Mr. Linam · Advanced 7th Grade Mathematics
The Longfellow building with handwritten math across the sky and pavement
Longfellow Career Exploration Academy · Dallas ISD

Advanced 7th Grade Mathematics

Mr. Linam · 2026–27
This week
This weekedit the Google Doc — it updates live

Start here

Quarter 1 · modules
Modules for the quarter: artifacts, videos, answers, and every due date.
Check Your Understanding
Worked answer keys for every Topic Overview Guide. Work the questions first, then check.
Student Resources
Topic Overview Guides, Mathia, the Desmos calculator, and STAAR materials.
Calendar · dates
The A/B/C week, quarter windows, and assessment dates.
Syllabus

Syllabus 26–27

Syllabus 26–27Google Drive
The year

8 Units

Unit 1 cover
Unit 1Transformations, Dilations & the Slope Bridge
Unit 2 cover
Unit 2Foundations of Linear Functions
Unit 3 cover
Unit 3Bivariate Data & Trend Lines
Unit 4 cover
Unit 4Real Numbers & Advanced Equations
Unit 5 cover
Unit 5Pythagorean Theorem & 3-D Measurement
Unit 6 cover
Unit 6Data & Financial Literacy
Unit 7 cover
Unit 7State Assessment Review
Unit 8 cover
Unit 8Probability & Statistics
Answer keys

Check Your Understanding

Work the questions first. Then check.

The Longfellow student crest
“Attempt to solve problems on your own. Ask for help when you cannot.”
Longfellow Essential 10
The 5% raise

A saved Topic Overview Guide with every Check Your Understanding question completed, turned in at the end of the quarter, raises that quarter's Standards Mastery Check score by 5% per guide. Only that quarter's guides count.

Pick a unit
Unit 1 · Guides 1A–1D · Artifacts 01–13

Transformations, Dilations & the Slope Bridge

“Mistakes are opportunities for reflection and improvement.” — Longfellow Graduate Mindsets

Topic 1A — Rigid Motions · worked keyGoogle Drive
Topic 1B — Dilations and Similarity · worked keyGoogle Drive

Topic 1C — Angle Relationships · 27 answers

1. The three interior angles of any triangle add to 180°. It lets you find a missing angle when the other two are known.
2. 70° (180-50-60)
3. 55° (180-90-35); the right angle uses 90°, so the other two angles must add to 90°.
4. x=20; angles 40°, 60°, 80° (2x+3x+80=180)
5. x=40; angles 40°, 60°, 80° (x+(x+20)+(x+40)=180)
6. 70° each ((180-40)÷2)
7. x=32; base angles 64° each, apex 52° (2x+2x+(x+20)=180)
8. x=40; angles 40°, 70°, 70° (x+(2x-10)+(x+30)=180)
9. Two right angles already total 180°, leaving 0° for the third angle. A triangle needs three angles that sum to 180°, so two right angles is impossible.
10. 105° (47+58); exterior angle theorem
11. 62° (120-58)
12. x=15; exterior angle 85° (5x+10=3x+40)
13. x=20; remote interior angles 80° and 60° (4x+3x=140)
14. Exterior angle =110°; interior angle at R=180-110=70°; check with the triangle sum: 50+60+70=180 — both give 70°.
15. Other remote interior angle =60° (130-70); interior angle next to the exterior angle =50° (180-130)
16. x=20; interior angle at R=80° (4x+5x=180, a linear pair)
17. A
18. The exterior angle and its adjacent interior angle form a straight angle: e+(interior)=180. By the triangle sum that interior angle =180-a-b, so e=180-(180-a-b)=a+b.
19. ∠2=70° (linear pair with ∠1, supplementary); ∠4=110° (vertical to ∠1); ∠5=110° (corresponding to ∠1)
20. C
21. x=30; angle =90° (corresponding angles equal: 3x=2x+30)
22. x=32; angles 64° and 116° (same-side interior angles are supplementary: 2x+(3x+20)=180)
23. x=30; angle =110° (alternate interior angles equal: 4x-10=3x+20)
24. ?=65°; corresponding angles
25. Third angle of each =70° (180-50-60); both triangles have angles 50°, 60°, 70°, so they are similar by the angle-angle (AA) criterion.
26. 12 (scale factor 9÷3=3, so 4×3=12; or 3/4=9/x)
27. At each parallel line the transversal forms corresponding angles, and corresponding angles are equal when the lines are parallel, so the transversal makes the same angle at every parallel line.

The worked key posts the same way as 1A and 1B.

Topic 1D — Introduction to Slope · 27 answers

1. Slope =\dfrac{rise}{run} — the vertical change (rise) divided by the horizontal change (run) between two points on the line.
2. 1/2=2/4; slope =1/2
3. 3/4
4. rise =6 (2/3=r/9)
5. run =15 (4/6=\tfrac{10}{run})
6. Points (5,2) and (10,4); line drawn through the origin
7. y=6 (3/4·8)
8. Every slope triangle on the line has a right angle and shares the line's angle with the horizontal, so all are similar by AA. Similar triangles have equal rise-to-run ratios, so the line has one constant slope.
9. slope =4/6=2/3; y=6 when x=9 (2/3·9)
10. 2 (8/4)
11. 2 (10-2/5-1=8/4)
12. -2 (0-6/3-0=-6/3)
13. 3 (+3 in y for each +1 in x)
14. 2 ft per day (24-14/12-7=10/5=2, and the same for every pair)
15. 2.80 per mile (17.00-8.60/5-2=8.40/3=2.80, and the same for every pair)
16. 2 (11-3/6-2=8/4)
17. Sample: (7,14) and (12,24) give 10/5=2; (12,24) and (20,40) give 16/8=2 — the equal rate confirms the points lie on one straight line.
18. Divide the change in y by the change in x (Δ y/Δ x) between two rows, using the actual differences — do not assume the x-steps are equal.
19. slope 2, y-intercept 4; y=2x+4
20. slope 3, y-intercept 2; y=3x+2
21. slope 1/2 (0.5), y-intercept 4 (at x=2, y=5, so b=5-0.5(2)=4); y=0.5x+4
22. slope 2.50 (2.50 per mile); y-intercept 3.00 (3.00) — the slope is the cost per mile and the y-intercept is the base fare before any distance.
23. y=35 (3·10+5)
24. slope 2, y-intercept 1; y=2x+1
25. Break-even (8,8) — cost y=0.5x+4 and revenue y=x meet where 0.5x+4=x, so x=8; at 8 units the cost equals the revenue.
26. y-intercept 5 (11=3(2)+b); y=3x+5
27. The slope is the rate of change — how much the total changes per unit (e.g. cost per mile or per hour). The y-intercept is the starting value when x=0 — the fixed or base amount before any units.

The worked key posts the same way as 1A and 1B.

Unit 2

Foundations of Linear Functions

One guide covers this unit. The key posts with the guide in Quarter 2.

Unit 3

Bivariate Data & Trend Lines

One guide covers this unit. The key posts with the guide in Quarter 2.

Unit 4

Real Numbers & Advanced Equations

Topic keys post with their guides in Quarter 3.

Unit 5

Pythagorean Theorem & 3-D Measurement

One guide covers this unit. The key posts with the guide in Quarter 3.

Unit 6

Data & Financial Literacy

One guide covers this unit. The key posts with the guide in Quarter 3.

Unit 7

State Assessment Review

Posts in Quarter 4.

Unit 8

Probability & Statistics

Keys post with the guides in Quarter 4.

A flock of flamingos on the water
Aug 11 – Oct 7 · Standards Mastery Check 1 on Oct 6

Quarter 1

Unit 1 — Transformations, Dilations & the Slope Bridge · Artifacts 01–13
How this page works

One module per Topic Overview Guide

Planned dates can shift slightly. Any change posts here and in the Family Guide. Out of fairness to families, the progression of assignments does not change.

Projects · Google Classroom

Project information, submission, and best tips are housed in Google Classroom. The project rows below carry only the dates.

Open Google Classroom

1ARigid MotionsArtifacts 01–04 · Weeks 1–3 · Aug 11–28
Artifact 01 Orientation and Congruence 8.10A 8.10B Week 1 · Aug 11–14 VideosAnswerspage planned
Due Syllabus signature page Fri Aug 14 · 1 pt
Classwork Mathematical Mindset Goals Week 1 · 1 pt
Artifact 02 Translations 8.10C Week 2 · Aug 17–18 VideosAnswerspage planned
Artifact 03 Reflections 8.10C Week 2 · Aug 19–20 VideosAnswerspage planned
Performance Task Performance Task 1.1 — Describing Orientation and Congruence Fri Aug 21 · 4 pts · revisions due Sep 11
Artifact 04 Rotations 8.10C Week 3 · Aug 24–27 VideosAnswersArtifact page
Classwork Site Map Selection: Improve Dallas Fri Aug 28 · 1 pt
Performance Task Performance Task 1.2 — Algebraic Representations of Transformations Fri Aug 28 · 4 pts · revisions due Sep 11
Mathematical Process Weeks 1–3 Fri Aug 28 · 1 pt
1BDilations and SimilarityArtifacts 05–07 · Weeks 4–5 · Aug 31–Sep 11
Artifact 05 Dilations and Similar Figures 8.3A 8.3B Week 4 · Aug 31–Sep 1 VideosAnswerspage planned
Artifact 06 Algebraic Rules of Dilations 8.3C Weeks 4–5 · Sep 2–11 VideosAnswerspage planned
Artifact 07 Area and Perimeter of Dilations 8.10D Week 4 · Sep 2–3 VideosAnswerspage planned
Studio Feedback and Revision Studio — closes PT 1.1 and 1.2 Fri Sep 4 · 2 pts
Mathia Mathia Mid-Quarter Check Fri Sep 4 · 1 pt
Performance Task Performance Task 1.3 — Representing Scale Factor Algebraically in class Tue–Wed, Sep 8–9 · 4 pts · revisions due Sep 18
Project Project Write-Up: Improve Dallas due Fri Sep 11 · 2 pts
1CAngle RelationshipsArtifacts 08–10 · Week 6 · Sep 14–18
Artifact 08 Triangle Sum Theorem 8.8D Week 6 · Sep 14–18 VideosAnswerspage planned
Artifact 09 Exterior Angle Theorem 8.8D Week 6 · Sep 14–18 VideosAnswerspage planned
Artifact 10 Parallel Lines and Transversals 8.8D Week 6 · Sep 14–18 VideosAnswerspage planned
Assessment Unit 1 Mid-Unit Assessment Fri Sep 18 · 6 pts · revisions due Oct 2
Mathematical Process Weeks 4–6 1 pt
1DIntroduction to SlopeArtifacts 11–13 · Weeks 7–8 · Sep 21–Oct 2
Artifact 11 Slope and Similar Triangles 8.4A Week 7 · Sep 21–25 VideosAnswerspage planned
Artifact 12 Calculating Slope and Rate of Change 8.4B 8.4C Weeks 7–8 · Sep 21–Oct 2 VideosAnswerspage planned
Performance Task Performance Task 1.4 — Angle Relationships Fri Sep 25 · 4 pts · revisions due Oct 2
Project Public Presentation: Improve Dallas Fri Sep 25 – Fri Oct 2 · 6 pts
Artifact 13 Slope and y-Intercept 8.4C Week 8 · Sep 28–Oct 2 VideosAnswerspage planned
Performance Task Performance Task 1.5 — Connecting Similar Triangles to Slope & Slope/y-Intercept Fri Oct 2 · 4 pts
Mathia Mathia End-of-Quarter Check Fri Oct 2 · 1 pt
SMCQuarter closeWeek 9 · Oct 5–7
Assessment Standards Mastery Check 1 Tue Oct 6 · 6 pts · not revised
Due Completed Topic Overview Guides 1A–1D — the 5% raise on Standards Mastery Check 1, per guide turn in by Wed Oct 7
Mathematical Process Weeks 7–9 1 pt
No school Fall Break Thu–Fri Oct 8–9
← Quarter 1
Artifact 04 · Topic 1A — Rigid Motions

Rotations

Turning a figure about the origin without changing its size or shape.

y x

The outlined image steps through 90° counterclockwise turns about the origin. One turn is (x, y) → (−y, x); each turn applies it again.

Objectives 8 & 9

I can determine the algebraic representation of a clockwise and counterclockwise rotation about the origin when given a verbal description of the rotation. 8.10C

I can determine the algebraic representation of a rotation about the origin when given the graph of the image and pre-image. 8.10C

Check

Topic Overview Guide 1A, Check Your Understanding 36–48. Answers

In class

Deck 04.1A ROTATIONS — quiz-quiz-trade.

The Longfellow atrium staircase

Student Resources

Check here for tools we use in class to be successful.
Check Your Understanding worked keys
Check Your UnderstandingWorked answer keys for every Topic Overview Guide. Work the questions first, then check.
Mathia
Carnegie Learning assignments, posted through the quarter. Graded twice each quarter: a Mid-Quarter Check and an End-of-Quarter Check.
Desmos calculator
The calculator built into the state assessment.
STAAR reference materials
The Grade 8 Mathematics formula sheet. Print one for your binder; you will see it again on test day.
Released STAAR items
Real questions from past state assessments.
Topic Overview Guides
Replacement copies by unit, if yours leaves your binder.
How revision works
Objective-by-objective revision, the one-week window, and how a Last Step slip banks a 4.
The Longfellow building on a sunny morning

Calendar

Two 90-minute classes and one 47-minute Friday, every week.
A / B / C days

How the week works

Classes meet twice a week for 90 minutes, plus Friday for 47 minutes.
Monday through Thursday alternate A days and B days. Your class meets on two of them.
Friday is a C day: every class meets. Most Fridays are consolidation, Performance Tasks, or review — some carry new content, depending on the week.
Quarters

Quarter windows

QuarterWindowNew learning
Quarter 1Aug 11 – Oct 7Unit 1
Quarter 2Oct 13 – Dec 18Units 2–3
Quarter 3Jan 6 – Mar 5Units 4–5, start of Unit 6
Quarter 4Mar 8 – May 21State assessment review, then Unit 8
Assessments

Assessment dates

AssessmentWhen
Standards Mastery Check 1Tuesday, October 6
Standards Mastery Check 2Tue–Wed, Dec 8–9
Standards Mastery Check 3Wednesday, February 24
State Assessment Snapshot Exam 1Week of March 22
State Assessment Snapshot Exam 2Week of April 5
Mathematics STAARWednesday, April 21

Planned dates can shift slightly. Any change posts here and in the Family Guide. Out of fairness to families, the progression of assignments does not change.

Revision due dates are printed with each assignment and in the Family Guide, weeks 1–37.

The whole year

Full-year calendar

Every graded assignment, week by week, all four quarters — to read through or plan ahead. Planned dates can shift slightly; the progression does not change.

Open the full-year calendar
Quarter 1Aug 11 – Oct 7 · Classwork 30 · Projects 8 · Tests 12
Week 1Aug 11–14
Syllabus Parent Signature1 ptClasswork
Mathematical Mindset Goals1 ptClasswork
Week 2Aug 17–21
Performance Task 1.1 — Describing Orientation and Congruence4 ptsClasswork
Week 3Aug 24–28
Site Map Selection: Improve Dallas1 ptClasswork
Q1 Mathematical Process (Weeks 1–3)1 ptClasswork
Performance Task 1.2 — Algebraic Representations of Transformations4 ptsClasswork
Week 4Aug 31–Sep 4
Feedback and Revision Studio — Revising Performance Tasks 1.1 and 1.2Revisions due Sep 112 ptsClasswork
Q1 Mathia Mid-Quarter Check1 ptClasswork
Week 5Sep 7–11
Performance Task 1.3 — Representing Scale Factor AlgebraicallyRevisions due Sep 184 ptsClasswork
Project Write-Up: Improve Dallas2 ptsProjects
Week 6Sep 14–18
Unit 1 Mid-Unit AssessmentRevisions due Oct 26 ptsTests
Q1 Mathematical Process (Weeks 4–6)1 ptClasswork
Week 7Sep 21–25
Performance Task 1.4 — Angle RelationshipsRevisions due Oct 24 ptsClasswork
Public Presentation: Improve Dallas6 ptsProjects
Week 8Sep 28–Oct 2
Performance Task 1.5 — Connecting Similar Triangles to Slope & Slope/y-intercept4 ptsClasswork
Week 9Oct 5–7
Q1 Mathematical Process (Weeks 7–9)1 ptClasswork
Q1 Mathia End-of-Quarter Check1 ptClasswork
Standards Mastery Check 16 ptsTests
Fall Break · Oct 8–12
Quarter 2Oct 13 – Dec 18 · Classwork 30 · Projects 8 · Tests 12
Week 10Oct 13–16
Revisiting Mathematical Mindsets Reflection1 ptClasswork
Week 11Oct 19–23
Performance Task 2.1 — Distinguishing Proportional Relationships4 ptsClasswork
Feedback and Revision Studio — Revising Performance Task 2.1Revisions due Oct 302 ptsClasswork
Week 12Oct 26–30
Q2 Mathematical Process (Weeks 10–12)1 ptClasswork
Performance Task 2.2 — Writing Linear EquationsRevisions due Nov 64 ptsClasswork
Week 13Nov 2–6
Project Write-up: Cost Analysis2 ptsClasswork
Q2 Mathia Mid-Quarter Check1 ptClasswork
Performance Task 2.3 — Identifying FunctionsRevisions due Nov 204 ptsClasswork
Week 14Nov 9–13
Unit 2 End-of-Unit AssessmentRevisions due Nov 203 ptsTests
Public Forum: Cost Analysis2 ptsClasswork
Week 15Nov 16–20
Q2 Mathematical Process (Weeks 13–15)1 ptClasswork
Public Presentations: Cost Analysis8 ptsProjects
Performance Task 3.1 — Trend Lines and ScatterplotsRevisions due Dec 44 ptsClasswork
Thanksgiving · Nov 23–27
Week 16Nov 30–Dec 4
Unit 3 End-of-Unit AssessmentRevisions due Dec 113 ptsTests
Week 17Dec 7–11
Growth Portfolio Entry 12 ptsClasswork
Standards Mastery Check 2Dec 8–96 ptsTests
Week 18Dec 14–18
Q2 Mathia End-of-Quarter Check1 ptClasswork
Q2 Mathematical Process (Weeks 16–18)1 ptClasswork
Winter Break · Dec 21 – Jan 5
Quarter 3Jan 6 – Mar 5 · Classwork 30 · Projects 8 · Tests 12
Week 19Jan 6–8
Mathematical Mindsets Reflection1 ptClasswork
Week 20Jan 11–15
Performance Task 4.1 — Ordering and Classifying Real NumbersRevisions due Jan 294 ptsClasswork
Week 21Jan 19–22
Performance Task 4.2 — Writing Equations with Variables on Both SidesRevisions due Feb 54 ptsClasswork
Q3 Mathematical Process (Weeks 19–21)1 ptClasswork
Week 22Jan 25–29
Unit 4 Mid-Unit AssessmentRevisions due Feb 53 ptsTests
Feedback and Revision Studio — Revising Performance Task 4.2 + Unit 4 Mid-Unit Assessment2 ptsClasswork
Q3 Mathia Mid-Quarter Check1 ptClasswork
Week 23Feb 1–5
Performance Task 5.1 — Pythagorean TheoremRevisions due Feb 124 ptsClasswork
Week 24Feb 8–12
Exploration Task: Advocacy Constructions1 ptClasswork
Performance Task 5.2 — Volume and Surface AreaRevisions due Feb 194 ptsClasswork
Q3 Mathematical Process (Weeks 22–24)1 ptClasswork
Week 25Feb 16–19
Application Task: Advocacy Constructions1 ptClasswork
Unit 5 End-of-Unit AssessmentRevisions due Feb 263 ptsTests
Week 26Feb 22–26
Standards Mastery Check 36 ptsTests
Week 27Mar 1–5
Performance Task 6.1 — College Savings Plan4 ptsClasswork
Public Presentation: Advocacy Constructions8 ptsProjects
Q3 End-of-Quarter Mathia Check1 ptClasswork
Q3 Mathematical Process (Weeks 25–27)1 ptClasswork
Quarter 4Mar 8 – May 21 · Classwork 30 · Projects 8 · Tests 12
Week 28Mar 8–12
Unit 6 End-of-Unit AssessmentRevisions due Mar 262 ptsTests
Spring Break · Mar 15–19
Week 29Mar 22–26
State of Texas Performance Task 1Revisions due Apr 24 ptsClasswork
State Assessment Snapshot Exam 15 ptsTests
Week 30Mar 29–Apr 2
State of Texas Performance Task 2Revisions due Apr 94 ptsClasswork
Week 31Apr 5–9
Q4 Mathematical Process (Weeks 28–31)1 ptClasswork
Q4 Mathia Mid-Quarter Check1 ptClasswork
State Assessment Snapshot Exam 25 ptsTests
Week 32Apr 12–16
State of Texas Performance Task 3Revisions due Apr 204 ptsClasswork
State Assessment Week · Apr 19–23
Week 34Apr 26–30
Q4 Mathematical Process (Weeks 32–34)1 ptClasswork
Week 35May 3–7
Performance Task 8.1 — Comparing Two PopulationsRevisions due May 144 ptsClasswork
Week 36May 10–14
Investigative Task: Who Decides Dallas?4 ptsClasswork
Peer Review Activity: Who Decides Dallas?1 ptClasswork
Portfolio Entry 2: Initial Draft1 ptClasswork
Week 37May 17–21
Public Presentations: Who Decides Dallas?8 ptsProjects
Public Presentations: Participation and Written Feedback1 ptClasswork
Portfolio Entry 2: Final Draft2 ptsClasswork
Q4 Mathia End-of-Quarter Check1 ptClasswork
Q4 Mathematical Process (Weeks 35–37)1 ptClasswork
Grading

Every quarter is 50 points

Three categories, weighted by the district. The bar below is drawn to scale.

30 points · 50%Performance Tasks, Feedback and Revision Studio, Mathematical Process, Mathia checks
8 points · 30%the quarter's public presentation
12 points · 20%unit assessments and district checks

Every assignment and grade is mapped out in the Family Guide.

The main grade

Performance Tasks

Multi-problem tasks completed independently in class, 30–40 minutes. Scored 1–4: Beginning, Developing, Proficient, Exemplary. The score is writing and explanation based; a 4 is earned through thorough explanation.

Revision · how a grade improves

Most graded work can be revised, objective by objective, with a reflection attached, within one week of return. A revised 4 becomes permanent after a Last Step slip — a short in-class demonstration that the objective now stands on its own. Only very few assessments (Standards Mastery Checks and Snapshot Exams) are not revised.

Mathematical Process

Graded on the process standards

Every three weeks each student turns in one exhibit of their own mathematical work and writes a short explanation of which process standard it shows. The standards are TEKS 8.1(A) through 8.1(G), written by the Texas Education Agency. Work done alone and work done with a team can both earn full credit. Sharing ideas will always be rewarded for generating new ideas.

GroupStandardsWhat it takes
Tools to Know8.1A · 8.1B · 8.1CClaimable with work done on your own.
Ways to Show8.1D · 8.1E · 8.1F · 8.1GNeed someone on the other end: a teammate, the class, or a reader who used the work.

Scored 1, 0.5, or 0. A 0.5 comes back with one reason and can be fixed for full credit. The only way to score a 0 is to turn in nothing.

Three grades per quarter, one every three weeks.

Before You Leave slips

End most class periods. Never scored individually; they count as evidence toward the Mathematical Process grade.

Check Your Understanding

Never graded. A completed guide turned in at quarter's end raises that quarter's Standards Mastery Check score by 5% per guide. Only that quarter's guides count.

Mathia

Two checks each quarter: mid-quarter and end-of-quarter.

The Longfellow library

Family Resources

Longfellow Career Exploration Academy · Dallas ISD
Family Guide 26–27 · 12 pagesGoogle Drive
Additional resources
Syllabus · 26–27
Also on the front page.
How grading works
50 points a quarter — Classwork 50%, Projects 30%, Tests 20%.
Projects · Classroom
Project information, submission, and best tips are housed in Google Classroom.
About

Mr. Linam

Mr. Linam

Originally from Fort Smith, Arkansas, Mr. Linam is proud to join the Longfellow team. He holds a Bachelor of Arts in Political Science from Washington University in St. Louis and a Master of Science in Education from Johns Hopkins University. In 2024 Mr. Linam received the Middle School and District Teacher of the Year award at Tulsa Honor Academy. He most recently taught at Greiner Exploratory Arts Academy in Dallas. A trained grassroots organizer and Teach for America alum, he sees education as one of the best and most powerful ways to make a difference.

Outside the classroom Mr. Linam enjoys running outdoors, reading historical and educational literature, and spending time in the park with his partner and dog. Entering his fifth year in mathematics education, he is excited to help students establish serious academic goals and cheer on every success.

Longfellow Career Exploration Academy — Your Career Begins Here
Contact

klinam@dallasisd.org — email is answered within one school day.