Mathsmate: Term 3, Sheet 2

Problem 22: Carl looked at the page numbers on the open book in front of him. The left and right page numbers added to 333. What were the page numbers?

Predict: I predict I will need to use division and addition in this problem.

Clarify:  I have no words, sentences or phrases to clarify.

Find the big question: What are the page numbers?

Solve:

  1. I need to start by splitting 333 in half, because they need to be consecutive. Picture a book, the page numbers are consecutive,, aren’t they?
  2. It is 166.5 but I will round that up to 167.
  3. 167+168=335.
  4. So I will round down to 166.
  5. 166+167=333!

Summary:

The mathematicians toolbox strategy I used in this problem was break it into manageable parts.

Mathsmate Term 3 Sheet 1

Problem 22: The sum of two consecutive whole numbers is 97. What are the two numbers?

Predict: I predict that I will need to use division adn addition in this problem.

Clarify: I have no words, sentences or phrases to clarify.

Find the big question: What are the two numbers?

Solution:

  1. The first thing I did was divide 97 by 2= 48.5
  2. but they are consecutive whole numbers. 
  3. So I rounded up to 49. But 49+50=99, not 97.
  4. So I rounded down to 48. 48+49=97!

The answer is 97.

Summary: The mathematicians toolbox strategy I used is this problem was work backwards.

Maths mate Term 2 Sheet 8

Problem 23: if you could roll the same number every time, what number would you choowe so that you could move from S to F in the least number of rolls.

image

 

Predict: I predict that this problem will take a lot of trial and error.

Clarify: I have no words, sentences or phrases to clarify.

Find the big question: What number would get me to the finish in the least amount of rolls?

Solution:

In this problem I am just going to test out each Number and how many rolls it will take. For each number I wrote it down, but I remembered to keep in mind the snakes and ladders!

Theses are my results:

1- infinite

2- five rolls

3- infinite

4- infinite

5- infinite

6-  infinite.

The answer is 2.

Summary: the mathematicians toolbox strategy I used in this problem was trial and error, and make a list.

Mathsmate Term 2 Sheet 7

Problem 23: Jack’s car can travel 15 kilometres per litre of petrol. He leaves Dubbo with 30 litres of petrol in his car and drives towards Maitland. Which town will he be closest to when he runs out of petrol?

Dubbo——-200 km———Wellington—-100 km—Mudgee—-150 km——Singleton——-200 km———-Maitland.

Predict: I Predict that I will need to use multiplication in this problem.

Clarify: I have no words, sentences or phrases to clarify.

Find the big question: Which town will he be closest to when he runs out of petrol?

Solution:

  1. First we need to find out how many kilonmetres he can travel on 30 litres of petrol.
  2. So we need to multiply 30 by 15: which equals 450.
  3. So he can travel 450 km on 30 litres of petrol.
  4. So, on the map, from Dubbo, add on 450 km.

+                     =300              +                   =450. 

Dubbo——-200 km———Wellington—-100 km—Mudgee—-150 km——Singleton——-200 km———-Maitland.

The answer is Singleton.

Summary: the Mathematicians Toolbox strategy I used in this sum was break the problem into managable parts.

 

 

 

 

 

Maths mate Term 2 Sheet 6

Problem 23: Jane rolls nothing but sixes in the game of snakes and ladders bellow. How many rolls of the die will it take her to move from S to F?

Snapshot 40

Predict: I predict I will need to use addition in this problem.

Clarify: I have no words, sentences or phrases to clarify.

Find the big question: How many rolls will it take to get from S to F, if she only rolls sixes?

Solve:

  1. Jump 6 places ahead, or add 6 to 0.
  2. Land on 6, it is a ladder, so move up to number 9.
  3. Jump 6 places ahead, or add 6 to 9..
  4. Land on 15, it is a snake, so move down to number 11.
  5. Jump 6 places ahead, or add 6 to 11.
  6. Land on 17, it is another snake, so move down to number 2.
  7. Jump 6 places ahead, or add 6 to 2.
  8. Land on 8.
  9. Jump 6 places ahead, or add 6 to 8.
  10. Land on 14.
  11. Jump 6 places ahead, or add 6 to 14.
  12. Land on F!
  13. Count how many times we rolled the dice.

 

The answer is 6.

 

Summary:

In this problem the mathematicians toolbox strategy I used was act it out.

 

 

 

Maths mate Term 2 Sheet 3

Problem 22: Five ballpoint pens cost as much as two fountain pens. How much are 6 fountain pens if one ballpoint pen costs $1?

Predict: I predict in this problem I will need to use division.

Clarify: I have no words, sentences or phrases to clarify.

Solution:

  1. We know that one ballpoint one costs $1.
  2. 5 ballpoint pens are $5.
  3. We need to divide 5 by 2 to know how much a fountain pen is.
  4. A fountain pen is $2.50
  5. We need to either add 2.50 to 2.50 6 times, or times 2.50 by 6.
  6. $2.50 x 6= $15.00

 

Maths mate Term 2 Sheet 2

Problem 22: Two compasses cost as much as three protractors. How much are six protractors, if one compass is $3?

Clarify: I have no words, sentences or phrases to clarify.

Find the big question: How much are six protractors?

Solution:

One compass is $3, so two compasses are $6. If three protractors cost as much as two compasses, we need to divide $6 by 3= $2. So each protractor is $2, then $2 x 6=$12! Six protractors are: $12.

Summary: The mathematicians toolbox strategy I used in this problem was break the problem into manageable parts.

Maths mate Term 2 Sheet 1

Problem 23: fill in the missing digits.

3 _
+ _ 8
——
6 5
Predict: I predict I will need to use addition in this problem.

Clarify: I have no words, sentences or phrases to clarify.

Find the big question: what are the missing numbers?

Solution: First, 8+ anything can’t equal 5 so it must equal 15 or any other number ending in 5. So, 8+7=15, so I’ll put the 7 in the box above the 8, and carry a one the above the three. So, I add the 1 to the 3=4, so 2+4=6, so I’ll put the 2 below the 3! Done!

Summary: the mathematicians toolbox strategy I used in this sum was break the problem into manageable parts.

 

Maths mate Term 1 Sheet 7

Question 22: Draw the missing figure.

image..

Predict: I predict that this will be a pattern problem.

Clarify: I have no words, sentences or phrases to clarify.

Find the big question: What is the missing figure?

Solution: the bottom row has a rectangle body and an oval body, so it must be a triangle body. The arms in the diagonal row, which has the box in it, all have straight arms. So there must be straight arms. Add the circle head and the legs, done!

Summary: The mathematicians toolbox strategy I used in this problem was work backwards.

Maths mate Term 1 Sheet 6

Question 24: Enter numbers in the circles so that numbers in each line equal the sum of the numbers on each end.

Predict: I predict that I will need to use division and addition in this problem.

Clarify: I have no words, sentences or phrases to clarify.

Find the big question: What numbers go in the circles?

Solution:

1. What adds up to 12? 6+6.

2. 6+?=18? 6+12=18.

3. Check- 6+6=12, 6+12=18, 6+12=18!

Summarise: The mathematicians toolbox strategy I used for this sum was break the problem into managable parts.