Grade/Subject: Algebra – Semester A
Lesson: 9
Lesson Outcomes:
Objective:
Standards:
What will students be able to do by the end of the lesson? (Younger children
What content, state and/or Common Core standards does this lesson and
and beginning English speakers will benefit from content objectives that are
objective align to?
written in simple, “student friendly” language)
Content Objective:
CCSS.MATH.CONTENT.HSA.REI.D.10
SWBAT create graphs of lines given two points or a slope and one point and
Understand that the graph of an equation in two variables is the set of all its
then use these graphs to create matching equations in slope intercept and
solutions plotted in the coordinate plane, often forming a curve (which could
point slope form.
be a line).
Language Objective:
SWBAT describe the usefulness of both forms of linear equation in creating the
representative graph.
Supplementary Materials:
List any supplementary materials that you will
include in the lesson to: scaffold student’s
understanding and provide opportunities for
language practice and application.
How will you organize these materials to promote
efficiency and student agency?
Key Vocabulary:
Which words from the unit plan will you be teaching
and/or reinforcing today? Select no more than 5-6
words. Reference the Unit Plan to see the 10-15
Content, General Academic and Functional
Vocabulary being taught in this unit)
→Be sure to include student friendly definitions for
teachers to share with students for each of the key
vocabulary terms identified.
→Consider any supplementary materials that you
can use to further assist in students’ understanding
these key terms and list these materials in the
supplementary materials section.
Explicit Connections to Prior Knowledge, Past
Learning and Building Background:
1.What prior knowledge and experiences might
students bring to this content (based on their life
experiences/world understandings)? How will you
explicitly activate students’ prior knowledge in the
lesson?
2- How does the content in this lesson connect to
the content learning from past lessons? How you
will name and explicitly link these in the lesson for
students?
3- Where might there be a need to build
background for students where gaps in knowledge
and/or experience may exist? What will you do to
build this background for students?
1
Do Now Half Sheets
Algebra1.A.LP9.Handouts (Explore, Practice, Exit
Ticket)
Slope intercept form
Point Slope form
Slope
Y intercept
1. Connections to students’ prior knowledge
& experiences:
● Students have spent much of their
mathematical careers exploring and
creating equivalent expressions that appear
different.
2. Connections to content of this lesson from
previous lessons:
● Students have spent the majority of the
semester developing understanding of
the slope intercept form of linear
equations.
3. Anticipated areas where building
background might be needed:
●
Plotting points
● Evaluating expressions
Assessment:
(Consider barriers to student expression of learning)
See Exit Ticket
Student Exemplar Response:
2. Infinite possible answers but all right answers include slope of ½.
4. Point Slope: infinite answers but all answers follow format y – y1 = -3(x-x1)
Slope intercept: y = -3x - 1
Attribution:
[Include any lesson design attribution here]
Agenda & Materials
Activity
Materials
Opening
Launch
Do Now
Explore
Explore Worksheet
Discuss
Practice
Practice Worksheet
Reflect / Closing
Exit Ticket
Lesson Methods:Guided Inquiry
Notes to/for Teacher:
Lesson Plan/Scripting:
Opening Time: Time:13 min
Content Note:
Learning Environment Note:
To what extent does this decision
(action, system, arrangement, etc.)…:
● promote relationships in
which students are seen and
heard as individuals?
● increase equity of access to
learning for all students?
Print out half-sheets with the Do Now, and also include some celebratory and affirming notes so that students have the
opportunity to see their names in writing linked to a specific success they’ve had this week. Consider using individual
student shout-outs related to perseverance, sense making, etc., or quoting specific lines that students have written on
yesterday’s assessment; avoid praise related to being “smart” or simply scoring highly. Also consider shout-outs or praise
related to students’ behavior and attitudes during the week as well (e.g. pair work using sentence starters, quick
transitions between activities). Ensure that your praise is affirming and reinforcing the behaviors and attitudes you most
care about and that are most aligned to students’ mathematical learning and experience of classroom culture, rather than
just finding any praise for the sake of giving praise. You may want to ensure that students whose work/thinking/attitude
●
push against systems of
has been publicly highlighted on the page feel special; while some students at this age feel uncomfortable with oral praise
oppression and promote
in front of the whole class, consider the following (these are just suggestions; choose something that feels authentic to
justice in your classroom
you):
community?
● provide clarity and the “what
● When these students enter the room, whisper “make sure you read the opening carefully, since I think you’ll see
and how” of engaging in the
something interesting!” or “hey, I think I saw your name somewhere… maybe in the opening?” (or whatever feels
task at hand?
like your personality)
● support and build excitement
● Offer students a sticker to put on their paper or to wear (only if this feels appropriate given your emerging
about the instructional
relationships with students; some teenagers love stickers, and others find them condescending)
goals?
● Instead of distributing the half-sheets at the door or through a paper-passing routine, have them placed on desks
before students walk in; add a post-it note with a personal word of encouragement or even a smiley face at the
UDL Note: (Consider the following
seats of highlighted students
● Print the shout-outs in larger font and post them on a bulletin board
guidelines)
●
●
1.2/1.3 Offer alternatives for
auditory/visual information
(directions)
3.3 Guide information
processing, visualization and
manipulation
7.1 Optimize individual
choice and autonomy
7.2 Optimize relevance,
value, authenticity
9.2 Facilitate personal coping
skills and strategies
Students should read the shout-outs and complete the warmup problem. Ask students to raise their hands and share
additional shout-outs for their peers; record these in writing on a bulletin board, piece of chart paper, piece of cardstock,
etc., so they are visible the rest of the day.
Directions: As you walk into the room, find your stack of papers for the day on your desk. Work independently and
silently on the do now question for 5 minutes.
Praise: You came in and got right to work! This energy inspires your classmates to do the same.
●
I can see that you’re actively trying other strategies, that shows courage in the face of new content.
Re-engage Learners:
●
What do you think is the first step?
Does this problem look like the ones we’ve been doing?
Students should be able to create the table of values fairly easily, because they have done so before. If necessary, remind
SIOP/LRT Note:
them that they can do so using substitution. A very small number of students might need an example, such as y = 4(1) + 3,
● Begin the lesson by sharing
but this should be a scaffold of last resort because it effectively gives away a key skill that students should already know
the content and language
objectives with your students and should feel comfortable applying in any context. Some students may not know what to do if the points they find
cannot be plotted on the graph (because they are off the axes); if this is the case, encourage students to start with points
● Introduce, reinforce, or
that will fit, like x-values of -1, 0, and 1 in this case, and if they can find enough points that fit, to just use those to draw
review the key vocabulary
that students will be using in the line. Otherwise, they can expand the graph.
the lesson
In the warm-up problem, some students may not know where to begin with the second method; if this is the case,
● Make explicit connections
provide moral support and encouragement. Use statements and probing questions such as:
between today’s content and
●
●
●
students’ experiences
Make explicit connections
between today’s content and
previous lessons
Explicitly build background
where gaps in
knowledge/experiences
might exist
●
●
●
●
●
●
What does your gut tell you about where the line should be?
Does this line have a larger or smaller slope than the other two? What do you think that means about what it will
look like?
Where will this line cross the y-axis?
[if students recognize that this line will be steeper and have the same y-intercept, but not know how to represent
this on paper] Okay, so if it has the same y-intercept, show me a point that you know will be on the graph.
What do you think a slope of 4 means?
If the y-value grows by 4 each time the x-value increases, where would the next point be?
If nearly half the class appears to be at a loss for an additional method, bring the class back together and ask whether any
pairs have ideas they’d be willing to share. Elicit several options without evaluating them (unless the class is truly at a
loss, in which case the above questions will be helpful), and then send pairs back to keep working.
(7 min)
Invite pairs to share their second methods by describing them. Ask follow-up questions like:
●
●
●
●
●
●
Did anyone else use a similar method?
Did you hear anything in this method that you also did?
Did you hear anything in this method that you’re not sure about, and want to learn more about? Do you have any
clarifying questions for your classmates about this method?
Do you think this method will always work? Why or why not?
Did anyone use a different method?
What is efficient about that method compared to creating a table of values?
As students share, revoice and highlight methods that start with a given point (the y-intercept) and use the slope to find
the next point, and connect the two points. Also reinforce methods that cross-check the procedure using intuition or a
conceptual understanding of the relative steepness of the line and how it should look as compared to the existing lines on
the graph.
By the end of this discussion, students should feel confident sketching a graph without creating a table of values. They
could do so by eyeballing or by counting up and over from a point that they know, like the y-intercept.
Survey: Time: 7 min
Content Note: Students are
introduced to the overarching task
for the lesson by engaging in a
whole-class discussion. The
discussion ensures that students
understand the various aspects of
the task well enough to get started
on student-led work in the “Explore”
instructional activity.
In the spirit of maintaining cognitive
demand, during the Launch, students
are NOT introduced to a particular
suggested solution
method. Students are positioned
with the context they need to drive
exploration of solution methods.
Learning Environment Note:
To what extent does this decision
(action, system, arrangement, etc.)…:
● promote relationships in
which students are seen and
heard as individuals?
● increase equity of access to
learning for all students?
● push against systems of
oppression and promote
justice in your classroom
community?
● provide clarity and the “what
and how” of engaging in the
task at hand?
● support and build excitement
about the instructional
goals?
SAY: We’ve come to the half way point of our summer class. Now, I would love to get your feedback on how I’ve been
doing. I told y’all at the beginning and I’ll say it again, my end goal is for you all to succeed and master this content. To
help me reach this goal, I wanna hear from you.
Directions: For the next 5 minutes you will be filling out a survey. There are 10 questions. Think through the summer so
far before you answer. I want your honest feedback so these will be anonymous.
Praise: I can tell that you are thinking critically about each answer. Thank you.
Re-engage Learners:
I can’t improve in ways you want if you don’t provide this feedback.
What do you wish I could do better as your teacher?
UDL Note: (Consider the following
guidelines)
● 1.2/1.3 Offer alternatives for
auditory/visual information
● 2.3 Support decoding of text,
mathematical notation, and
symbols
● 2.5 Illustrate through
multiple media/multiple
formats
● 3.1 Activate or supply
background knowledge
● 3.2 Highlight patterns, critical
features, big ideas, and
relationships
● 3.3 Guide information
processing, visualization, and
manipulation
● 7.2 Optimize relevance,
value, and authenticity
Explore- Making Predictions: Time: 20 min
Content Note: Students work
independently and/or collaboratively
to develop and reflect on strategies
for problem-solving. They are
encouraged to communicate with
precision, using clear definitions in
their reasoning, and examining each
other’s claims.
Check for understanding on the task and how students should engage with one another/what they will produce.
SAY: Personalize scripting. Frame the lesson: yesterday, you considered how to create graphs from equations in slopeintercept form, and the day before, learned how those equations were connected to situations. Sometimes, however, we
don’t have enough information to determine both a slope and an intercept from a situation (like the example we just
looked at). In today’s lesson, we’ll figure out how to create graphs from these new situations, so that we can use them to
analyze and make predictions. Provide directions for students to approach the task with their partners.
Students make sense of and
persevere through problems: They
analyze givens, constraints,
Consider where/how you would want to break these 20 minutes up. Are there any questions you think may yield a
particular misconception as you ANTICIPATE? Are there particular questions that you think students may get stuck on and
<META-MOMENT>
relationships, and goals. They make
conjectures about the form and
meaning of the solution and plan a
solution pathway rather than simply
jumping into a solution attempt.
They consider analogous problems,
and try special cases and simpler
forms of the original problem in
order to gain insight into its solution.
They monitor and evaluate their
progress and change course if
necessary. Mathematically proficient
students check their answers to
problems using a different method,
and they continually ask themselves,
"Does this make sense?" They can
understand the approaches of others
to solving complex problems and
identify correspondences between
different approaches.
Learning Environment Note:
To what extent does this decision
(action, system, arrangement, etc.)…:
● promote relationships in
which students are seen and
heard as individuals?
● increase equity of access to
learning for all students?
● push against systems of
oppression and promote
justice in your classroom
community?
● provide clarity and the “what
and how” of engaging in the
task at hand?
● support and build excitement
about the instructional
not be able to move forward? These may be natural places to bring students back together as a class before the end of 20
minutes. If students are working productively during the whole block (and they eventually will after doing this routine so
many times) chunking may be less necessary. Most students will struggle to work continuously for 20 minutes, especially
if they are frustrated. Bringing students back together can help students get ideas to sustain their thinking and move their
progress forward.
Directions: For the next 20 minutes you will work with a partner to make it though our explore worksheet. This should
be at Partner level volume. We will be coming back together at times throughout to check in so listen for me call back.
Praise:
“You are pushing through confusion. That perseverance will carry you through.”
“XYZ is showing their partner their strategy. This collaboration helps us all learn together.”
Re-engage Learners:
“Which problem are you going to do first?”
“How do you think point slope and slope intercept form relate? What can that show us?”
Support students to focus on the conceptual and persevere through problems.
As they work, they’ll likely struggle with the equations they’re being asked to write, because unless they remember how
to create equations in point-slope form from the year, they’ll have had nothing this summer to help them do so.
Encourage students to try and come up with a method, or to make a prediction for how they might approach the
equation. Students may use their graphs to find the intercept, and then construct an equation in slope-intercept form;
this method should be affirmed for creative thinking and applying prior knowledge even though it isn’t ultimately the
method students should learn in this lesson. The struggle during this phase is intentional, because it will help students
recognize that there are things they do know and can figure out—like how to graph—and places where more information
might be helpful.
Probe and extend student thinking with back-pocket questions.
Look for student ideas to elevate in Discuss / prepare them to share their thinking, evidence, and reasoning through
questioning.
While conferring, focus on ensuring that all students can graph successfully so that during Discussion, it’s possible to
focus primarily on the equations. Consider asking 1-2 students who finish early to create their (correct) graphs on the
board (or on posters, or some other form that is visible to the entire class). If this doesn’t feel like something you’re
goals?
UDL Note:
● 3.4 Maximize transfer and
generalization
● 5.1 Use multiple forms of
communication
● 5.2 Use multiple tools for
construction and
composition
● 5.3 Build fluencies with
graduated levels of support
for practice and performance
● 6.2 Support planning and
strategy development
● 6.4 Enhance capacity for
monitoring progress
● 7.2 Optimize relevance,
value, and authenticity
● 8.3 Foster collaboration and
communication
● 9.3 Develop self-assessment
and reflection
comfortable with for reasons of class culture, have the graphs prepared ahead of time (or ask a non-teaching collab
member to create them) so that class time isn’t spent waiting for the teacher to create them.
<META MOMENT>
Note that question #7 requires students to make predictions by reading the graph or by evaluating an expression (solving
an equation). This skill hasn’t been formally taught in the summer, but it shouldn’t be challenging to students because of
their prior mathematical experience (in middle school and during the past school year); what’s likely to be hard is figuring
out what the question is asking, because students may be accustomed to being told to evaluate an expression, or solve an
equation, or read a graph. It’s not critical that all students answer this question during Explore, because it’s not the target
mathematical objective for today’s lesson, but it is helpful to informally assess, as you circulate, whether most students
seem to find this fairly straightforward or if they appear to be completely lost. If the latter, you’ll want to use your flex
time next week to do a mini-lesson.
Discuss: Formally establish new ideas Time: 20 min
Content Note: Students present their
strategies to the class in a purposeful
sequence (facilitated by the teacher)
that supports the evaluation of
strategies for validity, accuracy, and
efficiency, as well as build on each
other to develop powerful
mathematical ideas.
Use an attention-getting signal to bring class together.
Elicit student ideas about the concept at hand.
If students have posted their graphs on the board, ask them to present their work by explaining how they created the
graphs. If the graphs are teacher-created, simply acknowledge that you saw many correct graphs as you were circulating
the room and give students a minute to silently check their answers by comparing key features (before doing this,
consider asking what they’ll pay attention to on the public graph and on their graph to make sure they’ve graphed
accurately: the intercept, the slope, and key points). You can also consider having various students come up to do
different parts of the graph, especially if students were missing some elements, but had others correct.
Students listen to or read the
arguments of others, decide whether
they make sense, and ask useful
questions to clarify or improve the
arguments. They justify their
conclusions, communicate them to
others, and respond to the
arguments of others. They reason
inductively about data, making
plausible arguments that take into
account the context from which the
data arose. Mathematically
proficient students are also able to
compare the effectiveness of two
plausible arguments, distinguish
correct logic or reasoning from that
which is flawed, and—if there is a
flaw in an argument—explain what it
is.
Learning Environment Note:
To what extent does this decision
(action, system, arrangement, etc.)…:
● promote relationships in
which students are seen and
heard as individuals?
● increase equity of access to
learning for all students?
● push against systems of
oppression and promote
justice in your classroom
community?
● provide clarity and the “what
and how” of engaging in the
task at hand?
Directions: Now that we’ve completed our explore, let’s come together and discuss the answers. We are going to
discuss the explore for the next 20 minutes whole group. Remember our discussion norms (POSTED) when answering
and commenting.
Praise:
“Sharing your answer and strategy takes courage. Thank you for taking academic risks in this class.”
“I see that your writing down as someone else shares a different strategy to you. That will help you if you get confused
when we are working independently.”
Re-engage Learners:
“What did you get for number one? XYZ got this.”
“Can you restate what XYZ just said?”
Refer to the Explore questions to guide student thinking to key observations and ideas about the concept at hand.
Focus the discussion on the equations; start with the first problem, and elicit students’ ideas and suggestions for how to
create an equation. If students remember how to use point-slope form, or remember parts of it, validate that and build
on what they remember. If nobody remembers, they’re likely to share processes of finding the y-intercept from the graph
and creating an equation in slope-intercept form, or else have suggestions that are farther off the mark. If this is the case,
find value in students’ contributions, even if it is as simple as “I noticed that you found a way to incorporate the slope into
the equation, which was an important part of yesterday’s equations too.” Offer “one way I can write the equation is like
this” and present the equation in point-slope form: y – 76 = 4(x – 3). Ask whether this looks familiar to anyone, and if so,
ask “what about this looks familiar?” Students should recognize the slope—and be able to tell you how you found the
slope, given their prior lessons this week—and recognize the point being used. State that this is called point-slope form,
which is different from the slope-intercept we’ve been studying, because to write it, we use a point and the slope.
Also ask how we could “prove” that the point-slope form of the equation and the slope-intercept form of the equation
are identical. Students should know that they can distribute and simplify to transform an equation from point-slope to
slope-intercept form, but if they do not, posing this question could easily derail the discussion into a conversation about
distribution; if you have seen students distributing successfully, however, earlier in this lesson or in previous lessons,
there’s great mathematical value in making this connection.
Have students make a conjecture about the concept at hand.
<META-MOMENT>
This is the CONNECTING phrase of mathematical discussion.
●
support and build excitement
about the instructional
goals?
Support students to bridge their thinking to mathematical language where appropriate.
Ask students how we would write the equation in point-slope form for #2 and #3; pause for a few seconds of silent thinkUDL Note: (Consider the following
time (at least 10), and then ask them to turn-and-talk to their partners to construct the equation. Elicit student equations,
guidelines)
and ask for agreement/disagreement. Suggest y – 1 = -2(x – 6), and ask whether this is correct; students should be able to
● 1.2/1.3 Offer alternatives for
indicate that it is not, because the x- and y- coordinate in the given point have been switched.
auditory/visual information
● 2.1/2.2 Clarify vocabulary
Reinforce the pattern/algorithm recognition with more at-bats.
and symbols/ syntax and
structure
Ask students to work with their partners to find the equations in point-slope form for #4 and #5 now, and give them a
● 2.5 Illustrate through
minute or so to do it; they will need to first calculate the slope, which might take them a little bit of time to figure out.
multiple media/ modes
Review the answers by eliciting students’ equations and asking for feedback from the class (ensure that students who are
● 3.2 Highlight patterns, critical
agreeing or disagreeing are providing rationale with evidence that highlights the slope and the x- and y-coordinates).
features, big ideas, and
relationships
● 3.3 Guide information
processing, visualization, and Key ideas: Students should leave this lesson knowing how to construct a graph when given two points, or a point and a
slope, in addition to being given a slope and an intercept.
manipulation
● 8.1 Heighten salience of
goals and objectives
Synthesize the conversation by explicitly making the connection between slope-intercept and point-slope form. Ask, and
● 8.2 Vary demands and
resources to optimize
consider having students turn-and-talk or stop-and-jot their answers:
motivation
● Yesterday and at the beginning of class, we considered slope-intercept form. What information did we need to
● 8.3 Foster collaboration and
know? How did we graph?
community
● How would you define point-slope form?
What’s similar about slope-intercept form and point-slope form? What’s different?
Practice: Time: 18 min
Content Note: Students engage in
additional “at-bats” with
mathematical problems aligned to
the instructional goal of the lesson,
including applying and extending
Directions: Now that we’ve learned more about how to graph and explored point slope form, we are going to do some
independent practice. This is your chance to show me what you know and highlight if you are confused with any of the
content. You will have 15 minutes to complete this worksheet silently and independently.
Praise:
“You focused well in class today, I can see how it helped you grasp the concept.”
“You have pushed through learning this new content well! That will carry you as the summer goes on.”
their knowledge to new contexts and
scenarios.
Re-engage Learners:
“I know that this is some new content and it can be overwhelming, but if you don’t try I can’t tell where you are getting
confused.”
“What problem do you think will be the easiest?”
Learning Environment Note:
To what extent does this decision
Students complete practice sheet.
(action, system, arrangement, etc.)…:
● promote relationships in
Plan back-pocket questions to assess student understanding throughout.
which students are seen and
heard as individuals?
● increase equity of access to
learning for all students?
● push against systems of
oppression and promote
justice in your classroom
community?
● provide clarity and the “what
and how” of engaging in the
task at hand?
● support and build excitement
about the instructional
goals?
UDL Note: (Consider the following
guidelines)
● 2.2 Support decoding of text,
mathematical notation, and
symbols
● 3.4 Maximize transfer and
generalization
● 4.1 Vary the methods for
response
● 5.1 Use multiple forms of
communication
● 5.2 Use multiple tools for
construction and
composition
● 5.3 Build fluencies with
●
●
●
●
graduated levels of support
for practice and performance
6.2 Support planning and
strategy development
7.1 Optimize individual
choice and autonomy
8.4 Increase masteryoriented feedback
9.3 Develop self-assessment
and reflection
Reflect/Closing Time: Time: 12 min
Content Note: Students codify their
learning and clarify definitions and
examples. They consider how they
are learning, how they are making
progress to their goals, and the value
they are seeing in learning the
content.
Directions: You will have 10 minutes to complete the exit ticket. This will be done silently and independently at your
seats.
Review content and language objectives: As we close out, lets check back into our objectives. Did we achieve them?
Where do we still need more work?
Praise: You worked really hard today, I’m sure this will show in the exit ticket.
You are truly diving into this content.
Re-engage Learners: Which of our strategies do you think would be most effective here?
What do we know based on the question?
Learning Environment Note:
To what extent does this decision
(action, system, arrangement, etc.)…:
● promote relationships in
which students are seen and
heard as individuals?
● increase equity of access to
learning for all students?
● push against systems of
oppression and promote
justice in your classroom
community?
● provide clarity and the “what
and how” of engaging in the
task at hand?
“We’re nearing the end of our class time for today. I’d love to get at least three people to summarize really quickly what
we focused on today in class and any major things that are important to remember on this topic?”
“As you leave today, I have an exit ticket for you to do that will tell me how well you are understanding the concepts and
help me know if we need more practice for our upcoming lessons.”
●
support and build excitement
about the instructional
goals?
UDL Note: (Consider the following
guidelines)
● 3.1 Activate or supply
background knowledge
● 3.2 Highlight patterns, critical
features, big ideas and
relationships
● 5.1 Use multiple forms of
communication
● 5.2 Use multiple tools for
construction and
composition
● 6.3 Facilitate managing
information and resources
● 8.3 Foster collaboration and
community
● 9.3 Develop self-assessment
and reflection
SIOP/LRT note:
Review the content and language
objectives covered in today’s lesson