equivalent fractions game

While looking for equivalent fraction activities, I found a game called Fraction Swap. Since I didn’t make the purchase, I don’t know the game’s instructions. But it inspired me just enough to develop a fun two-person game with the fraction rods we already have.

Supplies:

fraction rods: ours are from Learning Resources. (One of our 1/8 pieces is missing, so we use a Lego substitute!)

2 blank wood cubes to use as dice: we had these left over from a craft project

2 sheets of paper, a permanent marker

Game Making:

Use a permanent marker to write fractions on the wood cubes. On both dice we wrote: 1/12, 1/10, 1/8, 1/6, 1/5, and 1/4.

Trace the full “one” fraction rod two times onto each sheet of paper.

Game Preparations and Goal:

Arrange all the fractions in order off to the side from smallest to largest (1/12, 1/10…1/3, 1/2). Place them between the players so everyone can reach. This is the bank.

Each player receives a sheet of paper with two one-unit rods drawn on it. Show students how each is the size as the one rod. Now explain that the one rod isn’t part of the bank, but it can be used during the game for measuring.

The goal is to fill up both rods on your paper with fraction pieces that are exactly equal to one. But, the winner is the person who can fill up their two rods with the least number of fraction pieces. The way to do this is by trading several smaller fraction pieces for equivalent larger fractions.

How to play:

Each player rolls a die. The person with the largest fraction gets to roll first.

For each turn, the player rolls both dice. They choose which of the two fractions they would like to take from the bank. If they roll 1/10 and 1/6, they might choose 1/6 because it is larger. They might choose 1/10 because they have many 1/10 fractions and might easily make an exchange. They may place the fraction piece anywhere on their paper—on one of their one rod spaces or under the rod spaces.

After rolling and choosing a fraction piece, players may make one exchange of a smaller set of fractions for an equivalent larger one. For example, you can exchange in two of the 1/10 pieces for a 1/5 piece. Exchanges are done with the bank, not other players. The player doing the exchange should say out loud what they are doing. For example, “I’m exchanging 2/4 for 1/2.” This way the other player can confirm exchanges.

The first player to decide they have filled their two rods in a way that uses the least amount of fraction pieces, makes the announcement that they’re done. The game continues until the second player is also finished, but there is a twist. The player who is finished still gets to roll the dice and choose a fraction piece each turn. This encourages the last person to finish quickly because there are fewer and fewer pieces remaining.

Notes:

With how we played, you can only exchange equivalent fractions of the same fraction for a larger fraction. You can’t add different fractions to make an equivalency. Perhaps if you’re practicing addition of fractions, you could make this change.

If both fractions that were rolled are no longer available, you can choose something equivalent to it from the bank. For example if the 1/4 fractions are all used up, you could take two 1/8 pieces. The kids get kind of excited about this!

You could play this game with three players and one person can be the banker.

After the game, students can prove to each other that their fractions are each equal to one. Ask them how they could do this. Many students will compare with the one rod or other rods. This is a great start. Students might also talk about more equivalencies, such as “this set of 5/10 is equal to 1/2, and I know 1/2 plus 1/2 equals one.” They might also prove it on paper by finding common denominators and adding the fractions.

An optional game change: For each turn, players can either roll and choose a fraction piece or exchange equivalent fractions. My kids adamantly didn’t want to try this version, but if you like this rule, start with it!

drawing a pokemón eevee with ordered pairs

I created this Pokémon Eevee for my daughter to practice plotting ordered pairs. I gave her the ordered pairs and told her the image was a surprise. She was so tickled when she realized it was her favorite Pokémon, Eevee!

Below are instructions on how I made the project, so you can make your own with any image. At the bottom of the page, you’ll also find the coordinates to draw Eevee.

1. Start with an image you want to use. Print it onto paper.

2. Print a blank coordinate plane. I used one that goes from -20 to 20 on both axis (it’s a free download on Teachers Pay Teachers). You could also use a piece of plain graph paper and draw the x- and y-axis and label them.

3. Place the blank coordinate plane in front of the image. Put both up to a glass window. With a pencil, pick places along the image lines to draw a point. Use as many or few as you need to get a nice image but also not too many where it becomes frustrating. Also, it’s easier if you place points on line intersections so your ordered pairs are whole numbers as much as possible.

4. Now look at your points and choose where to start. Think about the path the ordered pairs should follow like a connect-the-dots drawing. For my image, the ordered pairs draw Eevee’s head and ears first, then her torso, then the tail, and finally the legs. Write out the ordered pairs in the dot-to-dot order. If it’s complex, divide the drawing into sections.

5. Have your students plot the ordered pairs and connect-the-dots as they go.

Here are the ordered pairs for the Eevee drawing. One page has descriptions for each section. Use this if you want your students to know it’s an Eevee ahead of time. The other page doesn’t give any clues as to what they’re drawing. Enjoy!

connect 4 inequalities

To practice math inequalities, I put together a Connect 4 version.

I labeled each of the 7 columns with a sticky label and the column number. Both players work on the same side of the board so they can see these labels.

I had the kids make up inequalities cards for the game. We decided the variable we’d use is “C” to stand for “Column”, meaning the column(s) you can or can’t play your checker in. For example, “C < 5” means “the column (you can play in) is less than or equal to 5. Therefore you can choose from columns 1-5.

The first player draws a card and plays their checker in whatever column their card allows, then discards. The second player draws a card and makes their move, then discards. The game continues until a player wins.

It’s a fun game if you don’t take it too seriously. You just have to be willing to laugh and groan when you see a place to win but can’t take it!

math mobiles

My kids had a blast solving math mobiles at home today. The original idea is from Mindset Mathematics Grade 6. 
-I introduced the activity with our science balance: We came up with numbers to balance on each side. Then we came up with symbols to represent the numbers. 
-We tried some of the puzzles in the Math Mobiles activity in Mindset Mathematics. It’s in section Big Idea 7: Using Symbols to Describe The World. (You don’t need the book though. Just jump into the website puzzles.)
-We worked through over an hour of the same types of puzzles on this website: https://solveme.edc.org. (It works in Chrome but not Safari.) We even created our own puzzles for others in the family to solve.

spontaneous math with pancakes

Not everyone will run across the same math pancake opportunity we did, but it’s an example of spontaneous learning you might come across when you’re curious about the world around you. Today we found math unexpectedly on a pancake mix.

We were given a gift with a shaped pancake pan and pancake mix. While we made pancakes, I noticed the mix makes six pancakes, but the nutritional information listed five servings. So I asked the kids what they made of it. We laughed at how strange it was that the mix couldn’t list nutritional information for six servings because it was supposed to make six pancakes. I didn’t have expectations beyond that yet. In fact I was occupied making sure the pancakes weren’t burning when my son said enthusiastically that each serving size is 1 1/5 of a pancake!

These sorts of moments energize me. I didn’t research this activity on Pinterest, collect materials, and think about how to present it to my kids, which of course I love to do. But with our pancakes, I just noticed something I found interesting and mentioned it to them. They found it interesting, and it became a spontaneous, real life math problem.

Maybe you’re wondering how we got to a place where my kids are volunteering to do math. I can tell you it’s been a life-long process, and I suppose I’m still unraveling how to explain it. But basically, we let each other know what we’re noticing, wondering, and thinking about. It plays itself out as nothing fancy, just conversations about things we find interesting. And yes, there are lots of Pokémon conversations. But we have just as many conversations about science, math, and what words mean. We talk about history, invention ideas, and recipes we’d like to try. My hope is that we’re cultivating a deep curiosity of all sorts of amazing things in our world…including pancakes and Pokémon.