Place value and integers
MY STUDENT, Maria Enrily D. Magtanong, who teaches mathematics to Grade 2 students in Ateneo de Manila Grade School, introduces the concept of place value through class donations.
At the start of the class, present this problem: Students are encouraged to donate money to share with Grade 2 public school students in Payatas. Your class has two Bigay Puso cans—blue and green. Which can has more money?
Show students the two cans filled with play money (scanned from real bills and coins). First, take out the money from the blue can. Ask volunteers to help you arrange the coins. There should be two piles: P1 coins and P10 coins.
Suppose you end up with eight P10 coins and nine P1 coins. Make a place value chart and ask students where the coins should go (P1 coins in the ones place, P10 coins in the tens place).
P10 P10 P10 P10 P10 P10 P10 P10 P1 P1 P1 P1 P1 P1 P1 P1 P1
How much money is in the blue can? Let’s start with the pile of ones. How many are there? (nine) How many tens? (eight) So we have 8 tens and 9 ones, or a total of P89.
Take the money from the green can. There are nine P10 coins. Show another place value chart and ask students where the coins should go.
P10 P10 P10 P10 P10 P10 P10 P10 P10
How much money is in the green can? Let’s start with the ones. How many ones are there? (zero) How many tens? (nine) So we have 9 tens, and 0 ones, or P90.
Which can has more money? (the green one)
How much money did your class collect for Bigay Puso? Merge the two charts into one. Let students discover that ten P10 coins equal P100.
Hundreds Tens Ones
P100 (ten P10 coins) P10 P10 P10 P10 P10 P10 P10 P1 P1 P1 P1 P1 P1 P1 P1 P1
We now have one in the hundreds column, seven in the tens, and nine in the ones, for a total of P179.
Discuss why it is important for students to learn place value. (Possible answer: Knowing place value helps us to count faster.) Show a place value video (www.youtube.com/watch?v=5W47G-h7myY).
Discuss the act of giving/sharing with the class. For example, say: “Good friendship starts when you help someone in need. Make a friend during recess or lunchtime by helping someone.”
My student, Mark Lester B. Garcia, teaches math to freshmen students at Ateneo High School. To spur interest in the topic of integer addition, he gives the following problem:
Mike and Lance play archery, where each target hit gives a score of +1 and each target missed is listed as -1. After four rounds, the two boys have the scores shown in this table:
Mike -3 -4 +3 +5
Lance -6 +5 -2 +7
Who has the higher total score?
Prepare 20 integer tiles (1 inch by 1 inch square tiles cut from cardboard), with a plus sign on one side and a minus sign on the other. Ask volunteers to go in front to act out given integers.
For example: +5 is modeled by five pieces of plus tiles, -4 by four pieces of minus tiles.
Look at Mike’s first two scores, -3 and -4. What is their sum?
Put three minus tiles and four minus tiles together. What happens when tiles of the same sign are put together? How many tiles are there and what is the sign shown by these tiles?
-3 + (-4) – – –
– – – –
Putting all the negative tiles together gives us a sum of -7. So -3 + (-4) = -7.
Look at Lance’s first two scores, -6 and +5. What happens when tiles of different signs are put together?
-6 + 5
– – – – – – + + + + +
Any real number has its negative. When positive and negative are added, the sum is zero. Regroup the tiles so that one plus tile is beside one minus tile to form a pair, thereby canceling each other out.
-6 + 5
– + – + – + – + – + –
In -6 + 5, five pairs of plus and minus tiles cancel each other out, so we are left with one minus tile. So -6 + 5 = -1.
To help students remember integer addition, sing to the tune of the nursery rhyme, “Row, Row, Row Your Boat”:
“Same signs, add and keep / Different signs subtract / Take the sign of the greater number / Then you’ll be exact.”
Finish solving the problem of Mike and Lance. At the end, Mike has a total of +1 point while Lance has a total of +4 points. Lance wins.
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