D
Donna Boucher
Guest
- Thread Author
- #1
There’s something pretty irresistible about telling a group of young students that you’re a mathemagician.
And with nothing more than a number cube, you can perform a little math magic that leads to some very important number sense.
This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. There is no additional cost to you, and I only link to books and products that I personally use and recommend.
The idea was inspired by Monica Neagoy’s book Planting the Seeds of Algebra: PreK–2, which explores ways to develop algebraic thinking with young children. I love the idea of using a bit of mathematical mystery to get students noticing patterns and relationships—and this particular trick provides a perfect opportunity to explore composing and decomposing 7.
For maximum dramatic effect, I’d use an oversized number cube. Tell students that you’ve developed the amazing ability to see through a number cube. No matter which number they choose, you can tell them the number hiding on the bottom.
Ask a student to choose a number—let’s say 4—and place the cube on the floor with the 4 facing up.
Study the cube. Squint a little. Maybe wave your hands mysteriously. You are a mathemagician, after all.
I’m seeing…3!
Pick up the cube and reveal the bottom.
3!
Record the pair where everyone can see it:
4 and 3
Then ask a student to choose another number. Suppose they choose 6. Place the cube with the 6 facing up and give this one the full theatrical treatment.
Hmmmm…yes…I’m getting something…I think it’s…1!
Lift the cube.
1!
Record:
4 and 3
6 and 1
One more time. A student chooses 2, you place the cube with 2 facing up, summon your extraordinary mathemagician powers, and correctly predict that 5 is hiding underneath.
Now your list looks like this:
4 and 3
6 and 1
2 and 5
Then stop.
Huh.
Look at the numbers.
Do you notice anything about my magic trick? Talk to your partner.
And then give them time to figure it out.
This is the part I wouldn’t rush. The fun isn’t really in showing students the trick. The mathematics is in letting them discover how the trick works.
As partners talk, listen for students who notice that each pair of numbers makes 7:
4+3=74+3=7
6+1=76+1=7
2+5=72+5=7
Eventually, students uncover the mathemagician’s secret: the numbers on opposite faces of a standard number cube always have a sum of 7.
Now the magic trick has become an exploration of composing and decomposing 7.
Students can find and record all the combinations that make 7. What pair haven’t we seen yet? If one part is 5, what must the other part be? What if one part is 0? How do we know we’ve found all the combinations?
You can represent the combinations with counters, number bonds, part-part-whole models, or equations, depending on where students are in their understanding.
The important idea is that 7 can be composed in different ways:
7=1+67=1+6
7=2+57=2+5
7=3+47=3+4
And those relationships work in both directions:
7=6+17=6+1
7=5+27=5+2
7=4+37=4+3
Students aren’t just memorizing a list of addition facts. They’re developing an understanding of the parts within 7 and how those parts are related to the whole.
Composing and decomposing numbers is foundational number-sense work. When students know the parts within a number, they can reason more flexibly rather than relying on counting by ones.
For example, knowing that 7 can be decomposed into 5 and 2 gives students a relationship they can use later when working with addition and subtraction. Knowing that 3 and 4 compose 7 means they can also reason that if they have 7 and take away 3, 4 remains.
These aren’t isolated facts to memorize. They’re connected relationships among numbers.
And that’s what I especially like about introducing the idea through the mathemagician trick. We aren’t beginning by telling students, Today we’re going to learn the combinations that make 7. We’re giving them something interesting to investigate and asking:
What do you notice?
The students get to uncover the relationship themselves.
What starts as a simple magic trick becomes a meaningful exploration of number relationships. Students are looking for patterns, making conjectures, talking about what they notice, and ultimately figuring out why the trick works.
And once they discover the secret, turn the tables. Let them become the mathemagicians! Give partners number cubes and have them take turns choosing a number and predicting the number hidden on the bottom. Each time they make a prediction, they can explain how they knew.
Now the magic trick has become practice composing and decomposing 7. Each turn asks students to use one part to determine the missing part, reinforcing the combinations for 7 again and again in a playful way.
The trick may be what hooks them, but the real magic is realizing that if they know one part of 7, they can figure out the other.
The post Magic Dice: Composing and Decomposing 7 appeared first on Math Coach's Corner.
This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. There is no additional cost to you, and I only link to books and products that I personally use and recommend.
The idea was inspired by Monica Neagoy’s book Planting the Seeds of Algebra: PreK–2, which explores ways to develop algebraic thinking with young children. I love the idea of using a bit of mathematical mystery to get students noticing patterns and relationships—and this particular trick provides a perfect opportunity to explore composing and decomposing 7.
Become a Mathemagician
For maximum dramatic effect, I’d use an oversized number cube. Tell students that you’ve developed the amazing ability to see through a number cube. No matter which number they choose, you can tell them the number hiding on the bottom.
Ask a student to choose a number—let’s say 4—and place the cube on the floor with the 4 facing up.
Study the cube. Squint a little. Maybe wave your hands mysteriously. You are a mathemagician, after all.
I’m seeing…3!
Pick up the cube and reveal the bottom.
3!
Record the pair where everyone can see it:
4 and 3
Then ask a student to choose another number. Suppose they choose 6. Place the cube with the 6 facing up and give this one the full theatrical treatment.
Hmmmm…yes…I’m getting something…I think it’s…1!
Lift the cube.
1!
Record:
4 and 3
6 and 1
One more time. A student chooses 2, you place the cube with 2 facing up, summon your extraordinary mathemagician powers, and correctly predict that 5 is hiding underneath.
Now your list looks like this:
4 and 3
6 and 1
2 and 5
Then stop.
Huh.
Look at the numbers.
Do you notice anything about my magic trick? Talk to your partner.
And then give them time to figure it out.
Let Students Discover the Secret
This is the part I wouldn’t rush. The fun isn’t really in showing students the trick. The mathematics is in letting them discover how the trick works.
As partners talk, listen for students who notice that each pair of numbers makes 7:
4+3=74+3=7
6+1=76+1=7
2+5=72+5=7
Eventually, students uncover the mathemagician’s secret: the numbers on opposite faces of a standard number cube always have a sum of 7.
Now the magic trick has become an exploration of composing and decomposing 7.
Students can find and record all the combinations that make 7. What pair haven’t we seen yet? If one part is 5, what must the other part be? What if one part is 0? How do we know we’ve found all the combinations?
You can represent the combinations with counters, number bonds, part-part-whole models, or equations, depending on where students are in their understanding.
The important idea is that 7 can be composed in different ways:
7=1+67=1+6
7=2+57=2+5
7=3+47=3+4
And those relationships work in both directions:
7=6+17=6+1
7=5+27=5+2
7=4+37=4+3
Students aren’t just memorizing a list of addition facts. They’re developing an understanding of the parts within 7 and how those parts are related to the whole.
Build Number Relationships
Composing and decomposing numbers is foundational number-sense work. When students know the parts within a number, they can reason more flexibly rather than relying on counting by ones.
For example, knowing that 7 can be decomposed into 5 and 2 gives students a relationship they can use later when working with addition and subtraction. Knowing that 3 and 4 compose 7 means they can also reason that if they have 7 and take away 3, 4 remains.
These aren’t isolated facts to memorize. They’re connected relationships among numbers.
And that’s what I especially like about introducing the idea through the mathemagician trick. We aren’t beginning by telling students, Today we’re going to learn the combinations that make 7. We’re giving them something interesting to investigate and asking:
What do you notice?
The students get to uncover the relationship themselves.
The Magic Is in the Mathematics
What starts as a simple magic trick becomes a meaningful exploration of number relationships. Students are looking for patterns, making conjectures, talking about what they notice, and ultimately figuring out why the trick works.
And once they discover the secret, turn the tables. Let them become the mathemagicians! Give partners number cubes and have them take turns choosing a number and predicting the number hidden on the bottom. Each time they make a prediction, they can explain how they knew.
Now the magic trick has become practice composing and decomposing 7. Each turn asks students to use one part to determine the missing part, reinforcing the combinations for 7 again and again in a playful way.
The trick may be what hooks them, but the real magic is realizing that if they know one part of 7, they can figure out the other.
The post Magic Dice: Composing and Decomposing 7 appeared first on Math Coach's Corner.