Like previous posts, students may not come up with the last two bullets however, you can introduce them one at a time if you like on individual stickies. 3 days ago (-3), I had 2 dollars less (-2).” for the right sticky, “I had 1 dollar.all three stickies represent the same function.both right and left stickies have a y-intercept of 1.any other connection from previous stages.the graph is a representation of the both stickies.the right sticky, takes you down the line from right to left.
You could also introduce a sticky like the one on the left below, and discuss its meaning by posing purposeful questions:īeing able to convert a positive slope into a double negative can help students graph points using only slope intercept form moving in the “opposite” direction. The question could be rephrased, “what is amount is repeated 3 times to yield 2 dollars?” As an equation, (x)3 = 2 where x is 2/3 so (2/3)3 = 2, which brings in a discussion of the multiplying of fractions. If I owe 2 dollars more every three days, then how much do I owe EACH day? Posing this purposeful question can create an opportunity to explore and build fractional understanding.
Relating it to the discussion immediately preceding this stage: if you owed 2 dollars more every 3 days, then you would have had 2 dollars more 3 days ago. Students may not come up with the last bullet above. a new equation with the negative in the denominator.a new equation with the negative in the numerator.If it is not made here, then it needs to be made on the Sticky Math Comparison that follows. The final bullet above is a key understanding conceptually to build fluency. As x increases, the entire term becomes more negative, which decreases the value of the expression and y. the negative is on the coefficient of x thus, it is a multiplier of x.If you think of the negative being in the denominator, then the it moves you right to left up the line.If you think of the negative being in the numerator, then the it moves you left to right down the line.the graph is a representation of the left sticky.How is the next Sticky Math Pair the same too? If you owed 2 dollars more every 3 days, then you would have had 2 dollars more 3 days ago. While they fit one equation literally, each one fits all the representations. You could introduce them one at a time on new stickies asking which representation they describe. Students may not come up with the final two bullets. for the right sticky, “I started with one dollar.for the left sticky, “I started with one dollar.putting the negative sign in front of the slope fraction like the Sticky Math Pair that follows.any of the representations from previous stages.Students could create their own representations these might include: The graph is a representation of BOTH stickies.Employing “rise over run” on the right sticky moves you right to left up the line.Employing “rise over run” on the left sticky moves you left to right down the line.The graph is a representation of the right sticky.The graph is a representation of the left sticky.
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