1.
Multiplying numbers with and without regrouping:
a. 3- to 4-digit numbers by a 1-digit number, and
b. 2- to 3-digit numbers by 2-digit numbers, with products up to 1 000 000.
2. Estimate the result of multiplying two numbers where the product is less than 1 000 000.
A. Problem Solving on Multiplication
B. Dividing Whole Numbers
A. Multiplying Whole Numbers
B. Estimating Products
C. Problem Solving on Division
Solving mathematical problems applying the MDAS Rule
Find the product of 136 × 4 using expanded form
a) Ask the learner express 136 in expanded form.
136 × 4 = (100 + 30 + 6) × 4
b) By distributive property we can have,
136 × 4 = (100 × 4) + (30 × 4) + (6 × 4)
= 400+ 120 + 24
= 400+100+20 + 24
= 500 + 44
So, 136 x 4 = 544
a. Estimate the product of 206 x 191
Solution:
Multiplicand Round to the nearest Multiplier Round to the nearest
hundreds hundreds
206 200 191 200
200 x 200 = 40, 000
Therefore, 206 x 191 is approximately equal to 40,000.
b. Estimate the product 57 x 3,822.
Solution:
Multiplicand Round to the nearest Multiplier Round to the nearest
hundreds hundreds
57 60 3822 4000
60 x 4000 = 240, 000
Divide using Pictorial representation (place value discs)
a. 426 ÷ 2
On a place value chart form 426 using discs.
Hundreds Tens Ones
100 100 1 1 1 1
10 10
100 100 1 1
Group the discs under each place value by 2s as shown below.
Hundreds Tens Ones
100 100 1 1 1 1
10 10
100 100 1 1
2 1 3
426 2 = 213
b . 6905 ÷ 3
Thousands Hundreds Tens Ones
10000 10000 10000 100 100 100
①①①
10000 10000 10000
100 100 100
①①
100 100 100
6 9 0 5
Group the discs under each place value by 3s as shown below.
Thousands Hundreds Tens Ones
10000 10000 10000 100 100 100
①①
10000 10000 10000
100 100 100
①
100 100 100 ①①
2 3 0 1
6905 ÷ 3 = 2301 r.2
Under the ones column, there 1 group of 3 and a remainder of 2.
Divide using Long Division
Recall: DMBS (Divide - Multiply - Subtract - Bring Down)
In long division, we write the dividend inside the division house and the divisor outside the division house. To easily
remember the division process, we think of the members of the family who lives in the house.
Representation: DMSB (Dad – Mom – Sis – Bro)
Order of Operations is a set of rules used in mathematics to determine the sequence in which operations should be
performed. For the four fundamental operations, MDAS is used to abbreviate the order of operations.
The order of operations performing two Operations at a time (i.E., AS rule and MD rule).
• AS rule stands for Addition and Subtraction rule. The rule states that you should perform addition or subtraction
whichever comes first, from left to right.
• MD rule stands for Multiplication and Division rule.
The rule states that you should perform multiplication or division whichever comes first, from left to right.
