*“***Mathematics is, in its way, the poetry of logical ideas.” Albert Einstein**

**Mathematics is, in its way, the poetry of logical ideas.” Albert Einstein**

## Since we all want to help our children learn math, it is often tempting to say, “The way you solved that problem was great, but now let me show you a faster way.” The most important thing to remember when engaging your children in mathematical problem solving is to support them to solve problems using their own strategies.

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### NUMBER ROUND UP

*This problem is an interesting context in which younger children can practice addition, and it can be solved in a variety of ways.*

### USE THE NUMBERS 1-6 IN EACH SET OF CIRCLES BELOW.

The sum of each side of the triangle should equal the number in the center of the triangular shape.

*For Your Youngest Children – *you may want to cut out the numbers 1-6 as pieces. This will allow for easy manipulation of the numbers’ positions.

#### Number Round Up -Template

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### WILL’S MARBLES involves complex reasoning about fractions that will challenge your children’s understandings of the concepts involved. It is a good example of how fractions relate to multiplication and division.

~Ages 7-11

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WILL’S MARBLES

### Will and his friend Sam walked along the road together. Will had a big bag of marbles.

### Unfortunately, the bottom of the bag split and all the marbles spilled out. POOR WILL!!

### One third (13) of the marbles rolled down the hill too quickly for Will to pick them up. One sixth (16) of all the marbles disappeared into the rain-water drain!

### Will and Sam picked up all the marbles they could, BUT half (12) of the marbles that remained nearby were picked up by other children who ran off with them!

### Will counted all the marbles he and Sam had rescued.

### Will gave one third (13) of these to Sam for helping him pick them up. Will put his remaining marbles into his pocket. There were 14 of them.

### How many marbles were there in Will’s bag before the bottom split?

### What fraction of the total number that had been in the bag had he lost or given away?

*Getting Started – How many marbles did Will and Sam rescue?*

How might this help you to work out the number of marbles which Will had before the bag *split?*

How might this help you to work out the number of marbles which Will had before the bag

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*SOLVING – w***e need to work backwards, beginning with the last part, and ending with the first.**

**e need to work backwards, beginning with the last part, and ending with the first.**

- Will walks away with 14 marbles, 2/3 of what was recovered. His friend walks away with 1/3 of what was recovered. 14 is 2/3 so to find out 1/3 I then half 14, getting 7. Sam had 7 and Will had 14. A total rescued of 14 + 7 = 21.21 is half (1/2) of what was lying around on the ground, the other half having been taken by the children. To find how many were on the ground nearby, we need to double 21. NOW, we have an answer of 42!

- 42 must be doubled to get the final answer, as 1/3 and 1/6 went down drains or hills (1/3 + 1/6 = 1/6 + 2/6 =1/2).

- This gives us a final answer of 84 marbles in the bag.

To find out what fraction of the marbles Andy had given away or lost you have to find the fraction of marbles he was left with. He was left with 14 out of 84 marbles (14/84). You then work out the fraction in its lowest form. Firstly divide 14 and 84 by 2 to get 7/42 then divide them by 7 to get an answer of 1/6. However 1/6 is what he is left with so he must have lost or given away 5/6 of his marbles!