NCDPI – AIG Instructional Resource: Background Information
Resource Title: Bicycle Dilemma
Subject Area/Grade Level (s):
Math/5
Time Frame: 1 class period
Common Core Standard Addressed:
Number and Operations in Base Ten
Perform operations with multi-digit whole numbers and decimals to hundredths.
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
strategy used.
Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
5. Use appropriate tools strategically.
Additional Standards Addressed: NA
Brief Description of Lesson/Task/Activity: This activity requires that students have an understanding of the impact (x10/÷10) the movement of
a decimal left or right has on a quantity. Students explore the standard algorithm for multiplication of decimal numbers as they begin the task by
solving various equations that utilize the same digits, which elicits the same digits for a product. The second part of the task involves analysis of
a calculation error when adding sales tax.
Type of Differentiation for AIGs (include all that apply):
Adaptations for AIGs:
Content
x Process
Enrichment
x Extension
Acceleration
Product
PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction
AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project
Explanation of How Resource is Appropriate for AIGs:Often gifted students either pick up on the standard algorithm for operating on decimals
quickly or come to school having learned to line up the decimals to add and subtract and multiply the numbers as if they are whole numbers,
placing the decimal in the product based on the number of digits to the right of the decimal in both factors. For division of decimals, students
are often taught to move the decimal in both the divisor and the dividend (adding zeros when necessary) the same number of times in order to
create a whole number divisor. This activity requires students to use their understanding of place value, the operations, and estimation in order
to explore the impact that decimal movement in one and/or both factors has on the product. The task also includes a writing piece that requires
students to analyze a calculation error when finding the sales tax, which allows students to describe, using mathematical vocabulary, their
understanding of what happens when decimals are moved or misplaced within a number.
Needed Resources/Materials:
 Task sheet
 Calculators
Sources: NA
TEACHER NOTES: It is recommended that this activity be completed in two parts, bringing the group of students together after ample time is
allowed for completion of each portion. Once students finish the first part, finding the products, the teacher may choose to have students
discuss their findings/thoughts about decimal placement before tackling the questions that go along with the first task.
Before posing the second portion of the task, finding the sales tax error, the teacher should facilitate a discussion about sales tax (how it’s
calculated, how 7% is written .07 for calculation, strategies for finding 7% of a number including the standard algorithm and finding 10% - 1% 1% - 1%) to make sure all students have an understanding of how sales tax is calculated, even though the formula is provided on the task.
PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction
AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project
NCDPI AIG Curriculum Resource Outline
STAGE ONE: ENGAGE
Have students complete the computation portion of the first task using their choice of mathematical tool (calculators should be provided). The
discussion on this task should affirm foundational understanding of the number sense needed about the use of decimals. Once students have
found all the products required, the teacher should ask, “What do you notice about the products?” This simple open-ended question should
prompt students to share that all the products have the same digits; some of the products are equal to each other, etc. The teacher should then
ask students to share any solution strategies they used for multiplying the factors if they chose to use pencil and paper.
The teacher should then pose the question, “What relationships do you notice between the factors and products in the equations?” Other
questions that may help probe students to share their thinking are…
What do equation 1 and the original equation have in common? How are they different? How does this difference impact the products?
How do the equations you solved compare to the original equation involving all whole numbers?
What impact does moving a decimal have on a number? How does moving the decimal change a number?
Once students have had the opportunity to share their thoughts and hear the thoughts of others, have them answer the questions for task 1.
STAGE TWO: ELABORATE
Pose the second task to students and allow time for them to ask questions regarding the situation. Have students work through the problem
independently. Encourage students to use tools that ensure accurate calculations based on their own comfort level with multiplication of
decimal numbers (Use appropriate tools strategically.). Have them complete the task independently.
STAGE THREE: EVALUATE
Task 2 includes criteria that should be addressed in student letters…
Students’ explanations should include …
 equations that are accurate.
 an explanation for each equation presented.
 precise mathematical vocabulary when discussing the movement of a decimal in a number.
 an explanation of where you think the salesman made his calculation error (3. Construct viable arguments and critique the
reasoning of others.).
Students’ work should be evaluated based on their ability to correctly compute for the sales tax and total cost, given the equation and a choice
of tools, as well as their ability to articulate the impact the salesman’s error in decimal placement had on the total cost of the bicycle.
TEACHER NOTES: NA
PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction
AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project