TEKS Math 6.4.A
The Standard
compare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive and multiplicative relationships
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students examine rules shown in words, tables, graphs, and equations. They decide whether each rule adds a fixed amount or multiplies by a fixed factor, then explain the evidence.
What Mastery Looks Like
- Students identify a fixed added amount versus a fixed multiplying factor in tables, graphs, equations, and descriptions. They translate between these forms and use several input-output pairs to justify their choice.
Common Misconceptions
- Students often confuse y = 3x with y = x + 3 because both use the same numbers. They may decide from one input-output pair instead of checking several pairs, or assume intersecting graphs represent the same rule.
How to Assess It
- Exit ticket: For x = 0, 1, 2, and 3, compare y = 4x and y = x + 4 in a table and graph. Label each relationship and justify your choice with one pattern.
Lesson moves
Ways to Teach It
Use linking cubes to model y = 3x as equal groups and y = x + 3 as an original amount plus three cubes.
Ask students to explain why y = 5x and y = x + 5 can match once but follow different patterns.
Run a card sort matching verbal rules, equations, tables, and graphs, then have partners defend any disputed matches.
Compare a $4-per-item purchase with a $4 fee plus $1 per item using tables and graphs.
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Printable 6.4.A Worksheet
A ready-to-print activity worksheet aligned to 6.4.A, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- 5.4.D
recognize the difference between additive and multiplicative numerical patterns given in a table or graph
- 6.7.B
distinguish between expressions and equations verbally, numerically, and algebraically
- 5.4.C
generate a numerical pattern when given a rule in the form y = ax or y = x + a and graph
- 8.5.I
write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations
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