# Simple Geometry Ideas that Take about 20 Minutes

Secret Shapes

Print out two copies of these shapes and cut them out. Place one of each shape in a file folder marked Secret Shape. One child is the leader, picks a file folder, and answers Yes or No questions about the Secret Shape. Place the cut out shapes on the table for kids to sort as they ask questions.

3D Shape Books

Make a page in a booklet for each of the 3D shapes (spheres, rectangular prisms, cylinders, and cones). Search in a magazine for the 3D shapes found in everyday objects. Cut out and glue them in your own 3D Shape Book.

Construction Flagging Shapes

Construction flagging tape is used by construction workers to, for example, rope off a new slab of concrete in the sidewalk. It costs only a few dollars per roll and can be found in home improvement stores and online. It isn’t sticky (though the name implies this), does not tangle like yarn does, and because it must be seen from a distance, flagging tape comes in fun fluorescent colors. You can use it to learn geometry by tying the ends together to make a loop about 40 feet long. Find a wide-open space and have 4 or 5 kids grab on to the flagging (you might have to get in on the action or invite the neighbor kids over). Can you make 2D and, gulp, 3D shapes? Talking together about the attributes of the shapes and working cooperatively to create them supports purposeful math-positive vocabulary development. Most of all, it’s fun mathematics education for even the most math-panicked parents!

Transform (adapted Copley, 2010)

Use playdough (or use homemade salt dough) to make 3D shapes then transform them into new shapes. For example, make a sphere then transform it into a cylinder by flattening the ends. Make rectangular/triangular prisms, cubes, pyramids, spheres, cones, and cylinders.

# Simple Measurement Ideas that Take about 20 Minutes

Explore the coin values with this concrete area model using grids. All the instructions are given in the video description here:

Click here to download the grid pieces to make your own set.

Three Act Tasks

Three Act Tasks are short video clips with real-world math modeling sequences. The video linked here is from the UHouston Math Youtube channel. This 90-second video gets kids wondering, How many drink cups can be filled with one 2-liter bottle of soda? What other Three Act Tasks can you find online for measuring volume? Try a few together!

Clay Worm Comparisons

Materials: playdough, activity sheet (download here)

Instructions: Have children roll out and place a worm on each of the worm drawings on the activity sheet. Then have children order the worms from shortest to longest. They can place the worms on a blank sheet of paper and trace around them for a permanent record of their work, if desired.

Turtle Pond, an interactive activity on the National Council of Teachers of Mathematics website, uses simple computer programming commands to move a turtle through a maze. Try it out with children for a fun introduction to 15-, 30-, 45-, 60-, 75-, and 90-degree angles.

# Simple Number Ideas that Take about 20 Minutes

Domino Parking Lots Addition Game

Print out a free Domino Parking Lot mat. The PreK Parking Lot goes up to 10. The Kindergarten through 2nd Grade Parking Lot goes up to 16. Next, sort your domino set. For PreK, you'll need total pips of up to 10. For older kids, you'll need total pips of up to 16. If you don't have dominoes, you can print some from the internet and cut them apart.

To Play: Take turns picking a domino out of a bag. Add the total pips and place the domino on the correct parking spot. For instance, if you pick a domino with 5 pips and 8 pips, it goes on the 13 parking spot. The winner is the person who, after all the dominoes have been used, has the tallest stack on any one parking space on their mat.

Base Ten Riddles

Play Base Ten Riddles (Van de Walle, Karp, and Bay-Williams 2019) to practice place value. Have children build the number with base ten blocks (use these online base ten pieces), draw, or write as you give clues. Here are a few to get you started, then work together to make up some new riddles.

• I have 23 ones and 4 tens. Who am I? (63)

• I have 4 hundreds, 12 tens, and 6 ones. Who am I? (526)

• I have 30 ones and 30 hundreds. Who am I? (3,030)

• I am 450. I have 250 ones. How many tens do I have? (20)

• If you put 30 more tens with me, I would be 1015. Who am I? (715)

Watch McGregor, a third grader, solve a few Base Ten Riddles.

The Sum What Dice Game

Have children write the digits 1 through 9 on a paper. Take turns rolling two dice. On each turn, the player may cover either the sum rolled on the dice or any two numbers that are still uncovered and that add to the sum rolled. For example, if a sum of 8 is rolled first, the player may cover: 8, or 1 and 7, or 2 and 6, or 3 and 5. Later in the game, if the sum of 8 is rolled again and the 5 is already covered, then the player cannot use the 3 and 5 combination and must play one of the other open possibilities. When a player cannot play, they are out and have a score of the sum of the uncovered numbers. Play continues for remaining players until everyone is out. The last person to go out will not necessarily win; the person with the lowest score wins. (Stenmark, Thompson, and Cossey 1986)

Watch McGregor and first grade brother, Quinn, play

the Sum What Dice Game.

Scaled Drawings

Scaled drawings can be fun ways to integrate art with math and think about multiplication as scaling (resizing). Each person draws a simple design with straight-ish lines (pine trees, sail boats, and flags work well) on a piece of centimeter grid paper. Trade papers and “blow up” the picture by making all the lines 2 times longer. For example, if drawing a pine tree, the trunk on the original might be 6 centimeters long and 2 centimeters wide, but on the scale drawing the trunk is drawn 12 centimeters long and 4 centimeters wide. Children might have to tape together several sheets of centimeter paper to have enough space for their double-sized drawing. Now make a scale drawing that is half as big as the original. This time the pine tree’s trunk is 3 centimeters long and one centimeter wide. Display all three masterpieces together and show off how multiplication by a whole number or a fraction resizes the drawings. This is an art and math project worthy of hanging on the fridge!

Sums of Ten Go Fish

Remove the face cards from a deck of playing cards. Each player gets seven cards. The rest of the cards are the fishing pond. Players look in their hand for two cards with a sum of 10 (number bonds for 10--examples shown here). If they find a number bond, they set it aside. Take turns asking other players for the card needed to complete a number bond. For example, if you have a 5 in your hand, ask another player for a 5. If they don’t have a 5, you “Go Fish” by picking up a card from the fishing pond. The winner is the player with the most number bonds for 10 when all the cards have been used.

From Math-Positive Mindsets page 150

Math-Positive Mindsets: Growing a Child's Mind without Losing Yours is filled with quick tips for adding a bit of math to the day. Here is an example of a Pause-ative Box (a play on the word positive) with an idea perfect for kids stuck at home in quarantine.

From Math-Positive Mindsets page 132

Do something with that stack of flower pots in the garage! Math! All you need for this activity are pots labeled with the digits (I used 0-5 in this video), and flower cutouts with number sentence (adding up to 5).

The Coin Trading Game offers fun practice with coin values and explicit trading between pennies, nickels, and dimes. You can find it on page 83 of Math-Positive Mindsets: Growing a Child's Mind without Losing Yours.

Watch a video of my sons playing The Coin Trading Game here.

Wrapping Paper Sets

Materials: wrapping paper scraps, markers

Instructions: Have children circle sets of two objects, such as two teddy bears, two presents, or two balloons—whatever pattern is found on the wrapping paper. Next time, have students circle sets of three, four, or five.

# Simple Sorting, Graphing, and Data Analysis Ideas that Take about 20 Minutes

Can Sorting/Graphing

Have children clean out the pantry or food storage area and sort the cans—fruits, vegetables, soups, and so on. Children arrange the cans in rows then make comparisons. (This is a concrete bar graph, meaning it is made of real objects instead of pictures.) Use terms like most, least, more than, less than, and equal to in your discussion. Note that data analysis is all about making informed decisions. What should you buy next time you're at the store? Soup? Fruit? What do we eat a lot of and what do we turn our noses up at?

Mean, Median, and Mode Shopping List Planning

Imagine that the pantry graph showed 8 cans of soup, 10 cans of fruit, and 15 cans of vegetables. Talk with children about which measure of central tendency (median, mean, or mode) is most useful in planning a grocery trip.

• The mean would tell us the average number of each type of food in the pantry. We add up all the cans then divide by the number of categories. 8 + 10 + 15 = 33 33 ÷ 3 = 11 Should we buy 3 cans of soup and 1 can of fruit to make it “even”?

• The median describes the middle number in the data set. If we list the number of cans in each category in order from smallest to largest—8, 10, 15—the median would be 10. Would we buy 2 cans of soup to make it reach the median?

• The mode is the number that occurs most often in a set of data. In our pantry example, we have no mode because no number appears more often than any other.

Shoe Sorting/Graphing

Does your pile of shoes look like the Cutler family's? What a mess. McGregor sorted the shoes and made a real-object bar graph. Looks like we have a lot of flip flops!

Stuffed Animal Sorting/Graphing

Children can use real objects, pictures, and graphs to represent data and make simple comparisons between sets of data: “Let’s use stuffed animals to represent the pets owned by the kids in our class. Lay all the dogs in a line. Then line up the cats. We are building a bar graph with objects that represent our pets. Which type of pet is the most popular? How many more cats are there than giraffes?”

Graph Hunt

Go on a news article hunt for surveys, polls, graphs, and tables. The weather page always contains a few interesting snippets of data. How can this data help your family plan their day? Are there ways the data could be misleading? Talk with children about how data helps us make informed decisions.

Tip: You don’t need fancy math manipulatives to build understanding of data analysis. Everyday objects from the contents of your kitchen junk drawer to canned goods to shoes make simple tools for investigations. Have fun keeping math real with real objects!

# Simple Algebra Ideas that Take about 20 Minutes

Three Bean Salad

Click here for Three Bean Salad recipes.

Ten Bead Bracelets

Children explore patterns (that's what makes this concept algebraic) in the sums of ten (see Number Bonds illustration above). Thread a pipe cleaner through ten same-colored beads and twist the ends to make a bracelet. See the sums of 10 by sliding the beads apart. This picture shows 1 + 9.

Penny Baggies

Learn about how a number can be pulled apart and put back together to solve problems efficiently. Penny Baggies gets kids thinking flexibly about numbers.

Commutative Bingo

Make two sets of cards numbered 4, 5, 6, 7, 8, 9 for a total of 12 cards. Each player uses their own Bingo board. A player picks two cards and multiplies the numbers. If you pick a 6 and a 5, you can decide whether to write the product, 30, in the 5 × 6 box or the 6 × 5 box, but not both. Put the cards back in the pile. The object of the game is to get 6 in a row horizontally, vertically, or diagonally. What strategy can you use to win the game?

The goal of this activity is to use the clues to find the secret number. Each player has their own printed hundred chart. Using beans or cubes, cover the numbers that CANNOT be the secret number. For example, if the clue says, "Tim's number is odd," you cover all the EVEN numbers (since they couldn't be Tim's number). After all the clues have been read, the only number uncovered on the chart will be the secret number.

Where's the math? In this video, my sons noticed important patterns in our number system as they covered numbers according to the clues. Our base ten system is packed with patterns. Play this game to find them alongside your kids.

# Simple Reasoning and Problem Solving Ideas that Take

# about 20 Minutes

A sliding NIM game from the Philippines. I learned this game from Dr. Constance Kamii at an NCTM annual conference. The game also appears in Dr. Kamii’s book, Young Children Reinvent Arithmetic (1985). It has been part of my reasoning task repertoire ever since I played it in that session. It’s a winner for ages 8-88.

Tapatan is pronounced TAP-uh-tan. It is a three-in-a-row game, where one player tries to get three of his or her counters in a row on the board. There are many different versions of three-in-a-row games from around the world.

You will need:

• A copy of the game board (download it here)

• Two players

• 6 counters – three of one color for each player

How to play

1. Each person takes three counters.

2. The game is played on the nine points where the lines cross (on the circles). Players take turns placing their counters on the board on empty points, alternating until all the counters are on the board.

3. The goal of the game is to place your counters in a row of three, either three across, three down or three on the diagonal.

4. After all the pieces have been placed on the board, take turns sliding a piece to an empty circle.

5. You may block the other player from making a row.

6. A counter cannot jump over another counter.

Assessment/Accountability: Write about it in your math journal. Explain the rules of the game to someone who has never played it. Tell about your strategy for winning the game.

###### Tapatan Board (click to download)

Double Digit (Family Math, 1985 & Math Positive Mindsets: Growing a Child's Mind without Losing Yours, 2020)

Materials: dice, paper, pencils

Workstation Instructions:

The object of this game is to see who can get closest to 100 without going over. Each person takes a turn rolling the die and writing down the number.

The number may be treated as either the value shown or the number shown times ten. After each player has rolled the die 7 times, the players see who came the closest to 100 without going over.

Use reasoning:

Look back at the 7 numbers rolled. What could the best total have been with those 7 rolls? What are some winning strategies? Play again and try to improve your reasoning about where to place the digits. Play again with a score sheet that has three columns -- hundreds, tens, and ones. Players try to get a sum closest to 1000.

Reverse Double Digit (Family Math, 1985)

Materials: die, pencils, paper

The object of the game is to come as close to 0 as possible, without going below zero. A player is out who goes below zero. A game consists of 7 turns for each player. Keep a tally count of the turns taken. Before the game begins, players write the numeral 100 at the top of their record sheets. Players then take turns rolling one die. Each player may choose to record the number he or she rolls on a turn as the number itself, or as ten times the number. For example, when a 5 is rolled, it may be recorded as 5 or 50. After each number is recorded, it is subtracted from 100, or from the remainder left from the previous turn. The game continues until each player has had 7 turns or cannot subtract and is out.The person closest to 0 after 7 turns is the winner. Play again and try to improve your reasoning about which number to choose. Extension: Play starting at 1000. Numbers on the die may be multiplied by 10 or 100.

Pico Fermi Bagels* (Family Math, 1985)

The object of the game is to guess the leader's secret 3-digit number.

Choose a leader; the leader picks a secret 3-digit number, whose digits are all different (for example 121, 442, 666 are not allowed). The leader writes the secret number on a slip of paper to refer to as the game progresses.

Players take turns making guesses; for each guess, the leader responds with the following clues:

BAGELS means none of the digits is correct

PICO means one of the digits is correct, but it is in the wrong place

FERMI means one of the digits is correct and in the correct place

Note that two or more correct digits requires several words:

"PICO PICO" means 2 digits are correct but neither is in the correct place.

"FERMI FERMI FERMI" means you have guessed the secret number.

This sample game will illustrate how the clues are given. (The secret number is 427.)

Guess Response Comments

109 Bagels 1,0, and 9 are eliminated from all places.

123 Fermi Only one digit is correct and in the correct place.

145 Pico One of the digits is correct but in the wrong place.

265 Pico Same

353 Bagels 3 and 5 are now eliminated from all the places.

426 Fermi Fermi Two numbers are correct and in the correct spot.

427 Fermi Fermi Fermi All correct!

Players or the leader should keep a record of guesses and leader’s responses. Play several times to improve your skill. Write in your math journal about the strategies and reasoning you used in the game.

Extension: Play with four digits or play with letters that form three-letter words.

*A note about the name of the game: Pico is a metric prefix meaning one trillionth or 10-12. Fermi was a famous nuclear physicist. Bagel is a hard roll with a center hole.

Parents and Teachers: All these ideas are found in Math-Positive Mindsets: Growing a Child's Mind without Losing Yours. Check it out!