Number Tricks

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Objective

SWBAT: • Define and identify inverse operations • Represent number tricks using algebra tiles • Explain why number tricks work using algebra tiles

Big Idea

Why do these number tricks work? How do these tricks connect to inverse operations? Students work with algebra tiles to understand how and why these number tricks work.

Do Now

7 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.   Today I want students to review the concept of inverse operations.  Inverse operations will come up later in the lesson and I want to make sure that students can define and identify inverse operations.

I call on students to share their answers.  Problem 2f may be a challenge for students and that is okay.  I push students to use numbers to create examples.  Some students may say that to undo this you have to divide by the starting number.  For instance 4 squared is 16 and dividing 16 by 4 will result in 4.  Other students may mention that you can take the square root of the number.  Squaring and number and taking the square root of a number are inverse operations.  

Math Magic

5 minutes

Notes:

  • When I print out the notes for students I will delete the words in parentheses.  I want students to fill in these words on their own notes.
  • Before this lesson, I use the data from the previous lesson’s ticket to go to Create Homogeneous Groups.

I have students move into their groups for the day.  I explain that we will work together as a class and then they will work with their group member.  I read through the math number trick two times.  Students choose their own number, record the missing words and determine their final number.  I tell students to show their work to prove their answer is correct.  Students participate in a Think Pair Share about their starting number and their ending number.

Algebra Tiles and Number Tricks

10 minutes

Notes:

 

I call on a student to read over the directions.  I tell students that we will fill out the Algebra Tiles pictures together.  As students work I walk around and monitor student progress and behavior. 

We come together and share out observations as a class.  I ask, “What different kinds of numbers does the trick work with?” and “Why do you think we always end with the same number?”  Some students may explain how dividing by two undoes the multiplying by two.  Starting with a number and then subtracting that number at the end cancels out to zero.  Adding five and then subtracting four results in one.  Other students may make the connection between the answer and the series of inverse operations.  If students are not making these connections, I ask questions but I do not explain the connections yet.

I pass out the Algebra Tiles.  We use the Algebra Tiles to model each step of the trick.  Since people choose different starting numbers, we can use the x tile to represent the starting number.  I ask students how we can use the tiles to show each step of the trick.  Once we finish the column I ask students to use the Algebra Tiles to explain why the ending number is three, no matter what number is the starting number.  Students participate in a Think Pair Share.  I call on students to share their ideas and ask other students to say if they are agree and why or why not.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others, MP4: Model with Mathematics, and MP7: Look for and make use of structure.

Practice

18 minutes

I review the task and the expectations with students.  Students are engaging in MP2: Make sense of problems and persevere in solving them, MP4: Model with Mathematics, MP5: Use appropriate tools strategically, MP6: Attend to precision, MP7: Look for and make use of structure and MP8: Look for and express regularity in repeated reasoning.

If students are struggling, I ask them one or more of the following questions:

  • What do you know?
  • Does the trick work with fractions and decimals?  Does it work with zero? How do you know?
  • How can you represent this step with Algebra Tiles?
  • Why do you end with the same number?
  • How does this trick connect with inverse operations?

If students successfully complete the problems they can move on to the challenge question.

Closure and Ticket to Go

10 minutes

I ask students, “How do the operations work in these tricks?” and “When the trick says to double, what is the inverse operation that you expect to see?”  I want students to see how each trick uses inverse operations to guarantee that you always end with the same number.  I also want students to explain that to undo multiplying by two you must divide by two.  I push students to use specific language to describe their observations.  Students are engaging in MP6: Attend to precision, MP7: Look for and make use of structure, and MP8: Look for and express regularity in repeated reasoning

I pass out the Ticket to Go and the Homework.