Activities here range from counting up through algebra. All have a hands-on, non-workbook approach to math.

Page contents:

Estimate and Measure

How Much Is A Thousand?

Family Math games:

Egg Carton Numbers

Button Sorting

Two-Dimensional NIM

Value of Words

Double Digit

Pico, Fermi, Bagels

Three Bean Salads

#### ESTIMATE AND MEASURE

Gather whatever tools you have for measuring—rulers, tape measure, scales, measuring cups. Choo se items to be measured using the various tools. List items to be measured down one side of a paper and make 3 columns for an estimate, a measurement, and the difference between the two. This was a favorite activity for my children for a number of years, and I used to make up a “measure paper” whenever I needed to keep them occupied and happy for a while. I made the lists and they estimated, measured and computed the difference, but children could make lists for themselves or for a sibling.

#### How much is a thousand?

One day my 5-year-old son asked me if a thousand was a lot bigger than a hundred. He could count to 100 but couldn’t picture 1000. I told him that, just like it took ten tens to make 100, it took 10 100’s to make 1000. Then I took a gallon jar filled with dried beans from the shelf and asked him how many beans he thought were in it. He was used to estimating, so we both took a guess and then asked others in the family for their estimates and wrote them all down. For about a week, anyone who came by was shown the jar and asked to estimate. Then we started counting. We had plastic placemats that we used to count out 10 piles of 10 beans, and he knew that was 100. Each 100 was dumped into a paper cup. We didn’t do them all at once. Visitors were often asked to count 100 beans so it never got tedious for anyone. We counted the paper cups saying 100, 200, etc instead of 1, 2, 3 and when we reached 1000, we dumped all the beans in the cups into a quart canning jar and kept on counting the ones into piles of 10 and dumping the 10 piles into the cups again. My son enjoyed this project and I think it gave him a sense of the relationship of place values. We talked about how the process would continue to reach a million but didn’t actually do it.

#### Family Math Games

We’ve found the book “Family Math,” by Jean Kerr Stenmark, Virginia Thompson and Ruth Cossey, which is fairly cheaply available used at Abe Books, helpful in making math accessible and enjoyable for kids of different ages. This was the source of the games about which our students at the afterschool program declared that they couldn’t possibly be math because they were fun.

Here are a few of their activities, from counting up through algebra, ranked approximately in rising order of age/complexity:

#### Egg carton numbers

*getting basic experience with numbers*

Label the sections of an egg carton with the numbers 1-12.

Then have your child count out small objects (beans, buttons, pennies…) into the sections: one bean in the section marked 1, two beans in the section marked 2… Make sure you have plenty of your chosen objects; you’ll need 78.

#### Button sorting

*observing similarities and differences, applying abstract categories to the real world; also a foundation for learning about sets/Venn diagrams*

Give your child a collection of buttons to sort in any way they like.

After they’ve done this, come and ask how they sorted them (by size, shape, color, hole number…)

Offer some more buttons for them to sort in the same way.

Then ask if they can picture any different way of sorting the same buttons.

Some ways may involve several categories (red buttons, white buttons, yellow buttons…) Others may involve a steady progression (lightest to darkest, smallest to largest…) Others still may involve binary sorting: green buttons and not-green buttons, round buttons and not-round buttons.

If you don’t have a button box, any other small objects that differ from each other in several ways will work.

#### Value of Words

*arithmetic, mental addition, estimation, problem-solving*

Write out the letters of the alphabet and assign them rising dollar values: A=$1, B=$2, C=$3, etc.

Then have your child add up the value of the letters in their first name.

Can they guess which family member has the priciest name?

Can they find a word worth $50? Worth $100?

#### Double Digit

*Place values, estimation*

Make score sheets for each player, like this:

TENS | ONES |

1. | |

2. | |

3. | |

4. | |

5. | |

6. | |

7. |

Players take turns rolling a die. Each player gets exactly seven turns.

At each roll, the player may record the number either in the tens column or the ones column. If it’s entered in the tens column, enter a 0 opposite it in the ones column. Thus a 4 entered in the tens column counts as 40.

After each player has rolled seven times, the players add up their numbers. The person who has gotten closest to 100—*without going over 100*-wins.

(Additional notes from the next page: The leader should have the target number written down and look at it as they give clues. Players should keep a record of guesses and responses.

Variations: allow repeated digits; guess longer numbers; play with letters that form three-, four-, or five-letter words)

#### Three Bean Salads

*Ratios and proportions; algebra*

Explanation from the book:

“The language of ratio and proportion is ver important in present-day mathematics. A **ratio** is the numerical relation between two quantities, usually determined by dividing one of the numbers by the other and expressing the result as a fraction or a percent. For example, a business might determine its ratio of assets to liabilities by dividing the value of the assets by the value of the liabilities…**Proportion** is a statement that two ratios are equal. For example, the ratio 1/2 is the same as the ratio 3/6 or 2/4. This is an important idea in algebra, since if any three of the numbers in a proportion are known, the fourth can be found–this is the “unknown” in algebra problems.”

Three Bean Salad recipes let students solve rather difficult algebra problems in a straightforward, hands-on way, and also to set up their own problems. In our afterschool program we noticed that kids who said they hated or weren’t good at math enjoyed and were able to think clearly about three-bean salad making.

You’ll need three different types of beans (or other small objects). All three types must go into each salad. Let students start by guessing numbers that might work, and then adjust until the recipe’s conditions are satisfied.

“For each salad, determine how many of each of the three types of beans (red beans, lima beans, and black-eyed peas) are needed.

1. This salad contains:

2 Lima beans

Twice as many Red beans as Lima beans

10 beans in all

2. This salad contains:

4 Red beans

1/2 as many Black-eyed peas as Red beans

10 beans in all

3. Lima beans make up 1/2 of this salad:

The salad has exactly 2 Red beans

The number of Lima beans is double the number of Red beans

4. This salad contains:

The same number of Red beans as Lima beans

3 more Black-eyed peas than Red beans

A total of 18 beans

5. This salad contains 12 beans

1/2 of the beans are Red

Lima beans make up 1/4 of the salad

6. This salad contains at least 12 beans

It has one more Lima bean than Red beans

It has one more Red bean than Black-eyed peas

7. This salad contains:

3 times as many Red beans as Black-eyes

One more Lima bean than Red beans

8 beans in all

8.This salad contains:

An equal number of Red beans and Black-eyed peas

5 more Lima beans than Red beans

No more than 20 beans

Make up a different salad.

Write instructions for someone else to make your salad.”

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