2018 DepEd –NCR Seminar Workshop in Mathematics

GRADE II

NUMBER SENSE EVERYWHERE

Some people use the term number sense to describe a group of key math abilities. You may hear people use the
term number sense when they’re talking about math. But what exactly does it mean? And how does it relate to
kids who struggle with math? Learn about the key skills covered under this session , and how to help our learners
I. Definition of Terms:
Number sense- a group of skills that allow the learners to work with numbers. These include the ability to:
Practice counting and grouping objects. Then add to, subtract from or divide the groups into smaller groups to
practice operations. You can also combine groups to show multiplication. Work on estimating. Build questions into
everyday conversations, using phrases like “About how many” or “About how much.”
Talk about relationships among quantities. Ask your child to use words like more and less to compare things.
Build in opportunities to discuss things like time and money. For example, you could ask your child to keep
track of how long it takes to drive or walk to the grocery store
Estimation is finding a number that is close enough to the right answer.
Block Model Approach. Block Model Approach employ the concrete- representation – abstract method of solving
word problems. The Block Model Approach helps pupils visualize situations because it creates concrete picture of
from abstract situation
Problem Solving Map(PSM) –is a graphical representations of important thinking processes needed to solve Math
problem successfully.
Act it- Out. Problem solving strategy in which students physically act out what is taking place in a word problem
The 3 Areas of Number Sense
Counting . Counting involves counting by ones, twos, fives, tens, and more. Counting is the ability to put
names to quantities. It is understanding how our number system is organized in groups of 10 – base 10.
Proportional thinking is thinking about how many times bigger or times smaller a number is compared to
another number (e.g. How many times bigger is 6 than 3? How many times smaller is 3 than 6? How many times
bigger is your mom’s arm than your arm?
Wholes and Parts . This is where you start to learn about and master fractions. Fractions are equal parts of a
whole.
II. Concepts .
A. Addition and Subtraction Situation
There are different types of word problem that students may encounter. For each of the different types there
can be further differences. For example, in word problems involving the change in amounts, the starting amount, or
the final amount, or the amount of change itself can be unknown.It is important that students learn to solve all these
different types of problem as this will demonstrate a full understanding of the meaning of the addition and
subtraction operations. The following examples shows different types of addition and subtraction Situations
1 Analyzing Parts and Whole. Analyzing parts and wholes is a basic and useful way of looking at a problem.
To analyze parts and wholes is to recognize the parts and understand how they form the whole.
Example 1. There are 5 apples and 6 oranges. How many fruits are there altogether?
Solution : 5 6

apples oranges
11

5 + 6 = 11 There are 11 fruits altogether

Example 2. A school has eight teachers. If two new teachers start working at the school, how many teachers
will there be in total?
Answer: There will be ten teachers in total.
Example 3. Luke had scored seven goals. After his last game his total moved up to ten. How many goals did he
score in his last game?
Answer: He scored three goals in his last game.
2. Comparing . Comparing is an effective way identifying the relationship between the variables in a problem.
Comparing the information in a problem helps us determine the difference in quantities, for example , more or less
of the variables. The more than concept involves whole numbers as well as the key words more than. When solving
problems involving the more than and fewer than concept you are encouraged to use the model drawing approach
to better visualize the comparison among the items.
Example 1: Sean has 12 pencils. His friend John has 16 more pencils than him. How many pencils does John have?
Solution:
12
16
Sean
John

12 + 16 = 28 John has 28 pencils

 Example 2: Ellen has 611 stickers. She has 133 fewer stickers than Derrick. How many stickers does Derrick
have ?
Answer : Derrick has 744 stickers
Example 3. Paul has 15 magnets, Jay has 18 magnets. Who has more magnets? How many more magnets does he
have?
Solution:
15

Paul ?
Jay

18
18 + 15 = 3 Jay has more magnets. He has 3 more magnets

Example 4. Mrs. Tan has 20 T-shirts. Mrs Jaya has twice as many T-shirts as Mrs. Tan. How many t-shirts do they have
altogether?
Exercises
1. John has 43 toy cars. His father gives him 23 more toy cars. How many toy cars have John in total?
2. Lola bought 46 lollipops. Jane bought half as many lollipops as Lola. How many lollipops did they buy in
all?
3. Jenny has 26 local stamps. She has 39 more foreign stamps than local stumps. How many foreign
stamps does Jenny have?
4. There are 35blue marbles in a bag. There are 24 more red marbles than blue marbles. How many red
marbles are in the bag?
5. Ali folded 34 paper cranes. Candy folded 18 more paper cranes that Ali. How many paper cranes did the
two children fold altogether?
6. Joseph had 18 paper planes at first. He then made a few more paper planes in the afternoon and
another 2 paper planes in the evening. He had 29 paper planes in the end. How many paper planes did
he make in the afternoon?
7. Romeo weighs 27 kg. His younger brother weighs 10 kg. less. Their father’s weight is two times their tot
al weight. What is theirs fathers weight? (88kg )
8. Laura pasted some flowers in the wall. Lilian pasted 23 flowers on the wall. She pasted 8 more flowers
than Laura. Rachel pasted 10, fewer flowers than Laura. how many flowers did Rachel paste?
9. Timothy and Ivan have the same number of seashells at first. Ivan then picks up 7 more seashells and
they now have 27 seashells. How many sea shells does Timothy have?
10. A famer has 48 cows. He sells 12 cows to another farmer. He buys another 26 cows. Hoe many cows
does the farmer have in the end?
Activity 1 Activity 2
Observe the digits below. Insert only once
any of the symbols +, -, X, and ÷ and a pair
of parentheses ( ), to get the largest result.

5 8 3 7 1

5 8 3 7 1

Proportional Activities
Drawing a diagram is very useful in proportional problem because we can see the patterns and relationship among
the data found in the problem.
Example 1. For every 2 adults, a girl stands between them. If there are 4 adults, how many girls will there be?
Solution:

There will be 3 girls.

 Example 2. Mother has three parcels: A, B and C. Parcel A is heavier than parcel B but lighter than Parcel C.
Which Parcel is the heaviest?
Answer: Paul C is the heaviest

Example 3. 3 oranges cost Php 20.00. Mother buys 15 oranges. How much does she spend altogether?
Answer: Mother spends Php 100.00
Exercises: Solve each item
1. If you have 8 pieces of pizza to divide between 4 friends, how many pieces of pizza should each friend
get?
2. Six workers can build a house in 3 days. Assuming that all of the workers work at the same rate, how
many workers would it takes to build a house in 1 day?
3. There is a group of children standing in a circle. To the left of Alex, between Alex and Nick, there are
4 children. To the right of Alex, between Alex and Nick, there are 7 children. What is the total
number of children in the circle ?
4. To cut a log into two equal parts, a logger had to pay 100 pesos: if a log is to be cut into 6 parts, how
much should the logger pay?
5. From one can of juice, Nena can make 6 glasses of juice drink. If she will have 26 visitors, how many
cans of juice should she buy?
6. One number is 4 more than 3 times another. Find the numbers if their sum is 60.

Activity 4
Measure how tall you are with a string. Cut the string and use it to discover what else is as big as
you in the classroom. Categorize items that are bigger than they are and smaller than they are.
Look for items that are twice your size. Look for items that are half your size.

3. Counting. In the primary and intermediate grades, number sense includes skills such as counting; representing
numbers with manipulatives and models; understanding place value in the context of our base 10 number system;
writing and recognizing numbers in different forms such as expanded, word, and standard; and expressing a
number different ways.
Example 1. Mr. Bobo, the balloon man, had this

Fill in the blanks to describe his balloons:

_______out of ______ balloons are round.
______ out of _______balloons are long.
______out of _______balloons have dots.
_____out of_________balloons are plain.

Exercises: Solve each item.

1. How many triangles can you find in this figure? Watch for all sizes!!
2. I started counting fom11 to 33: 11,12,13…. 32,33. The first number I counted was 11,
and then last number I counted was 33. How many numbers do I count in all ?
3. What is the sum of the first 50 whole numbers?
4. Today is my birthday. If my age in months is 99 greater than my age in years, how many
years old am I now?
5. This puzzle piece was cut from a hundred board. Fill in the missing numbers:

Activity 5 Activity 6. Read the problem,

analyze and complete the
Write the numbers 1, 2, 3, 4,5,6,7,8,9 on table.
your scratch paper. Which number should
be remove , so that the sum of the Mike likes to collect spiders.
remaining weight numbers would be 36? 9 Fill in the chart to show how
many eyes and legs he sees
on his spiders.
Activity 7. Act- it- Out

Six rabbits had a race. Peter and another rabbit tied for second place. Pokey came in last. Flopsy was ahead of
Cottontail. Cottontail beat Hopper. Mopsy was beaten by only one other rabbit.
Who won the race?
Show the order in which they crossed the finish line:
First: ___________
Second:___________and____________
Third: ___________
Fourth: ___________
Fifth: ___________
B. Multiplication and Division
Example. Mr Lee decides to donate some books to the school library. The books are packed into 5 groups. Each
group has 4 books. How many books are there altogether?
Sol.

4 x 5 = 20. There are 20 books

Exercises: Solve each item

1. Jill counted the number of petals on five flowers that are all alike. When she finished she
had counted 20 petals. How many petals are on each flowers?
2. Luke made flowerpots for his friends. He has 32 flowers. If he puts six flowers in each
pot how many pots will he make?
3. Mrs. Hall planted 15 flowers in rows of five each. How many rows did she plant?
4. If 35 is subtracted from a number and the difference is divided by 15, the result is 21. What is the
number?
5. Add seven 5s, seven 6s and seven 7s. What is the result?
6. Estimate the product of 63 x 77 by rounding each factor to the nearest 10.
7. There are 5 cows and 3 chickens in a farm. How many legs are there altogether?
8. In a flower shop, there are 235 flowers. Four flowers will be put in each vase. How many vases are
needed?
9. A book that is 3 cm thick each will be placed on a shelf that is 74 cm long. How many books may be
placed on the shelf?

C. Fraction
Example 1; 2 children ate 1/6 of a pizza. What fraction of the pizza was left?
Solution :

1/6+1/6+1/6+1/6 = 4/6 of the pizza was left

Example 2: Mrs. Lim baked a cake. Her son ate 1/3 of the cake. Her daughter ate 2/9 of the cake.
a. What fraction of the cake was eaten? b. . What fraction of the cake was left?.

Exercises: Solve each item.

1. What must be added to the sum of ¼ and 1/6 to make 1 whole?
2. 2/5 of the pupils in a class are girls. There are 12 boys in the class. Find the total number of pupils in the
class.
3. There are 16 boys and 20girls in teachers Bels class, one-fourth of the boys and one-fifth of he girls joined
the Science Cub, one fourth of the class joined the Math club. Those remaining joined the Music club.
How many more joined the Music club than the Math club?
4. Remy had PhP 240.00. She spent one third of her money in one store. She spent
another third of her money in another store. After going to the next store, she
had only 5 pesos left. How much did she spent in the last store?
5. What fraction of the figure below is shaded

Activity 8 Take a sheet of paper . Fold it in half.

Y Without opening up the sheet of paper, fold it in Number of Folds Number of Sections
half again. If you opened up your sheet of paper now, 0 1
how many sections would there be? Open up your 1 2
sheet to check out your answer! Repeat this 2
process several times, each time adding one more 3
fold to your sheet of paper. Do you see a pattern? 4
5
6

Prepared by: Narcisa F. Alacapa SDO Makati