Grade 8 · Statistics & Modeling · MAT-08-SP-001
Create and Interpret Scatter Plots
Represent and solve create and interpret scatter plots problems using precise mathematical notation, multiple representations, and justified reasoning.
Learning objectives
What you should be able to do
- Represent and solve create and interpret scatter plots problems using precise mathematical notation, multiple representations, and justified reasoning.
- Interpret and verify create and interpret scatter plots results in context, including units, constraints, and reasonableness.
Prerequisite check
Make sure the foundation is ready.
Grade 8 uses this prerequisite as active knowledge in a more formal representation.
Learn
Build the idea from meaning, not memorization.
Meaning and structure
Create and Interpret Scatter Plots belongs to statistics & modeling. Identify the governing property or relationship before choosing a procedure.
Multiple representations
Represent create and interpret scatter plots numerically and symbolically, then connect it to the Grade 8 Math Box. Tables, graphs, equations, coordinate models, diagrams, and verbal descriptions must agree.
Verification and interpretation
Check with substitution, an inverse operation, an equivalent representation, geometric invariants, estimation, or context. State whether the result is exact or approximate and preserve relevant units and constraints.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Scatter Plot Lab
- Model create and interpret scatter plots in the Math Box.
- Change one input and predict which quantities or invariants should change.
- Explain what the visual, equation, and numerical result say about the same relationship.
Worked examples
Twenty different ways to see the concept work.
Plot observation (1,6) as one scatter-plot point.
(1,6)Each point pairs two measurements from the same observational unit.
Plot observation (2,2) as one scatter-plot point.
(2,2)Each point pairs two measurements from the same observational unit.
Plot observation (3,14) as one scatter-plot point.
(3,14)Each point pairs two measurements from the same observational unit.
Plot observation (4,-1) as one scatter-plot point.
(4,-1)Each point pairs two measurements from the same observational unit.
Plot observation (5,19) as one scatter-plot point.
(5,19)Each point pairs two measurements from the same observational unit.
Plot observation (6,-1) as one scatter-plot point.
(6,-1)Each point pairs two measurements from the same observational unit.
Plot observation (7,24) as one scatter-plot point.
(7,24)Each point pairs two measurements from the same observational unit.
Plot observation (8,-4) as one scatter-plot point.
(8,-4)Each point pairs two measurements from the same observational unit.
Plot observation (9,32) as one scatter-plot point.
(9,32)Each point pairs two measurements from the same observational unit.
Plot observation (10,-7) as one scatter-plot point.
(10,-7)Each point pairs two measurements from the same observational unit.
Plot observation (11,37) as one scatter-plot point.
(11,37)Each point pairs two measurements from the same observational unit.
Plot observation (12,-7) as one scatter-plot point.
(12,-7)Each point pairs two measurements from the same observational unit.
Plot observation (13,42) as one scatter-plot point.
(13,42)Each point pairs two measurements from the same observational unit.
Plot observation (14,-10) as one scatter-plot point.
(14,-10)Each point pairs two measurements from the same observational unit.
Plot observation (15,50) as one scatter-plot point.
(15,50)Each point pairs two measurements from the same observational unit.
Plot observation (16,-13) as one scatter-plot point.
(16,-13)Each point pairs two measurements from the same observational unit.
Plot observation (17,55) as one scatter-plot point.
(17,55)Each point pairs two measurements from the same observational unit.
Plot observation (18,-13) as one scatter-plot point.
(18,-13)Each point pairs two measurements from the same observational unit.
Plot observation (19,60) as one scatter-plot point.
(19,60)Each point pairs two measurements from the same observational unit.
Plot observation (20,-16) as one scatter-plot point.
(20,-16)Each point pairs two measurements from the same observational unit.
Practice
Guided practice with hints
01Plot observation (21,68) as one scatter-plot point.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: (21,68)
02Plot observation (22,-19) as one scatter-plot point.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: (22,-19)
03Plot observation (23,73) as one scatter-plot point.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: (23,73)
04Plot observation (24,-19) as one scatter-plot point.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: (24,-19)
05Plot observation (25,78) as one scatter-plot point.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: (25,78)
06Plot observation (26,-22) as one scatter-plot point.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: (26,-22)
Practice
Independent practice
01Plot observation (27,86) as one scatter-plot point.
Answer: (27,86)
02Plot observation (28,-25) as one scatter-plot point.
Answer: (28,-25)
03Plot observation (29,91) as one scatter-plot point.
Answer: (29,91)
04Plot observation (30,-25) as one scatter-plot point.
Answer: (30,-25)
05Plot observation (31,96) as one scatter-plot point.
Answer: (31,96)
06Plot observation (32,-28) as one scatter-plot point.
Answer: (32,-28)
07Plot observation (33,104) as one scatter-plot point.
Answer: (33,104)
08Plot observation (34,-31) as one scatter-plot point.
Answer: (34,-31)
Common mistakes
Learn to catch the error, not just the answer.
Association alone does not establish cause.
A fitted line summarizes a trend and produces estimates.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Analyze paired numerical data for trends and make cautious model-based predictions.
- Compare categorical groups with conditional percentages in two-way tables.
Challenge problems
Plot observation (35,109) as one scatter-plot point.
(35,109)
Plot observation (36,-31) as one scatter-plot point.
(36,-31)
Plot observation (37,114) as one scatter-plot point.
(37,114)
Plot observation (38,-34) as one scatter-plot point.
(38,-34)
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 8 Algebra & Modeling Sprint
Solve create and interpret scatter plots problems and justify each result with a valid verification method.
Practice
Mastery check
01Plot observation (39,122) as one scatter-plot point.
Answer: (39,122)
02Plot observation (40,-37) as one scatter-plot point.
Answer: (40,-37)
03Plot observation (41,127) as one scatter-plot point.
Answer: (41,127)
04Plot observation (42,-37) as one scatter-plot point.
Answer: (42,-37)
05Plot observation (43,132) as one scatter-plot point.
Answer: (43,132)
06Plot observation (44,-40) as one scatter-plot point.
Answer: (44,-40)
07Plot observation (45,140) as one scatter-plot point.
Answer: (45,140)
08Plot observation (46,-43) as one scatter-plot point.
Answer: (46,-43)
Terminology
Words to know
- bivariate data
- Paired measurements of two variables for the same observations.
- association
- A pattern showing how variables or categories vary together.
- line of best fit
- A line summarizing an approximately linear scatter-plot trend.
- conditional relative frequency
- A category frequency divided by the relevant row or column total.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Grade 8 instructional guidance, mathematical practices, modeling, and progression toward high-school mathematics.Common Core State Standards for Mathematics — Grade 8
Grade-level expectations for real numbers, equations, functions, geometry, and statistics.Principles to Actions: Ensuring Mathematical Success for All
Research-informed emphasis on reasoning, representations, discourse, productive struggle, and conceptual understanding.