Illuminations: Comparing Connecting Cubes

Comparing Connecting Cubes


Balancing

This lesson encourages students to explore another model of subtraction, the balance. This model leads naturally to recording with equations. Students use actual and virtual pan balances in their explorations and record the modeled subtraction facts and the related addition facts in equation form.

Learning Objectives
 
Students will:
  • explore the balance model of subtraction
  • write the subtraction modeled on the balance in equation form
  • write the addition sentence related to a given subtraction sentence

Materials
 
Pan Balance with weights
Connecting cubes in two or more colors
Spinners or number cubes
Paper bag
Shape Balance

Instructional Plan

Note that in this lesson, the balance model for subtraction will be demonstrated using both an actual and a virtual pan balance.

Display a pan balance and review with the students how it operates. Explain that when the scale balances, both sides have the same value.

 

 

Then ask a volunteer to place 7 connecting cubes in the left pan of the balance beam and 4 connecting cubes on the other side. Ask the students how many connecting cubes are needed on the lighter side so that the scale balances. Accept and model all student responses. When the response “3” is given, ask the children what question “3” answers. [How many more than 4 is 7?] Then ask them to record the answer using the equation form 7 – 4 = 3. Ask if they know what addition sentence would also fit the situation. [3 + 4 = 7 or 4 + 3 = 7.] Continue with other weights until the students are comfortable with the process.

Divide the students into pairs and give each pair a die. Assign each child one side of the pan balance. Tell individuals to roll the die, read the number of dots on the upward face, and place that number of connecting cubes on their side of the balance. Then have partners work together to balance the scale by adding connecting cubes in a different color. They should record the subtraction equation that shows what they did. Have them repeat the activity several times.

Now call the class together and demonstrate how to use the Pan Balance - Shapes tool.

Pan Balance - Shapes Pan Balance - Shapes

Assign some students to work with this site. Because the shapes represent different values, advise the students to use only one shape as they explore with the online balance. While some children are using the online balance, others can play “What’s in the Bag?” To start the game, provide pairs of children with a pan balance, a paper bag, and some connecting cubes. Assign one child to go first, placing up to 10 connecting cubes in the bag and placing the bag on the left side of the scale. Then that child will place up to 10 loose connecting cubes on the right side. The other child is to add connecting cubes to the lighter side until the scale balances. Then each child writes subtraction and addition equations to describe the situation. Have them repeat the activity several times, switching roles each time.

Questions for Students
 

When you modeled comparison subtraction on the balance, what did you do first? Then what? How did you record this?

Suppose you put 7 connecting cubes on the left hand side of the balance and 3 connecting cubes on the right hand side. How would you balance the scale by adding cubes? What equation tells what you did?

How did you find out how many connecting cubes were in the bag?

How would you explain to a younger child how to make the sides balance?

Choose one equation that you wrote when you played the game. How does this equation show what you did? Can you write another subtraction equation with the same addends? Can you use those addends to write an addition equation?

How could you use the balance to complete this number sentence: 3 + _ = 5?

What does it mean when the scale balances before you add any cubes?

If I have 5 red cubes and 7 blue cubes, what addition and what subtraction equations can I write about the cubes?

Assessment Options
 
  1. Because a new model for subtraction has been added today, you may wish to make more entries on the Class Notes sheet begun earlier in this unit.

Teacher Reflection
 
  • Which students met all the objectives of this lesson? What extension activities are appropriate for these children?
  • Which students did not meet the objectives of this lesson? What instructional experiences do they need next? What, if any, misconceptions that need cleared up?
  • Which parts of the lesson helped the students achieve their learning goals? Which parts would you change the next time that you teach this lesson?

NCTM Standards and Expectations
 
Number & Operations Pre-K-2
  1. Count with understanding and recognize "how many" in sets of objects.
  2. Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.
  3. Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections.
  4. Understand the effects of adding and subtracting whole numbers.
  5. Develop and use strategies for whole-number computations, with a focus on addition and subtraction.
  6. Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.
This lesson prepared by Grace M. Burton.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics

 Activities
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