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*“Recent research has shown that place value remains difficult in third and fourth grade, in spite of the fact that it is taught repeatedly in every primary grade.”* –Constance Kamii

Why is place value so important and so challenging for learners? If students have a weak understanding of place value, a critical concept for all other math concepts, they have a difficult time understanding decimals and may assume the number of digits means that a number is larger. Students find place value challenging because they do not have a deep conceptual understanding of the multiplicative relationships in the base 10 number system. Playing fun games or engaging in activities as a family is a great opportunity to gain a deeper conceptual understanding of place value.

**Knock, Knock!**

You need: a deck of cards, place value mats (you can print or make your own!) for each player, and 20 coins. Please note that aces are worth 1 and face cards are worth 0.

- Each player gets four cards, with each card representing a place value (hundredths, tenths, ones, tens places). The rest of the cards make the “draw pile.”
- Players take turns discarding one of the cards in their hands. For every card they discard, they can pull another card from the draw pile.
- The goal is to create the greatest possible total value.
- When one player thinks he or she has the largest total, he or she says “KNOCK, KNOCK” – locking in his or her cards. Everyone else gets another chance to discard and pull. (Note: if you run out of cards from the draw pile, shuffle everyone’s discarded cards to make a new draw pile)
- All players then show their best hand and explain their hand in terms of place value (how many tens, ones, tenths, and hundredths).
- If the person who called “Knock, Knock” wins the round with the greatest hand, he or she gets two coins.
- If the winner did not call “Knock, Knock,” he or she only gets one coin.
- Repeat steps 1-7 until all the coins are used up – the winner is the one with the most coins!

**Variations of this math game**

• **Two winners:** To add some place value addition to this game, players can add up all of the hands they’ve played through the game. The second winner is the person whose hands made the greatest sum.

• **Mix it up:** When there are 10 coins, expand out the place values out to ten thousands, thousands, hundreds, tens, ones, tenths, hundredths, and thousandths and have each player draw eight cards. You can also mix it up every round, by changing the number of places and cards each player can play with.

• **Pair up:** Play with a partner and discard, pick up two cards at the same time.

**For discussion** After experimenting with the variations or playing several rounds, have a discussion with your learner(s) to check how their understanding of place value is coming along.

• What does it mean to have 7 tens? What about 7 ten thousands? What is bigger (or is it the same?): 5 thousands or 5 thousandths? Why?

• Did you prefer playing as a pair or solo? Did you find discussing which cards to discard and keep helpful? Why?

• When did you get rid of a card and then afterwards, wish that you hadn’t? How come?

Place Value Hangman

You need: a deck of cards, a chalkboard, whiteboard, or large piece of paper. Please note that ace = 1, kings = 0. Set aside the 10s, jacks, and queens.

- Split into even teams. Draw two hangmen’s nooses, one for each team.
- Each team needs to draw spaces for the places of a number, depending on which place values you want them to play with. Each team should also identify each place value. Ex:

_ _ ,_ _ _, _ _ _ ._ _ _

*ten millions, millions, hundred thousands, ten thousands, thousands, hundreds, tens, ones.tenths, hundredths, thousandths* - Have one learner from each team draw a card. As a group, the learners should decide where to place the the card on your place value space (above), to make the largest number possible. Once a card is placed, it’s locked in to that place until the number is completed.
- Repeat step 3, until everyone gets a turn. The final learner who places a card should read off the number the group came up with.
- Given the digits available, did each group really come up with the largest possible number? If not, the team(s) hangman gets a body part added to that team’s noose!
- Repeat steps 2-6 until one team’s hangman is complete. The other team is the winning team!

**Variations of this math game**

• **Play solo:** Each player gets their own number and hangman’s noose and must avoid being the first person to complete his or her hangman against another solo opponent.

• **For young players:** Instead of hangman, call it Make House – if a team came up with the largest possible number, they get to add a wall to their house. The winning team is the first team to build a house (ed. note – as a little girl, I got anxious about death, pain and injury, so we always played Make House, instead of Hangman)

• **Scale:** Introduce 10s, jacks and queens back into the deck – each of those cards represents an opportunity to move the decimal one place. If learners can correctly rename each place value, this gives them an advantage for the round. If they miss, the other team or opponent gets a chance to move the decimal and rename each place value.

**For discussion:** After playing several rounds, spark some conversations with your learners and get a pulse for where they are with place value!

• How do you think you can win if we play again? Why?

• If you get a chance to move the decimal, in what direction would you want to move it? How come?

• What would you rather have: 7 tens or 70 cheerios? What about 7 thousand or 7 thousandths minutes playing a fun math game?

**Motion Math Zoom, our interactive number line for place value!**

You will need one iOS device, such as an iPad, iPhone or iPod touch.

- Download Motion Math Zoom from the App Store. You get six levels for free – unlock all 24 with in-app purchase.
- Play through the intro level, popping bubbles to place the number where it should be on the zoomable, stretchable number line!
- Explore place value by zooming in to see the amoebas in the thousandths and zoom out to see the dinosaurs in the thousands! What happens if you try to put a number where it doesn’t belong?
- Want an extra challenge? Play with The Needle!

Tap the person icon to create a new player. That way, different kids can compare their scores and discuss their experiences with the game.

**For discussion:** After playing this game, talk to your kids about what they’ve just played:

• Can you name all of the different animals you saw? Which place value did each one represent?

• What does three hundreds mean? What would I multiply or divide by if I needed to get to three tens? What about three thousands?

• Did you like playing with the needle? How come?

• What do you think of place value, now that you’ve played Motion Math Zoom?

We’ve pulled together three place value games you can play as a family. You might want to play Knock, Knock! gathered around the kitchen table, but other games, such as Motion Math Zoom, can be played anywhere. Let us know which of these games your family has played and what you think! If you have other place value activities or games you like, please share them in the comments!

Elizabeth, on May 28th, 2012 at 1:00 pm Said:Hi,

I must say that the Motion Math Zoom is one of the most impressive Math Apps I have seen. I would just add some randomality but other than that, perfect.

Elizabeth

An, on May 28th, 2012 at 10:09 pm Said:Thanks for stopping by and commenting, Elizabeth. What exactly do you mean by randomality? We’d love to know!

Chauncey Hardemeyer, on August 18th, 2012 at 7:59 pm Said:This is a fun way to teach the lesson on kids. I think anyone can teach this and still have some fun on the way.