Source: Wiggins, G., & McTighe, J. Understanding by Design. Merrill Prentice Hall: 1998.
For further information about Backward Design refer to http://www.ubdexchange.org/
Title: How Many Thousands
Topic: Divisibility Rules
Subject/Course:
Pre-Algebra
th
Grade(s): 7
Designer(s): Angela Gilliam
Stage 1 – Desired Results
Established Goal(s)
Strand 1—Problem Solving
 Problem Solving Strategies, Reasoning, Estimation Strategies, Mental Computation
o Standard 1: Selects and uses problem-solving strategies such as reading a problem, drawing a
picture or diagram, using trial and error, etc.
o Standard 38—Selects and uses appropriate problem-solving strategies to solve single-and
multiple-step problems.
Strand 2—Patterns & Relationships; Algebra
 Expressions, Equations, Inequalities
o Standard 5: Students will identify the use of a variable as a placeholder in an algebraic
expression or equation.
o Standard 7: Writes and solves one-step algebraic equations using addition.
o Standard 13: Writes and solves an equation for a given word problem.
Strand 3—Whole Number Computations; Estimation; Whole Number Operations
 Whole Numbers, Fractions, Decimals, Computation, Problem Solving
o Standard 14: Student will use addition, subtraction, multiplication, and division (interpreting
remainder in the context of problem) in computation and problem solving with whole
numbers, fractions, or decimals.
Strand 5—Number Sense & Numeration; Fractions & Decimals
 Divisibility
o Standard 34: Students will use the divisibility rules for 2, 3, 5, 6, 9, 10.
Enduring Understanding(s)
Essential Question(s)
Students will understand that...
1. Knowledge of variables can be applied to
many different applications
1. What is a variable?
2. Variables are used to represent unknown
quantities in algebraic expressions.
2. How can you use algebraic expressions to
problem solve?
3. The use of algebraic expressions can be
applied to different types of word problems
Q
Source: Wiggins, G., & McTighe, J. Understanding by Design. Merrill Prentice Hall: 1998.
For further information about Backward Design refer to http://www.ubdexchange.org/
Students will know...
Students will be able to...(Bloom’s Verbs)
1. a variable is a placeholder and can be used
to represent unknown values in many
different applications, not just equations
2. a number is divisible by 2 if the ones digit
is either 0, 2, 4, 6, or 8
3. a number is divisible by 3 if the sum of the
digits of the number is divisible by 3
4. a number that is divisible by both 2 and 3 is
also divisible by 6
1.
Synthesize knowledge of the divisibility
rules of 2, 3, and 6
2. Determine multiple possibilities for the
value of a variable in a problem
3. Apply knowledge of equations to
determine other possible values of the
variable in a problem
4. Reason toward multiple solutions to the
problem?
5. an equation is a mathematical sentence with
an equal sign
6. an algebraic expression is a phrase
involving at least one variable and
sometimes numbers and operation symbols
K
Stage 2 – Assessment Evidence
Performance Task(s) Summary in G.R.A.S.P.S. form
1. Students will work through the computer based activities independently. Student understanding will
be assessed by the quantitative scores achieved on each skill.
2. Student understanding will be determined through their ability to clearly communicate their method on
the word problem, using mathematical terms appropriately, to arrive at a reasonable solution.
T
Key Criteria:
Students will demonstrate clear communication of the targeted goals by preparing a visual display that
clearly explains the process used to solve the problem How Many Thousands?.
Other Evidence
o Teacher observation of students working on tasks
o Assess understanding through class conversation and questioning
o Ask students for their interpretation of the Essential Question.
o Cooperative groups will problem solving methods.
Source: Wiggins, G., & McTighe, J. Understanding by Design. Merrill Prentice Hall: 1998.
For further information about Backward Design refer to http://www.ubdexchange.org/
Stage 3 – Learning Plan
Learning Activities Consider the W.H.E.R.E.T.O. elements.
Students will visit the computer laboratory to build foundational skills needed to solve the word problem.
The students will be led through the sequence of computer activities (4) with a brief instructional
discussion of each divisibility rule followed by student practice.
1. Computer based practice with immediate feedback (divisibility by 2)
http://www.slcs.org/petrova/aaabrite/g72_dix1.htm
2. Computer based practice with immediate feedback (divisibility by 3)
http://www.slcs.org/petrova/aaabrite/g72_dix2.htm
3. Computer based practice with immediate feedback (divisibility by 6)
http://www.slcs.org/petrova/aaabrite/g72_dix5.htm
4. Computer based practice with immediate feedback (solving equations)
http://www.slcs.org/petrova/aaabrite/g725_ex2.htm
(InterMath Connection)
Students will work in cooperative groups to devise a problem solving plan for the following InterMath
word problem:
How Many Thousands?
The eight-digit number 79,12A,504 is divisible by 6. What are the possible values of A ?
(Source: Adapted from Mathematics Teaching in the Middle School, Sep-Oct 1994)
http://www.intermath-uga.gatech.edu/topics/nmcncept/integers/a57.htm