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• Can you tell how many handshakes were shown? Before the singing competition begins, the 6 contestants shook hands with each other for good luck. How many handshakes in all had taken place? • Bea needed extra money for her tuition fee, she sold her watch to a friend for P800. • After a month, she bought it back for P1000. After a month she sold it again for P1, 200. • Since it has a sentimental value, Bea bought it again from her friend who was very understanding. She bought it for P1, 400. • Did Bea gain or did she lose? By how much? Using different combinations • If you are asked to choose, one solid food and a drink. What would it be. What are the possible combinations can you come up with? Solid food: Pancit, bibingka, Goto, Turon Drinks: pineapple juice, buko juice, sago-gulaman, mango juice Irene is ordering matching shirts for the debate team. They can get polo shirts, sweatshirts, T -shirts, or jacket. Each type of shirt comes in purple or blue. Given these choices, how many different combinations of shirt and color does Irene have to choose from? A is twice of B A= B= B half of A A= B= A= B= A is thrice of B B is one third of B 5 A is 5 more than B B is 5 less than A Using the BLOCK method Mr. Santos is 34 years older than his son Tony. Their total ages is 54 years. How old will Tony be in 25 years time? Rosa is three times as old as Pat, Maria is 8 years older than Pat. The sum of their ages is 78 years. How old is each? The price of a pair of pants is twice the price of a shirt. If the total costs of the items is P900. How much is the price of each. John’s age is half the age of Paul. George is 5 years older than Paul. Their total ages is 130. Find the age of each. Friends Aida, bands. Lorna and Fe make loom Aida made 20 loom bands. Lorna made 8 less than Aida’s loom bands Fe has thrice Aida’s loom bands. a.) How many loom bands did Lorna and Fe make? b.) What is the total number of loom bands the three girls made? Anthony buys 2 hamburgers and 3 cans of juice for P121. Each can of juice costs three times as much as one hamburger. How much more does each can of juice cost than each hamburger? A baseball team scored an equal number of field goals ( 3 points) and touch downs (6 points) Complete the puzzle below to find their score (3 X ___ ) + ( 6 x ___) = ___ + 30 = 45 My uncle owns chickens and cows in his farm. When I visited his farm, I saw some cows and chickens. I counted 12 heads and a total of 38 legs. How many chickens and cows did I see? 12 x 2 = 24 legs 38 - 24 = 14 14 ÷ 2 = 7 cows 12 – 7 = 5 chickens There are 14 vehicles (cars and motorcycles) in the parking lot. I counted 40 tires in all. How many cars and motor cycles? 14 x 2 = 28 tires ------>1.) # of vehicles x 2 40 - 28 = 12 12 ÷ 2 = 6 cars ----->2.) # of tires – (answer in 1) ------->3.) (answer in 2) ÷ 2 --------->4.) total # of vehicles – # cars motorcycles 14 - 6 = 8 PATTERNS Routines provide order and efficiency in carrying our tasks Routines are patterns in real-life ROUTINES Patterns can help us find the solutions to a problem What pattern do you see on the list of mathematical expressions 3 x 4 = 12 300 x 400 = 120 000 3 x 40 = 120 300 x 4 000 = 1 200 000 30 X 4 = 120 3 000 x 400 = 1 200 000 30 x 400 = 12 000 3 000 x 4 000 = 12 000 000 12 ÷ 3 = 4 120 ÷ 3 = 40 120 ÷ 30 = 4 1200 ÷ 300 = 4 12 000 ÷ 30 = 400 12 000 ÷ 300 = 40 12 000 ÷ 3000 = 40 120 000 ÷ 30 000 = 4 120 000 ÷ 3 000 = 40 120 000 ÷ 3 00 = 400 How do we round –off numbers? 64 754 - 64 800 64 754 - 65 000 64 754 - 60 000 Estimation 170 754 3 692 754 62 579 754 98 579 754 - 200 000 4 000 000 60 000 000 100 000 000 The Reyes sisters are saving a part of their money daily allowance to get a gift for their mother on her birthday. The table shows the amount saved by each sister every day. If they save in this manner for five days a week for four weeks, how much money will they save in all in four weeks? Daily savings Php 25 PhP 40 PhP 55 Php 70 A scientist observes how each bacteria grows. What would be the size after 7 minutes? Bacteria A Minute 1 2 3 Size in mm 1 4 9 16 4 5 6 7 25 Bacteria B Minute 1 2 3 Size in mm 1 4 9 16 4 5 25 6 7 1 + 2 + 3 ..... 98 + 99 + 100 101 101 101 There are 50 sets of 101 101 x 50 (100 x 50) + (1 x 50) 5 000 + 50 5 050 1 + 2 + 3 ..... 8 + 9 + 10 11 11 11 There are 5 sets of 11 5 x 11 (5 x 10) + (5 x 1) 50 + 5 55