Download
1 / 18
190 likes | 322 Vues
More number patterns, and an introduction to pronumerals. including “There is more than one way to do maths” Run in full screen mode. Only use mouse to move between slides. Aunt Sally’s Christmas.
E N D
More number patterns, and an introduction to pronumerals including “There is more than one way to do maths” Run in full screen mode. Only use mouse to move between slides.
Aunt Sally’s Christmas • Aunt Sally buys Christmas presents for her dog, and her 5 nieces and nephews. She always spends $10 on her dog. She is always fair with the children. She spends the same amount on each one. • If she spends $5 on nephew Tim, how much is she spending in total ? • In another year she spends $20 on niece Sylvia. How much is she spending in total ?
What is Aunt Sally’s Christmas Spending Rule ? Bruno Tim Sylvia Nigel Bob Jane $10 $? $? $? $? $? Total = $???? (write it on your worksheet before you go to the next slide) Aunt Sally
What is Aunt Sally’s Christmas Spending Rule ? You should have something like :- “Aunt Sally spends five times the amount she spends on each niece and nephew plus ten dollars.”
What is Aunt Sally’s Christmas Spending Rule for Lazy Mathematicians? Mathematicians are lazy, and don’t like writing much. They would say, let s be the amount Aunt sally spends, let c be the amount spent on each child. :- “s = 5 x c + $10”
I’m not just being lazy, I’m saving paper (and trees) “s = 5 x c + $10” Is much shorter than “Aunt Sally spends five times the amount she spends on each niece and nephew plus ten dollars.”
Pronumerals In s = 5 x c + $10 s and c are symbols used to represent numbers. These symbols are called pronumerals. The values of pronumerals can change. One year Aunt Sally spent $5 per child, so c was $5. In another year c was $20.
Toothpick Squares • Mohsan was really bored at a family wedding. During the speeches he played with the toothpicks on the table. He lined them up into a string of squares, then counted the toothpicks he had used. “Hey, I can see a pattern here”, he said to himself. • Can you see the pattern too?
Toothpick squares Complete this table, and write a rule on your worksheet, using words.
Argument at a Wedding • Mohsan’s cousins gather around his toothpicks. • Mohsan tells them his rule, but they tell him he is wrong, and suggest other rules. • Help them solve the argument by choosing the correct rule on the next slide.
Click on the Correct Rule • “The number of toothpicks is one plus three times the number of squares.”, claimed Mohsan • “The number of toothpicks is the number of squares plus the number of squares plus the number of squares + 1”, stated Oonah • “The number of toothpicks is four times the number of squares minus (the number of squares minus 1)”, refuted Ramon • “The number of toothpicks is three times the number of squares plus one.”, argued Alice Done
The number of toothpicks is one plus three times the number of squares. This rule is correct. Mohsan built his squares like this. Check out the other rules too.
The number of toothpicks is the number of squares plus the number of squares plus the number of squares + 1 This rule is great. Oonah built her squares like this. Check out the other rules too.
The number of toothpicks is four times the number of squares minus (the number of squares minus 1). This rule is interesting and correct. Ramon built his squares like this. Check out the other rules too.
The number of toothpicks is three times the number of squares plus one. • Great Rule. Alice built her squares like this. Check out the other rules too.
All Rules Were Correct • The number of toothpicks is one plus three times the number of squares. • The number of toothpicks is the number of squares plus the number of squares plus the number of squares + 1 • The number of toothpicks is four times the number of squares minus (the number of squares minus 1) • The number of toothpicks is three times the number of squares plus one. • Before you go to the next slide, write rules using pronumerals for these four rules, on your worksheet.
If t is the number of toothpicks, and s is the number of squares • t = 1 + 3 x s • t = s + s + (s + 1) • t = 4 x s – (s – 1) • t = 3 x s + 1 • All these rules are correct, so the cousins don’t need to argue
The End • Remember to hand your completed worksheet to your teacher, or post it to them. • If you want to e-mail it, fill it in with word, then e-mail the word document. • Have a nice day.
