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# CHEAT SHEET

## Table of Contents

❶Solutions to Check Your Progress Problems.

## Solutions by Chapter

Make a th Day Necklace. Show your kindergartener how to count to by tens, and he'll get an adorable cheerio necklace in the process! Try a th Day of School Scavenger Hunt with your preschooler, and send her on the search for objects of different colors!

Have your student draft a blueprint for a haunted house, and trick or treat them into learning about geometry in the process. Halloween is approaching, so why not create some ghost flash cards that will help your child learn her numbers the spooky way. Make a Menorah Light Chart. Your child can brush up on her math skills by charting the length of time that each candle on the menorah takes to burn.

Make a Christmas Addition Tree. The Christmas Addition Tree is a great way to get kids actively involved in math practice through art projects over the holiday break. Make a Pumpkin Math Book. Construct a Kid Size Cardboard Castle. Help your little builder move up in the world with this recycled cardboard castle that's just the right size for a young king and his loyal stuffed subjects.

Here's how you and your child can work together to craft your own story problems from scratch. How to Paint like Georgia O'Keeffe. Show your child how to paint in true Georgia O'Keeffe style. He'll enjoy painting art inspired by a master, and boost his math skills, too. Introduce your child to science with something she sees everyday--her shadow! Count and Sort Fruit Salad. In this fun snack-time activity, kids boost counting, sorting, and color recognition skills as they make a delicious and nutritious snack.

Help your child apply his math skills the next time you cook a family meal similar to one you'd buy at a restaurant. This fun activity encourages her to develop her skills in not only taking measurements, but also in working with the measurements themselves.

Autumn More or Less. Encourage you child to compare and contrast a wide variety of autumn-themed items as she learns to weigh the various objects and record her findings. Your child can count out six pumpkins or six crayons, but what is a six all by itself? This competitive inequalities card game is a great way to help your child understand the connection between numerals and the values they represent. But first, we have to verify your age!

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Thus we make a diagram that allows us to concentrate on the essential information. See the figure at the left. Because there are many routes, we consider the similar but simpler diagrams shown below. The number at each street intersection represents the number of routes from point A to that particular intersection.

It appears that the number of routes to an intersection is the sum of the number of routes to the adjacent intersection to its left and the number of routes to the intersection directly above. For instance, the number of routes to the intersection labeled 6 is the sum of the number of routes to the intersection to its left, which is 3, and the number of routes to the intersection directly above, which is also 3.

Review the Solution Ask yourself whether a result of 35 seems reasonable. If you were required to draw each route, could you devise a scheme that would enable you to draw each route without missing a route or duplicating a route? The number in each hexagon represents the total number of different routes that a ball from A can take to reach the top of that particular hexagon.

A ball dropped from A on striking the vertex of an hexagon has equal probablility of going to either left or right. So the ball can have many different routes to reach a paticular hexagon. When the ball touche a vertex, it can either go left or right. To find the total number of possible routes between two point, concentrate on the initial and final point and proceed by first considering motion in one particular direction, say left, this will give one route.

Now, the other route will be the one with all the initial motion in left direction and final motion towards right. Then consider the next possibility where the second last motion is towards right and so on. Write the number of routes in each hexagon and then look for a pattern. From the diagram considered above, a pattern can be observed that, all the outer hexagons have 1 inside them. So, Hexagon B and F will have value 1. Also note that all hexagons other than the outer ones have value equal to the sum of values of two hexagons on the above row sharing boundary with the hexagon under consideration.

Hence hexagon C has value , hexagon D will have value , hexagon E will have value. Carry Out the Plan: Using the pattern discovered, it was found that, hexagon C has value , hexagon D will have value and hexagon E will have value 4.

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