Maths Mate Term 4 Sheet 4 Question 24

Predict: I predict that this question will be about addition and money.

Read: How much is one book according to the diagram?

Book x2 + Paint pallet = $ 45

Book x4 + Paint pallet = $85

Clarify: I had nothing to clarify in this question.

Mathematician’s toolbox: The strategy I used from the mathematician’s toolbox was to test all possibilities.

Big question: The big question is how much does one book cost.

Solve: Firstly, I started at the first diagram. Two books plus one paint pallet is $45. I tried making them $15 each, but then 5 groups of 15 was more than 85. Then I tried making the books $20 and the paint pallet $5. This worked for $45, and it also worked on $85. So the answer was $20.

Summary: This problem was quite easy to solve, but I’m still surprised that a paint pallet was $5. It must have been bad quality.

Maths Mate Term 4 Sheet 3 Question 22

Predict: I predict that this question will be about multiplication.

Read: Fill in the missing number. 8 x [?] = 56

Clarify: I had nothing to clarify in this question.

Mathematician’s Toolbox: The strategy I used was prior knowledge.

Big question: The big question is what times 8 is 56.

Solve: Firstly, I though, and because I have some trouble with the times tables near 50. I had some thinking time at the start. Then I realised that I had know it before, I just had to clarify. 8 x 7 = 56, so that is the answer.

Summary: This problem wad easy to solve if you had memorised your times tables.

Maths Mate Term 3 Sheet 5 Question 22

Predict: I predict that this question will be about the four operations.

Read: I think of a number, divide it by 2 and then add 12. If the result is 20, then what was the original number?

Clarify: I had nothing to clarify in this question.

Mathematician’s Toolbox: The strategy I used from the mathematician’s toolbox was to work backwards.

Big question: The big question is what was the original number?

Solve: Firstly, I used inverse operations and worked backwards. First, I subtracted 12 from 20, and that was 8. Then it said that it was divided by 2, so I multiplied 8 by 2. That was 16, now I had to clarify. 16 divided by 2 is 8, add 12 is 20. The answer is 16.

Summary: To solve this problem, you would have to work backwards or test all possibilities. Working backwards was faster.

MAths MAte term 3 sheet 2 question 21

Predict: I predict that this question will be about addition.

Read: The sum of three consecutive whole numbers is 96. What are the three numbers?

Clarify: I had nothing to clarify in this question.

Mathematician’s Toolbox: The strategy I used from the mathematician’s toolbox was to test all possibilities.

Big question: The big question is what are the three numbers.

Solve: Firstly, I knew that 30 x 3 was 90, so then I knew that all I had to do was find three consecutive numbers added together to equal six and add one to each 30. 1, 2 and 3 equalled 6, so I added them to 30. The answer I got was 31, 32 and 33.

Summary: This problem was easy to solve if you knew addition.

 

Maths Mate Term 3Sheet 1 Question 22

Predict: I predict that this question will be about addition.

Read: The sum of two consecutive whole numbers is 97. What are the two numbers?

Clarify: I had nothing to clarify in this question.

Mathematician’s Toolbox: The strategy I used from the mathematician’s toolbox was to work backwards.

Big question: The big question is what two consecutive numbers equal 97?

Solve: Firstly, I divided 90 by 2, which was 45. Then I knew that 4 and 3 was 7, and they were consecutive, so I added them onto 45 and 45 so that the two numbers were now 48 and 49, and when added together they were 97. So the answer is 48 and 49.

Summary: This problem was quite easy to solve if you knew what the word consecutive meant.

Maths Mate Term 2 sheet 5 Q 22

Read: A single digit number sits in each circle, and it must equal the difference between the two numbers it sits on. What number belongs in the shaded circle?

 

Clarify: I had nothing to clarify in this question.

Mathematician’s toolbox: The strategy I used from the mathematician’s toolbox was test all possibilities

Big question: The big question is what is the number in the shaded circle.

Solve: Firstly, I found the difference between the 1 and 9 on the bottom row. It was 8, so I put that in. Then 9 and 9 was 0, so I put that in. 8 and 0 was 8, and then I worked out that because of the 5 at the top, 3 must be the number next to the 8. Then I worked out that the difference between 0 and something was 3, and that number was 3, and then the difference between 9 and something was 3, and that number is 6, and 6 is in the shaded circle. The answer is 6.

 

Summary: This question was one where you had to work backwards.

Maths Mate Term 2 Sheet 3 Q22

Predict: I predict that this problem will be about addition.

Read: Four erasers cost as much as two pairs of scissors. How much is one pair of scissors, if one eraser is $1.50?

Clarify: I had nothing to clarify in this question.

Mathematician’s toolbox: The strategy I used from the mathematician’s toolbox was ‘Have I seen a similar problem?’

Solve: Firstly, I remembered that some of the previous problem were like this, so I solved this one in the same way as I solved the others. Four erasers cost as much as two pairs of scissors, and one eraser is $1.50, so that means that two erasers cost as much as one pair of scissors, and two erasers cost $1.50, and $1.50 + $1.50 = $3.00. So one pair of scissors costs $3.00.

Summary: This problem was very easy to solve, and it didn’t take much time, but you just had to get the equations in your head first.

Maths Mate sheet 7 Q:23

Predict: I predict that this will be about addition

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

Clarify: I had nothing to clarify.

Big question: The big question is what two digit number have a digit sum of nine.

 

Solve: First, I tried finding the first number that had a digit sum of nine. The first one was 18, which was 1+8. Then I tried finding the next one. I had to the to go into the 20′s, and it was 27 because 2+7 is 9. You had to go down one in the unit’s and up one in the tens. All the number were in the nine times tables and this was the list: 18, 27, 36, 45, 54, 63, 72, 81 and 90. So there are 9 two-digit numbers with a digit sum of 9.

Maths Mate term 4 sheet 1 question 23

Predict: I predict that this problem will be about the order of operations.

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

Clarify: I had nothing to clarify.

Big question: The big question is what was the original number.

 

Solve: To solve this problem I worked out the answer by doing the sum backwards. The answer to the sum is 6, and before getting to 6 the person divided a number by three. 6 x 3 = 18, and 18 divided by 3 equals 6, so now we have 18. Now because the person subtracted 5 from the original number, we need to add 5 to 18. 18 + 5 = 23, so now we know that the original number was 23.

 

Maths Mate term 4 sheet 2 question 23

Predict: I predict that this question will be about problem solving and patterns.

Read:  Deduce the 3 digit number. [A cow means a number is correct in value but in the wrong position. A bull shows that a number is both correct in value and is in the right position.

 

Clarify: I had nothing to clarify.

Big question: The big question is what is the secret number.

 

Solve: First I looked at all the columns to see what they had. The 1st row had 456, and 2 cows. On the 2nd row they 957, so the 5 had been kept, but there were no cows and no bulls, so 4 and 6 must have been right. In the last row, there were 2 cows, and 7 had already been eliminated in the last row, and 6 was already in the right place on the first row but had been moved, so 8 must be in the middle of 4 and 6 because their right positions were at the start and end. So the secret number is this: 486.