# Identify the mathematical goals of the lesson, both short term and

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Identify the mathematical goals of the lesson, both
short term and long term.
Short Term Goals:
Students will be able to add three or more addends using multiple strategies.
Students will be able to provide an explanation of why the commutative property
works for addition.
Students will be able to use the commutative property effectively.
Long Term Goals:
Students will be able to apply and generalize the commutative property to other
mathematical situations i.e. 2 digit addend + 2 digit addend, multiplication,
subtraction, etc.
Identify the ways in which the task can be solved.
 Which of these methods do you think your
students will use?
 What misconceptions might students encounter?
 What errors might a student make?
Adapted from The Thinking Through a Lesson Plan Protocol (TTLP). Developed by M. Smith &amp; V. Bill, School of Education at University of Pittsburgh
Lesson Planning Template *
Adapted from The Thinking Through a Lesson Plan Protocol (TTLP). Developed by M. Smith &amp; V. Bill, School of Education at University of Pittsburgh
Lesson Planning Template *
Launch: How will you introduce students to the
task so as not to reduce the problem solving
aspects of the task(s)?
What will you hear that lets you know students
understand the task(s)?
**See Attached Page for other Ways To Solve Problems
Misconceptions:
 Students may think they can’t change the order of the addends.
 Students might think if they change the order than they would create a
subtraction situation.
 Use addends to show a mathematical expression using two
addends and a sum. (addends: 3, 5, 7)(ex: 3+5=7)
Errors:
 Students may make the ten but forget to add third the addend.
 Students may add one addend twice.
Example: 6+4+4=14
 Calculation errors
Introduction for whole group
1. Teacher will call students to the carpet with manipulative bag.
2. Teacher will read problem aloud to students and ask students to visualize
what is going on.
Story Problem
Jake is building with cubes. He has a tower of 2 green cubes, a tower of 5 blue
cubes, and a tower of 3 yellow cubes. How many connecting cubes does he have?
3. Teacher will write on the board, 2 green cubes, 5 blue cubes, and 3 yellow
cubes after story problem is read aloud.
Adapted from The Thinking Through a Lesson Plan Protocol (TTLP). Developed by M. Smith &amp; V. Bill, School of Education at University of Pittsburgh
Lesson Planning Template *
4. Teacher will model with the snap cubes.
5. Ask students to retell the story in their own words. This will allow us to
know if students understand the story.
6. Have students retell the story to a partner or group of 3.
7. Call on student to retell story for whole group. (checking again
for understanding)
8. Students will have two minutes to solve problem individually with a
partner on the carpet.
Students would sit with a partner.
9. Discuss strategies for solving. Record strategies on
chart/SMARTboard/ whiteboard.
10.Teacher poses question if possible: Some of you changed the order of the
numbers around and added them together and you still got the same answer.
We are going to explore this idea further at different stations. Think about
this question while you are working on the different problems. Do you
think this will be true to the other problems you will be working on?
Partner work: Students will complete two centers first then one after
check in. Fourth problem will be used for whole group discussion at
end.
Story Problem: (on a worksheet that has the highlighted guided
prompts)
Students will begin “centers” with completing two story problems.
Teacher will then pull group back together to have a check in time.
Jake went to the store with his mom. While they were there they bought 6 blue
cars, 3 green cars, and 4 yellow cars. How many cars did they purchase?
Explore: As students are working independently
or in small groups:
 What questions will you ask to focus their
thinking?
 What will you see or hear that lets you know how
students are thinking about the mathematical
Mady went to the apple orchard to pick some apples. She picked 6 yellow apples,
ideas?
8 red apples, and 5 green apples. How many apples did Mady pick?
 What questions will you ask to assess students’
understanding of key mathematical ideas,
Kelly went on a leaf hunt. She found 8 red leaves, 5 yellow leaves, and 5 brown
problem solving strategies, or their
Adapted from The Thinking Through a Lesson Plan Protocol (TTLP). Developed by M. Smith &amp; V. Bill, School of Education at University of Pittsburgh
Lesson Planning Template *
representations?
 What questions will you ask to advance students’
understanding of the mathematical ideas?
 What questions will you ask to encourage
students to share their thinking with others or to
assess their understanding of their peers’ ideas?
leaves. How many leaves did she find?
Marcy went to the pumpkin patch. She bought 5 big pumpkins, 2 medium
pumpkins, and 3 small pumpkins. How many pumpkins did she buy?
Questions/Prompts: (On a discussion notecard)
3.Would this this strategy be true for other numbers?
1.Try adding the numbers in different orders i.e. 2+5+3 or 5+3+2
What happens if the smallest number goes first? Largest number?
Think about if you can change the order of the numbers without changing the
total.
4.Does it work all of the time or only some of the time?
4. When you change the order of the numbers do you get the same
answer? Why do you think so?
2.Show me another way to solve this problem.
What you will see:
Collaborative grouping Pair/Share – students sharing ideas or thoughts
Students using different strategies to solve the problem
Thinking aloud – “I know…”
Manipulating cubes, tens frame number line, etc.
Asking each other questions within the group using the prompt cards
Asking the teacher for more support
Students arguing
Students shutting down – overwhelmed.
What you can prompt with:
Can you show me what your brain is thinking?
Tell me more.
Teach me what you’re thinking.
Adapted from The Thinking Through a Lesson Plan Protocol (TTLP). Developed by M. Smith &amp; V. Bill, School of Education at University of Pittsburgh
Lesson Planning Template *
“If the principal comes in, what would you say to convince her that you can add
numbers in any order and get the same answer? How could you help him
understand why this works?”
What if…
Will that work for other numbers?
Does it work every time? How do ou know?
Check in discussion points:
Ask student to share how they got started.
Did you find another way to solve the problem?
Did you do something different at your second station?
Ask class “Does someone have another way to solve this problem?”
Have students share by using the manipulatives so they have a
concrete understanding of how to use them.
Send students out to complete the last two centers with the question
“Would this strategy work every time? How can you prove it?”
Whole Group Discussion: after they complete last center
In your own words, could you explain the strategy that your classmate used?
We might see students trying different strategies that classmates have shared.
Strategically pick a student who used the addends in order
presented in story.
Ask if someone has a different strategy. Compare the different
strategies presented by students. (What is the same and what is
different?)
Use the fourth story problem for whole group discussion/practice.
Adapted from The Thinking Through a Lesson Plan Protocol (TTLP). Developed by M. Smith &amp; V. Bill, School of Education at University of Pittsburgh
Lesson Planning Template *
Which solution paths do you anticipate will come
up and which do you want to have shared during
the class discussion in order to accomplish the
goals for the lesson?
 Which will be shared first, second, etc.? Why?
 In what ways will the order of the solution paths
helps students make connections between the
strategies and mathematical ideas?
Students who kept the addends in the order they were given:
Concrete Manipulatives – Number line – Tens Frame – Number sentences
What will you see or hear that lets you know that
students in the class understand the mathematical
ideas of problem solving strategies that are being
shared?
Students can share in their own words what a classmate explained. Students can
further explore using a strategy that someone else shared.
Students who move the addends around:
Concrete Manipulatives – Number line – Tens Frame – Number sentences
Students who broke numbers apart to create new addends:
Concrete Manipulatives – Number line – Tens Frame – Number sentences
Adapted from The Thinking Through a Lesson Plan Protocol (TTLP). Developed by M. Smith &amp; V. Bill, School of Education at University of Pittsburgh
Lesson Planning Template *
Ways Students May Solve Task
Adapted from The Thinking Through a Lesson Plan Protocol (TTLP). Developed by M. Smith &amp; V. Bill, School of Education at University of Pittsburgh
Lesson Planning Template *
8+5+5
Adapted from The Thinking Through a Lesson Plan Protocol (TTLP). Developed by M. Smith &amp; V. Bill, School of Education at University of Pittsburgh
Lesson Planning Template *
6+8+5
Adapted from The Thinking Through a Lesson Plan Protocol (TTLP). Developed by M. Smith &amp; V. Bill, School of Education at University of Pittsburgh
Lesson Planning Template *
Adapted from The Thinking Through a Lesson Plan Protocol (TTLP). Developed by M. Smith &amp; V. Bill, School of Education at University of Pittsburgh
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