options: Represent and analyze quantitative relationships between dependent and independent variables.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Perform arithmetic operations on polynomials.

Solve systems of equations.

Use the four operations with whole numbers to solve problems.

Rewrite rational expressions.

Write and interpret numerical expressions.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Understand properties of multiplication and the relationship between multiplication and division.

Generate and analyze patterns.

Create equations that describe numbers or relationships

Reason about and solve one-variable equations and inequalities.

Represent and solve equations and inequalities graphically.

Gain familiarity with factors and multiples.

Use properties of operations to generate equivalent expressions.

Solve equations and inequalities in one variable.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Understand the connections between proportional relationships, lines, and linear equations.

Represent and solve problems involving multiplication and division.

Work with addition and subtraction equations.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Add and subtract within 20.

Understand and apply properties of operations and the relationship between addition and subtraction.

Understand the relationship between zeros and factors of polynomials.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Work with radicals and integer exponents.

Write expressions in equivalent forms to solve problems.

Represent and solve problems involving addition and subtraction.

Use polynomial identities to solve problems.

Analyze patterns and relationships.

Interpret the structure of expressions.

Multiply and divide within 100.

Work with equal groups of objects to gain foundations for multiplication.

Understand solving equations as a process of reasoning and explain the reasoning.
problem_activity: Narrative
The purpose of this activity is to notice the pattern that when 0 is added to a number, the number stays the same and the pattern that when 1 is added to a number, the total is the next number in the count sequence, or 1 more (MP7).
MLR2 Collect and Display.
Collect the language students use to describe what they notice about the value of the expressions when 0 and 1 are added. Display phrases such as: “When we add 0, the total is the same number that we started with, because nothing was added.” During the synthesis, invite students to borrow language from the display as needed.
Advances: Conversing, Reading
Representation: Internalize Comprehension.
Synthesis: Some students may benefit from reiterating the patterns of adding zero and adding one. Make a connection between the two patterns students should notice. For example, “When you add zero to any number you get the same number because adding zero is adding nothing”, “When you add one to any number the total is the next number in the count sequence, or one more.”
Supports accessibility for: Conceptual Processing, Organization
Launch
Groups of 2
Display student book
“Diego and Mai recorded their addition expressions and their values on this page. What do you notice? What do you wonder?” (They always added 1 or 0. Sometimes the first and last number are the same.)
30 seconds: quiet think time
1 minute: partner discussion
Share and record responses.
Activity
“Which expressions show that 0 were added?” (
\(4 + 0\)
,
\(2 + 0\)
, and
\(8 + 0\)
)
30 seconds: quiet think time
Share responses. Highlight or circle the expressions that show
\(+ 0\)
.
“When you played the game, what did you do when you had to add 0?” (Nothing. Zero means none so none were added.)
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
“What do you notice about the value of the expressions when 0 are added?” (It stays the same.)
1 minute: quiet think time
1 minute: partner discussion
Share responses.
“When we add 0, the total is the same number that we started with, because nothing was added.”
Repeat the steps above with
\(+ 1\)
.
Student Facing
\(4 + 0\)
4
[IMG]
\(2 + 0\)
2
[IMG]
\(8 + 0\)
8
[IMG]
\(3 + 1\)
4
[IMG]
\(9 + 1\)
10
[IMG]
\(1 + 1\)
2
[IMG]
Student Response
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Activity Synthesis
“
\(3 + 0\)
is how many?” (
\(3 + 0\)
is 3.)
“
\(2 + 0\)
is how many?” (
\(2 + 0\)
is 2.)
“How do you know that
\(2 + 0\)
is 2?” (Because we didn’t add any more, so the 2 stayed the same.)
Repeat with
\(2 + 1\)
.


correct_option_index: 1