Mathematical Process Standards>Communicating Mathematical Ideas with Multiple Representations(TEKS.Math.6.1.D)
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Texas 6th Grade Math › Mathematical Process Standards>Communicating Mathematical Ideas with Multiple Representations(TEKS.Math.6.1.D)
Words: Three-fourths of a class of 24 students passed the test. Which representation shows the same relationship?
Words: One-fourth of the class passed, which is 6 students.
Symbols: $\frac{3}{4} \times 24 = 18$
Diagram: A bar divided into 4 equal parts with 1 part shaded to show those who passed.
Graph: A line $y=1.25x$ with the point (24, 18) highlighted.
Explanation
Taking three-fourths of 24 gives $\frac{3}{4}\times 24=18$, so 18 students passed. The other choices mismatch the proportion or show a different relationship.
Symbols: $y = 0.6x$. Which choice is an equivalent representation of this relationship?
Words: $x$ is 60% of $y$.
Symbols: $y = \frac{x}{0.6}$.
Diagram: A bar for $x$ split into 5 equal parts with 2 parts shaded to represent $y$.
Data: Ordered pairs that fit the rule: (10, 6), (20, 12), (50, 30).
Explanation
If $y=0.6x$, then pairs like (10,6), (20,12), and (50,30) satisfy the rule. The other choices invert or change the proportion (40% or $\approx1.67x$), so they are not equivalent.
Table: The ratios of red paint to blue paint are equivalent: 2 red : 3 blue, 4 red : 6 blue, 6 red : 9 blue. Which equation represents the relationship between red ($x$) and blue ($y$) amounts?
Symbols: $y = \frac{3}{2}x$
Symbols: $y = \frac{2}{3}x$
Words: For every 3 parts red there are 2 parts blue.
Graph: A line through the origin with slope $\frac{2}{3}$ passing through (3, 2).
Explanation
The ratio blue:red is 3:2, so $\frac{y}{x}=\frac{3}{2}$ and $y=\frac{3}{2}x$. The other options reverse the ratio.
Words: A store discounts a 50 dollar jacket by 20%. Which representation shows the same relationship?
Words: Subtract 20 from 50 to get the sale price of 30 dollars.
Symbols: $50 \times 0.8 = 40$
Diagram: A bar for the price split into 4 equal parts with 3 parts remaining to show the sale price.
Graph: The point (20, 50) lies on a line that gives the sale price from the original price.
Explanation
Taking 20% off means keeping 80% of the price, so $50\times 0.8=40$. The other choices subtract the percent as dollars, show 75% instead of 80%, or mismatch the quantities on a graph.