December 8

Maths Mate Sheet 7 Question 23 (Term 4 2014)

Prediction: I predict this question  will be about addition because of the repeated pluses in the question.

Read: The digit sum for 95 is 9 + 5, or 14. How many two digit numbers have the digit sum of 9.

Clarification: None needed.

The Big Question: How many two digit numbers have the digit sum of 9.

Mathematician’s Toolbox: Have I seen a similar problem?

Solving: Firstly I know that all the nine times tables with two digit numbers add up to nine so I did: 2×9,3×9,4×9,5×9,6×9,7×9,8×9, 9×9 and 10×9. Thats 9 sums so the answer is 9.

Conclusion: So the answer was 9.

November 20

Maths Mate Sheet 6 Question 23 (Term 4 2014)

Prediction: I predict this question  will be about addition because of the repeated pluses in the question.

Read: The dight sum for 195 is 1 + 9 + 5, or 15. The digit sum for 200 is 2 + 0 + 0, or 2. Find the two consecutive numbers that have the digit sums of 27 and 1.

Clarification: None needed.

The Big Question: Find the two consecutive numbers that have the digit sums of 27 and 1.

Mathematician’s Toolbox: Work backwards/Have I seen a similar problem?

Solving: Firstly I figured out what the factors of 27 were 1,3,9, and 27. That means 999 was the first number because 3 times 9 is 27 and 999 has 3 9’s in its digit sum. Since the numbers must be consecutive I figured 1000 was the second number because it has the digit sum of one and it’s consecutive.

Conclusion: So the answer was 999 and 1000

October 21

Maths Mate Sheet 2 Question 23 (Term 4 2014)

Prediction: I predict this problem will be about working backwards.

Read: I think of a number , add 9 and then multiply it by 3. If the result is 30, what was the original number?

Clarification: None needed.

The Big Question: What was the original number?

Mathematician’s Toolbox: Work backwards/Have I seen a similar problem?

Solving: First I worked backwards from 30. I used division because multiplication is division backwards. So I did 30 divided 3 which is 10. After that I subtracted 9 because addition is the inverse operation of subtraction. So I subtracted 9 and I got the result of 1.

Conclusion: So the answer was 1.

October 14

Maths Mate Sheet 1 Question 23 (Term 4 2014)

Prediction: I predict this problem will be about predicting or estimating.

Read: I think of a number , subtract 5 and then divide it be 3. If the result is 6, what was the original number?

Clarification: None needed.

The Big Question: What was the original number?

Mathematician’s Toolbox: Work backwards/Have I seen a similar problem?

Solving: First I worked backwards from 6. I used multiplication because division is multiplication backwards. So I did 6 times 3 which is 18. After that I added 5 because subtraction is the inverse operation of addition. So I added 5 and I got the result of 23.

Conclusion: So the answer was 23.

September 14

Maths Mate Sheet 8 Question 23 (Term 3 2014)

Prediction: I predict this problem will be about patterns.

Read: An archeologist found some ancient numbers written as follows: (I’ll use keyboard symbols instead).

!!## For 52. !@@@ For 40. And @@### For 13. What did !@### equal?

Clarification: None needed.

The Big Question: What did !@### equal?

Mathematician’s Toolbox: Have I seen a similar problem?/Test all Possibilities

Solving: First I used the first clue to figure out what  is ! and #. I evened it and got the following results !=25 and #=1. After that I used the second clue by taking away 25 from the total and was left with 15 then I divided that by 3 because there were 3 symbols and got @=5. Then I added them all up: 25 + 5 + 1 + 1 + 1 = 33.

Conclusion: So the answer was 33.

September 8

Maths Mate Sheet 5 Question 23 (Term 3 2014)

Prediction: I predict this problem will be about code breaking and patterns.

Read: An archeologist found some ancient numbers written as follows: (I’ll use keyboard symbols instead).

$$ For 72        $%% For 48    and    %&&& For 9   What did $%%&& equal?

Clarification: None needed.

The Big Question: What did $%%&& equal?

Mathematician’s Toolbox: Have I seen a similar problem?/Test all Possibilities

Solving: First I used the first clue to figure out what $ is. Since there were only 2 $ symbols I halved it and got 36. Then I moved on to the second clue I first took 36 six away from 48 because that ions out the symbol we already know, after that I was left with %% is 12 so I halved it and got 6 for each %. Before I went onto the equation I looked at the third clue. I took away six from nine ,because % is six, and then I was left with the total 3 and 3 symbols so that means & equals 1. Then I added them all up: 36 + 6 + 6 + 1 + 1 = 50.

Conclusion: So the answer was 50.

September 8

Maths Mate Sheet 7 Question 23 (Term 3 2014)

Prediction: I predict this problem will be about code breaking.

Read: An archeologist found some ancient numbers written as follows: (I’ll use keyboard symbols instead).

!!@@ For 202        !### For 130    and    ##@@@ For 23   What did !#@@@ equal?

Clarification: None needed.

The Big Question: What did !#@@@ equal?

Mathematician’s Toolbox: Have I seen a similar problem?/Test all Possibilities

Solving: First I used my test all possibilities strategy and the first clue to find that ! is 100 and @ is 1 because 100 + 100 + 1 + 1 = 202. Then using the second clue I figured out that # equals 10 because 100 + 10 + 10 + 10 = 130. So then I added it all up: 100 + 10 + 1 + 1 + 1 = 113

Conclusion: So the answer was 113.

September 2

Maths Mate Sheet 6 Question 23 (Term 3 2014)

Prediction:I predict this problem will be about coding, because of the strange symbols.

Read: An archeologist found some ancient numbers written as follows: (I’ll use keyboard symbols instead)

$$£ for 33.    $€€€ for 28.  And €££ for 6.  What did $€€£ equal?

Clarification: None needed.

The Big Question: What did $€€£ equal?

Mathematician’s Toolbox: Look for a pattern/Test all possibilities

Solving: First I tried to use the first clue to work out what $ means. After I’d tried many ways I came up with 16 = $ and 1 = £. I then skipped the second clue and went onto the third.  Since I know £ is one I take away two from six which is 4, so that’s what € is. Now we’ll add the amounts up. 16 + 4 + 4 + 1 = 25.

Conclusion: So the answer was 25.

August 13

Maths Mate Sheet 4 Question 24 (Term 3 2014)

Prediction: I predict this problem will be about distances.

Read: Towns A to F are connected by fibre optics cables along existing roads. Calculate the minimum length of cable required.

Clarification: None needed.

The Big Question: Find the minimum length of cable.

Mathematician’s Toolbox: Test all possibilities.

Solving: I saw all the ways the towns could be connected and came up with multiple equations. The one that I found to have the lowest out come was 18 + 22 + 16 + 23 + 15 = 94.

Conclusion: So the answer was 94.

August 13

Maths Mate Sheet 3 Question 23 (Term 3 2014)

Prediction: I predict this will be a problem were I’ll have to complete a sum.

Read: Fill in the missing digits in the subtraction.

8-6

–75

=43-

Clarification: None needed.

The Big Question: Complete the subtraction.

Mathematician’s Toolbox: Have I seen a similar problem?

Solving: I first worked out the missing digit in the units column would be 1 because 6 minus 5 is 1. Then I figured out that the digit in the tens would be 0 because since you can’t take away 7 from 0 you must borrow to make 10, and 10 take away 7 is 3. Now to work out the last digit you must realize that the 8 is now 7, since the end number has a 4 in the hundreds we know that the last digit must be 3. This is because 7 minus 3 is 4.

Conclusion: So the answer was

806

-375

=431