10 8 9 567 1234 Triangular Numbers Learn

10 8 9 567 1234 Triangular Numbers Learn to identify and describe triangular numbers Mrs J’s Resource Creations ©

What do you think a triangular number is? Do you remember how Square Numbers looked like squares? Well Triangular Numbers look like triangles! But we use dots to form the shape of a triangle. . . See -> Mrs J’s Resource Creations ©

Let’s Take a Closer Look at Some Triangular Numbers. . . On a piece of paper, draw what you think the next one will look like. Then turn to the person sitting next to you and see if you agree with each other. I got. . . Did you get the same? Mrs J’s Resource Creations ©

Can you see the Pattern? 1 3 6 10 So 1, 3, 6, and 10 are triangular numbers. Turn to the person sitting next to you and describe to one another what pattern you Remember to can see. SHARE HOW YOU WOULD DESCRIBE THE PATTERN WITH YOUR CLASS. Mrs J’s Resource Creations © raise your hand wait for your turn first!

Describing the Pattern of Triangular Numbers 2 Rows of dots 1+2=3 3 Rows of dots 1+2+3=6 4 Rows of dots 1 + 2 + 3 + 4 = 10 - So each time we are adding an extra number in the sequence because we are adding an extra row. - each time the highest extra number we add will be 1 higher than the last highest number added. This is because there will be an extra dot in the new row added.

See if you can work out the next triangular numbers in the pattern. . . ? 1 + 2 + 3 + 4 = 10 1 + 2 + 3 + 4 + 5 = 15 ? ? 1 + 2 + 3 + 4 + 5 + 6 = 21 ? ? 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28

Activity Time Your Task: By drawing dots, using counters or just using the pattern rule by adding the number of rows each time, explore and record on your sheet as many triangular numbers as you can find. You will be using the triangular numbers you find for a game afterwards. The more you find the better chance you have of winning. GOOD LUCK!

Game Time GAME INSTRUCTIONS Get your triangular numbers ready for triangular number bingo! On the grid of 10 boxes you will need to fill out the triangular numbers you found (one per box). If you did not find 10 triangular numbers, you will now need to randomly add the rest of the numbers to you list at the bottom of the sheet to play If you found more than 10 triangular numbers, you can only choose 10 of them for your bingo card. Numbers called will be between 1 -100 ONLY. If you discovered a triangular number higher than 100, firstly WELL DONE, then let your teacher know.

Triangular Bingo First person to cross out all of their numbers, stand up and call Bingo WINS! 15 1 91 45 66 3 6 78 45 28 10 55 36 That’s all of the triangular numbers under 100. Well done to those who found 10 or more triangular numbers!

Interesting Fact About Triangular Numbers Add two neighbouring triangular numbers - what do you notice? 10 3 6 + + 6 10 = = 9 ? + What’s special about these numbers? re a y he T re 16 a u Sq bers! Num 15 = 25

Lesson Review • Triangular numbers are found from a pattern of dots that form a triangle. • Some triangular numbers are: 1, 3, 6, 10, 15, 21, 28, 36, 45. . . So on. • By adding another row of dots and counting all the dots we can find the next number of the sequence. • Every time you add a row, there will be an extra dot in that new row. • Adding two triangular numbers that sit next to each other will equal a square number.

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