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

Represent and solve equations and inequalities graphically.

Rewrite rational expressions.

Solve systems of equations.

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

Perform arithmetic operations on polynomials.

Interpret the structure of expressions.

Write expressions in equivalent forms to solve problems.

Multiply and divide within 100.

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

Gain familiarity with factors and multiples.

Work with addition and subtraction equations.

Generate and analyze patterns.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Reason about and solve one-variable equations and inequalities.

Add and subtract within 20.

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

Create equations that describe numbers or relationships

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

Use polynomial identities to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

Work with radicals and integer exponents.

Understand the relationship between zeros and factors of polynomials.

Write and interpret numerical expressions.

Use properties of operations to generate equivalent expressions.

Analyze patterns and relationships.

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

Use the four operations with whole numbers to solve problems.

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

Solve equations and inequalities in one variable.

Represent and solve problems involving multiplication and division.

Represent and solve problems involving addition and subtraction.

Understand solving equations as a process of reasoning and explain the reasoning.
problem_activity: Narrative
The purpose of this activity is for students to find all of the compositions and decompositions of 10 in the context of a Put Together/Take Apart, Both Addends Unknown story problem. Monitor for students who:
change the number of red and yellow counters on a 10-frame (MP5).
move the beads on a bead tool (MP5).
use their knowledge, possibly from memory, of different decompositions of 10.
use patterns such as switching the number of pigeons in the fountain and on the bench (MP7).
The purpose of the activity synthesis is to use the 10-frame and the bead tool to visualize how the parts that make 10 are related, specifically that adding one to one number takes one away from the other number in the decomposition.
Action and Expression: Internalize Executive Functions.
Invite students to plan a strategy, including the tools they will use, to figure out all the different ways to make 10. Students can take turns verbally sharing their plan with their partner and work on an overall plan to find all the ways to make 10.
Supports accessibility for: Organization, Conceptual Processing
Required Materials
Materials to Gather
10-frames
Connecting cubes or two-color counters
Materials from a previous activity
Required Preparation
Students can use their bead tool from a previous lesson.
Create a chart displaying solutions to be used during the lesson synthesis.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col", "style": "text-align:center"}, "br": [{}], "_values": ["pigeons in the", "fountain"]}, {"_attributes": {"scope": "col", "style": "text-align:center"}, "br": [{}], "_values": ["pigeons on the", "bench"]}]}]}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "p": [{"_value": "9"}, {"_value": "8"}, {"_value": "7"}, {"_value": "6"}, {"_value": "5"}, {"_value": "4"}, {"_value": "3"}, {"_value": "2"}, {"_value": "1"}]}, {"_attributes": {"style": "text-align:center"}, "p": [{"_value": "1"}, {"_value": "2"}, {"_value": "3"}, {"_value": "4"}, {"_value": "5"}, {"_value": "6"}, {"_value": "7"}, {"_value": "8"}, {"_value": "9"}]}]}]}]}]}
Launch
Groups of 2
Give students access to connecting cubes or two-color counters, bead tools, and 10-frames.
Display and read the task statement.
“Work with your partner to show all of the ways that the 10 pigeons could be in the fountain and on the bench.”
Activity
7 minutes: partner work time
Student Facing
There were 10 pigeons.
Some of the pigeons were in the fountain.
The rest of the pigeons were on the bench.
How many of the pigeons were in the fountain?
Then how many of the pigeons were on the bench?
Show your thinking with objects, drawings, numbers, or words.
Student Response
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Activity Synthesis
Display a 10-frame with 9 red counters and 1 yellow counter and a bead tool with 9 beads on the left and 1 on the right.
[IMG]
[IMG]
“How do the 10-frame and the bead tool show a solution for the story problem?” (There can be 9 pigeons in the fountain and 1 pigeon on the bench.)
Switch one red counter to yellow, as pictured, and move 1 bead from the right to the left.
[IMG]
[IMG]
“What if I change one of the red counters to yellow? What if I move one bead over?” (Then 8 pigeons are in the fountain and 2 pigeons are on the bench.)
“Can I keep changing red counters to yellow? Can I keep moving the beads to the other side? What will happen?” (Yes, more pigeons will be on the bench and fewer pigeons will be in the fountain.)


correct_option_index: 0