Download Agile Mind Course Content Page

Agile Mind Course Content Page
Deliver
instruction
Lesson
3.1
9/2/13 2:50 PM
Lesson
3.2
Lesson
3.3
Lesson
3.4
Lesson
3.5
Lesson
3.6
Lesson
3.7
Lesson
3.8
Lesson
3.9
Lesson
3.10
Deliver instruction (Lesson 3.1)
Agile Mind materials
Overview of the day
Lesson activities
Lesson materials
Foundations of algebra:
Lesson 3.1 “Variables, expressions, and properties”
Student Activity Book
Student whiteboards, markers, and erasers
Lesson preview
Suggested
time
Activity
Goals
10 min.
Opener
Investigate patterns in arithmetic
30 min.
Core activity
Use variables and expressions to understand the mathematics of magic number
puzzles
10 min.
Process homework
Learn from reviewing the homework due today
25 min.
Consolidation activity
Explore expressions and algebraic properties used in magic number puzzles
5 min.
Wrap up and introduce
homework
Reflect on the day’s lesson and understand tonight’s homework assignment
Lesson activities
OPENER (10 minutes)
Students each complete an arithmetic puzzle by following directions, then compare the result with their partners to find the
pattern. The Opener provides an entry point for students to explore and review ideas related to variables, expressions, and
algebraic properties (including the distributive property) in today’s lesson.
Online page 1
Students complete the puzzle and then compare their answers with their partner. (If done correctly, the final result will be
a three-digit number: the first two digits correspond to the student’s age, and the final digit corresponds to the number of
siblings the student has.) Then students discuss and record why they think the puzzle works. Note that the puzzle “works”
only as long as the number of siblings is 9 or less. [SAB, questions 1-3]
Quickly debrief, making sure students found the pattern. Do not spend too much time on student responses about why the
puzzle works. Students should just have a sense that algebra can be used to explain why the puzzle works. (The puzzle is
not “magic,” despite its name.) Tell students that they will use magic number puzzles to investigate some important
algebraic ideas in the next activity.
Classroom strategy. If some students have figured out why the puzzle works, you might ask them to write up an
explanation and submit it to you. You might also tell students that you will leave this question as an open-ended challenge,
encouraging them to think about it and work on it on their own.
Online page 2
http://farmington.agilemind.com/LMS/content/work/03x_03_Effort/content/support/deliver_instruction_1.html
Page 1 of 4
Agile Mind Course Content Page
9/2/13 2:50 PM
Preview the activities and learning goals for the day’s lesson.
CORE ACTIVITY (30 minutes)
Students solve magic number puzzles to develop algebraic thinking; define and formalize the concepts of variable, algebraic
expression, and algebraic equation; and explore and test algebraic field properties, including the distributive property.
Online page 3
Students solve magic number puzzles for different starting numbers.
Have students work individually on questions 1 and 2. [SAB, questions 1 and 2] When they finish, have them discuss the
questions with their partners. Then briefly discuss these questions as a class. Students should verify that the ending number
for question 1 will always be 2. Their work on question 2 should confirm that the ending number is always 4 greater than
the starting number.
Online pages 4-8
Students are introduced to key vocabulary and then identify correct magic number puzzles, informally exploring algebraic
properties, order of operations, and equivalent expressions.
Page 4: Use this page to formalize the algebraic term variable. (Students will use a math journal in tonight’s homework
assignment to organize their understanding of the algebraic terms presented in today’s lesson.)
Page 5: Use the animation on this page to demonstrate to students how the letter variable n can be used to represent the
outcome of the magic number puzzle they completed in question 2. Before playing the animation, ask students to record
(on whiteboards) what happens to the variable in each step; then use the animation to check, discussing any differences
between students’ expressions and the ones on the screen.
Step 4: Pause the animation when it shows
(3n + 12) ÷ 3. Ask: Why are there parentheses around the 3n + 12?
Continue animation and ask: What happened to get from (3n + 12) to n + 4? Why isn’t it n + 12?
Note to teachers. The animation on page 5 foreshadows the idea of the distributive property, which will be taught later in
this topic. In panel 4 of the animation, the magic number puzzle moves from the expression (3n + 12) ÷ 3 to the expression
n + 4. Students have had experience with this magic number puzzle from the opener and from the previous online pages
and already know the end result of the puzzle. They will be able to grasp this movement from step 3 to step 4 without the
formal introduction of the distributive property.
Page 6: Have students work with their partners on question 3 in the activity book. They are asked to use the variable n to
represent the outcome of two magic number puzzles. [SAB, question 3] After sufficient time has passed, ask students to
share their resulting expressions for the tables in question 3. Then, use the checks on this page to verify students’ thinking.
Page 7: Use this page to define algebraic expression. Emphasize that all the terms in the results column are algebraic
expressions, even single terms like n and 3n.
Page 8: Use this page to formalize the definition of an algebraic equation. Some questions to ask to check for
understanding:
Can anyone tell us what a variable is in their own words?
What about an algebraic expression?
How is an expression different from an equation?
Who can provide an example of an algebraic expression?
Who can provide an example of a numeric equation? [Sometimes we call these “number sentences.”] How about an
algebraic equation?
Online pages 9-12
Students are introduced to additional vocabulary. They will investigate the associative and commutative properties of addition and
multiplication by looking at several shape equations.
http://farmington.agilemind.com/LMS/content/work/03x_03_Effort/content/support/deliver_instruction_1.html
Page 2 of 4
Agile Mind Course Content Page
9/2/13 2:50 PM
Page 9: Pose the question on the page to students. Ask:
What number could the square represent that would make the equation true?
Are there other numbers that would make the equation true?
Why do you think the equation will be true no matter what number you use?
Page 10: Ask students to complete the activity in their activity book. [SAB, question 4] Use this page to verify students’
responses to question 4. Ask students to explain why they think each equation is true or false. If students think the
equation is false, ask them to provide an example that supports their response.
Page 11: Use this page to formalize the definitions for the commutative properties of multiplication and addition.
Page 12: This page formalizes the definitions for the associative properties of multiplication and addition.
PROCESS HOMEWORK (10 minutes)
Online page 13
Students process the homework due today: Homework 2.5 and Staying Sharp 2.5.
CONSOLIDATION ACTIVITY (25 minutes)
Students practice working with expressions. They will build expressions from a starting number n in a magic number puzzle and
translate verbal descriptions into expressions. They will also use what they learned about the commutative and associative
properties to identify correct magic number puzzles and justify their selections.
Online page 14
This page cues students to work with their partner on the Consolidation activity.
To debrief questions 1 and 2, select students to share their magic number expressions. Pay particular attention to order of
operations and make sure students have correctly applied the distributive property. Since the distributive property will be
covered in the next lesson, you may want to have students use numerical examples to see whether their expressions match
the verbal descriptions.
Classroom strategy. To debrief question 3, have the groups do the third puzzle on the whiteboard. Have them hold up their
whiteboards and have the class scan the answers. Ask students to discuss their reasoning as a class. You can ask questions
like:
Some of you said that Alisha was right, and some of you said that Brianna was right. Who would like to explain why
you think [Alisha’s answer] is the correct answer?
Who would like to explain why you think [Brianna’s answer] is correct?
Now that you’ve heard your classmates’ explanations, which answer do you think is correct?
WRAP UP AND INTRODUCE HOMEWORK (5 minutes)
Online page 15
Homework 3.1
The homework problems are modeled after the problems in today’s lesson. Additionally, students use a math journal to
reflect upon and organize their understanding of the math concepts variable, algebraic expression, equation,
commutative property, and associative property.
Staying Sharp 3.1
The main concepts and skills students will review in these problems are:
1. Finding the sum and product of two given numbers (in a “square box” structure)
2. Writing an algebraic expression to describe a sequence of operations (“magic number”)
3. Finding subsequent terms of a given arithmetic sequence
4. Translating from a graphical representation to a table
http://farmington.agilemind.com/LMS/content/work/03x_03_Effort/content/support/deliver_instruction_1.html
Page 3 of 4
Agile Mind Course Content Page
9/2/13 2:50 PM
5. Generating examples of addition and subtraction of signed integers to find patterns
6. Writing statements articulating structure in addition and subtraction of signed integers
http://farmington.agilemind.com/LMS/content/work/03x_03_Effort/content/support/deliver_instruction_1.html
Page 4 of 4