
= 54
PB
Multiplying 3-digit numbers by 6
www.scholastic.com/primemathematics
42 ÷ 6 =
54 ÷ 6 =
Chapter 4: Exercise 2
5
Develops Metacognition in Learners
through Various Instructional Devices
The instructional design of the program empowers students to develop mathematical thinking
abilities and habits, leading to effective problem solving.
1.
Thought bubbles model the
thinking process for students.
This trains them to monitor
their own thinking and to
regulate their responses.
Danny has 34 key chains.
He buys 5 more.
How many key chains does he have now?
How many key chains does Danny have?
What does he do?
How many more does he buy?
What do I have to find?
34
5
?
1. Understand
2. Plan
5=
34
Danny has
3. Answer
4. Check
key chains now.
2. There
are It
124 green apples and 32 red apples.
Think
About
many apples are there altogether?
offers How
opportunities
32
for mathematical 124
communication, reasoning
and justification.
?
32 =
124
There are
0
cm
1
2
3
4
The length of the pencil
is 10 centimeters.
1. Understand
2. Plan
5
6
7
8
9
10
No, it is longer than
10 centimeters.
Sam
3. Answer
apples altogether.
Yen
Who 4.is Check
correct? Why?
Choosing units of measure
28 cm
34
Usethegivenwordsandnumberstowrite
a) oneadditionwordproblem.
b) onesubtractionwordproblem.
6
Dia
stamps
giveaway
Julio
stickers
how many
Andy
left
Yara
gamecards
altogether
483
163
buy
342
erasers
Practice 3
2m
?
The length of the Mathematics textbook is
28 centimeters.
Problem posing tasks in
Create Your Own require
students to create word
The height of the
classroomthat
door is
2 meters.
problems
are
realistic
and solvable.
My hand is about
84
www.scholastic.com/primemathematics
Solvethewordproblems.
Drawbarmodelstohelpyou.
35
centimeters long.
Effectively Measures Students’
Conceptual Understanding
Dividing 3-digit numbers by 6
Mathematics checks student readiness to learn new concepts and offers
opportunities
for
Multiplication Tables
Divide 709 by
6. formative and summative assessment.
TM
of 6, 7, 8 and 9
709 ÷ 6 =
11
6 709
6
10
Assess readiness for new 6
learning through tasks that 4
118
6 709
6
10
6 1 2 3
1.
14 9
24 8
3
4 1
Divide the
ones by 6.
4 × 3 = 12
1
6 709
6
1
require students to recall
prerequisite knowledge.
Divide the
hundreds by 6.
Divide the
tens by 6.
1 2 3 4
4×3=3×4
These are related
multiplication facts.
1
2
3
3×4=
709 ÷ 6 = 118 R1
1.
2.
Divide.
b) 6 8 9
a) 6 9 6
c)
6 342
d) 6 2 7 5
10 ÷ 5 =
3.
PB
×
Practice 1
1.
2.
5 × 2 = 10
So, 10 ÷ 5 =
2
Chapter 4: Exercise 4
1 3 6
4
4
Multiply or divide.
136 × 4 =
d) 24 ÷ 6
First, multiply the ones.
Regroup the ones.
Then, multiply the tens.
Regroup the tens.
Lastly, multiply
the hundreds.
a) 7 × 6
b) 43 × 6
c)
e)
f)
g) 405 ÷ 6 The h)
562 ÷of6 136 and 4 is
product
80 ÷ 6
628 × 6
94 × 6
Fill in the missing numbers.
a) 6 ×
= 36
b)
× 4 = 24
7×
= 42
d)
× 6 = 60
c)
.
. Practice
section at the end of
the lesson provides summative
To find the product,
and consolidation
weassessment
multiply.
of concepts and skills learned.
Multiplication
Tables
88
of 6, 7, 8 and 9
94
95
Exercise 1 Multiplying and Dividing by 6
Newly taught concepts are
supported through formative
assessment in the Practice
Books. They also integrate
previously learned topics via
a series of useful summative
assessment reviews.
1.
Complete the multiplication sentences.
a)
b)
6×6=
5×6=
6×5=
c)
d)
www.scholastic.com/primemathematics
7
TM
Mathematics Components
Coursebooks
Two Coursebooks at each level introduce and develop concepts and skills leading to mastery.
Practice Books
Two Practice Books for each level link directly to the Coursebooks. They contain practice
exercises and reviews for formative and summative assessment.
Teacher’s Guides – Professional Learning
The Teacher’s Guide for each Coursebook contains
comprehensive lesson plans that free up teachers to
spend more time with students.
Page-by-page lesson notes show teachers how to
effectively deliver each lesson.
Professional learning tips, such as student mistakes and
how to avoid them.
Digital Resources
Interactive Whiteboard versions of
Coursebook and Practice Book provide
innovative instructional content. Tools
include adding and editing notes,
inserting attachments, highlighting text,
bookmarking pages, accessing chapter
list, showing and hiding answers, and a
dashboard where teachers can access all
Coursebooks and Practice Books.
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