Decimal Game Day

10 min

Narrative

The purpose of this True or False? is to elicit strategies and understandings students have for adding decimals. The reasoning students do here helps to deepen their understanding of the properties of operations. It will be helpful later in the lesson when students need to be able to add decimals.

Launch

  • Display one equation.
  • “Give me a signal when you know whether the equation is true and can explain how you know.”
  • 1 minute: quiet think time
Teacher Instructions
  • Share and record answers and strategies.
  • Repeat with each equation.

Student Task

Decide if each statement is true or false. Be prepared to explain your reasoning.

  • 0.99+0.1=0.9+0.1+0.090.99 + 0.1 = 0.9 + 0.1 + 0.09
  • 0.99+0.01=0.9+0.10.99 + 0.01 = 0.9 + 0.1
  • 0.99+0.1=1.990.99 + 0.1 = 1.99

Sample Response

  • True: 0.99+0.1=0.9+(0.09+0.1)=0.9+(0.1+0.09)0.99 + 0.1= 0.9 + (0.09 + 0.1) = 0.9 + (0.1 + 0.09)
  • True: 0.99+0.01=0.9+(0.09+0.01)=0.9+0.10.99 + 0.01 = 0.9 + (0.09 + 0.01) = 0.9 + 0.1
  • False: (0.9+0.09)+0.1=(0.9+0.1)+0.09=1+0.09(0.9 + 0.09) + 0.1 = (0.9 + 0.1) + 0.09 = 1 + 0.09

Synthesis

  • Display the first and third equations.
  • “How can you justify your answer without evaluating both sides?” (For the first problem, I noticed that there are 9 tenths on the right and left and also 10 hundredths. For the third problem, I saw that the right side is almost 2 so it's much larger than the left side.)
Standards
Addressing
  • 5.NBT.7·Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
  • 5.NBT.B.7·Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

15 min

20 min