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Magic Ten: Practicing Combinations to Ten with a Card Trick

  • Lesson
Pre-K-2
2
Number and OperationsAlgebra
Laurie A. Penney
Acton, MA

Everyone loves a good card trick, and this lesson allows young students to learn a fun and impressive trick while simultaneously practicing and mastering the all-important combinations of ten. In this trick one student is a “mathemagician.” He presents a deck of cards to his classmate, who removes three cards from the deck. After some fancy card work, the identities of the three cards are “magically” determined to everyone’s amazement.

Preparation 

It is important to become proficient at presenting the card trick in order to model it properly. The quicker you can do the trick, the more impressive, and a flair for the dramatic makes it even more exciting.

Opening Activity 

Begin by looking at a complete deck of cards with the children (without the King, Queen, Jack, and 10s cards). It is worthwhile to spend a few minutes getting to know what makes up a deck of cards, recognizing and naming the suits and noticing the numbers and pictures. Explain to the children that in this card trick, the ace will represent the number one. You remind your students that they can count the pips on the cards to help determine if they have ten or not.

Main Activity 

Day 1 

videos Magic Ten Card Trick 

Demonstrate the trick to the students as in the video:

    1. Hold out the shuffled deck, and ask one student to choose any three cards.
    2. Ask the student to determine if any two of his cards add to ten. If so, he must return one of the two to you and choose a replacement. Repeat this until the child has three cards, no two of which add to ten. Tell the student you will determine which cards he has. The student can put these three cards aside while you perform the trick.
    3. Begin the card trick by simply turning each of the remaining cards face up in front of you, one at a time. As soon as you see any two cards that add to ten, cover those two with the next two cards from the deck.
    4. Continue on in this manner, covering pairs that add to ten every time you see them, until the deck is finished. If there are no such pairs, place the next card out to form a new pile. Note: if you are left with only one card in the end, simply make a new pile.
    5. When the cards in your hand have all been turned over, remove the pairs of piles whose top cards add to ten.
    6. There should be three remaining piles. Determine the missing cards by finding the addend that goes with the top card of each pile to make ten.

Once you have wowed your students with your magical abilities, it is time to teach the trick to them. Walk them through the steps slowly, having them help you find the pairs to ten as you go. One nice thing about this trick is that if a pair is missed it will not affect the outcome of the trick.

When the students understand how to do the trick, break them up into groups of 2–4, and give each a prepared deck of cards. If some children do not feel quite ready to try the trick on their own (or if you determine they need more instruction), invite them to stay with you and practice.This is also a good opportunity to circulate the room and use the Student Data Chart.

pdficon Magic Ten Student Data Chart 

In their groups, one child can be the mathemagician and the other(s) can choose the three cards. Remind children to be sure there are no pairs to ten in the three cards they choose from the deck. Once those have been hidden away, each child in the group should help go through the process of pairing the remaining cards and revealing the identities of the hidden ones.

Day 2 

pdficon  Magic Ten Student Activity Sheet 

pdficon  Magic Ten Teacher Answer Key 

Review the trick with students and have them continue practicing in small groups or with a partner until they can do the trick with some fluidity. Students should have an opportunity to complete the Magic Ten Student Activity Sheet. Children who have become proficient with the process can work together to try and determine how the trick works.

Inevitably, a student will ask how the trick works. It is beneficial for all students to understand the mathematics behind this trick. Individual teachers can choose whether they want to explain the mathematics or ask students who are ready for an extension to figure out how the trick works and explain it to their classmates. This trick works because every card in the deck has a partner with which it combines to make ten. By systematically removing (covering) each pair in the deck, the last remaining three cards will be the partners of the cards that were removed, thus allowing the mathemagician to determine the identities of the previously removed cards using simple algebraic reasoning  (ex: 4 + x = 10).

Closing Activity 

Gather students back together to reflect on the activity and share ideas about performing the trick and remembering their math facts. Students who have determined how the trick works can share their findings with their classmates.

In the ClassroomSuccessStoryThumb

"I used this activity with giant cards at a math night for parents. The parents and kids LOVED it! Kids think it's real magic—almost hate to burst the bubble by telling them why it works." -Monique Gunnels, Elem. Resource Teacher (Columbus, GA)

Assessment Options  

  1. While observing students, use the Student Data Chart to keep track of which facts students know and which they are still working on.
  2. Assign students to practice the trick on someone at home, and write a journal entry about the experience, including an explanation of how the student was able to determine the hidden cards.
  3. Use the Magic Ten Student Activity Sheet

Extensions 

  1. Students who are ready can try to determine the mathematics behind the trick: why does it work?
  2. Ask students to find a way to make the trick work if the face cards were left in the deck and were assigned values of 11(jack), 12 (queen), and 13 (king).

Questions for Students 

1. Why do you need to make sure that no two of the three cards picked add up to ten?

[If a pair of cards is in your hand, there will be only one unpaired card at the end of the trick, and there will be no clues to know which pair is being held.]

2. How could the trick be done if the tens and face cards were left in the deck?

[Simply cover face cards and tens as they are turned over, no need to pair them. Those left in the end should simply be picked up with the remaining pairs.]

Teacher Reflection  

  • Was students’ level of enthusiasm/involvement high or low? Explain why.
  • How did students discover a way to find card matches if they did not know their facts fluently?
  • How did students stay engaged even when they were not performing the trick? If they did not stay engaged, how could this lesson be modified such that they are?
  • How did you set clear expectations for your students?

Learning Objectives

Students will:

  • Practice and gain fluency with 2-addend combinations to 10.
  • Find missing addends to 10.

NCTM Standards and Expectations

  • Develop fluency with basic number combinations for addition and subtraction.
  • Illustrate general principles and properties of operations, such as commutativity, using specific numbers.

Common Core State Standards – Mathematics

-Kindergarten, Counting & Cardinality

  • CCSS.Math.Content.K.CC.A.1
    Count to 100 by ones and by tens.

-Kindergarten, Counting & Cardinality

  • CCSS.Math.Content.K.CC.A.2
    Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

-Kindergarten, Algebraic Thinking

  • CCSS.Math.Content.K.OA.A.1
    Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

-Kindergarten, Algebraic Thinking

  • CCSS.Math.Content.K.OA.A.2
    Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

-Kindergarten, Algebraic Thinking

  • CCSS.Math.Content.K.OA.A.3
    Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

Grade 1, Algebraic Thinking

  • CCSS.Math.Content.1.OA.B.3
    Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

Grade 1, Algebraic Thinking

  • CCSS.Math.Content.1.OA.B.4
    Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.