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Core Concepts
Core Skills
A The value of a quantity is not specified 2. Use and interpret quantities and units cor- 3. Use and interpret quantities and units cor- C Quantities can be multiplied or divided to 4. Use units as a way to understand prob- create new types of quantities, called de- Example Tasks
• Labor: $125 base price plus $0.79 per square The following question was posted on an In- For a job tiling an area of 550 square feet, what is the amount of the bid, based on the mate- of soil I need for my gardens but have no idea how much a yard of soil actually is.
The nursery says they deliver 6 yards in a If there are 8 × 1012 hydrogen molecules in a dump truck. I realize that a yard is 3 feet.
volume of 4 × 104 cubic centimeters, what is the But what is a yard of soil—is that 3 feet average number of hydrogen molecules per cubic long and 3 feet high? I’m clueless! LOL Write a helpful response to the person who posted miles long and cost $8 billion to build. Divide one A textbook printed the following formula for of these numbers by the other. What is the mean- Signs in Canada give the speed limit in kilo- Kim had never studied geometry, but she knew meters per hour. If the speed limit is 100 km/hr, there must be a typographical error in this for- and you’re driving at a speed of 65 mph, are you over or under the speed limit? By how much? As a flooring contractor, Lupe sets floor tile for a living. She submits a bid for each new job.
a land area of 2,175,600 square kilometers. By When preparing a bid, she measures the area of what factor is the population density of the United the floor to be tiled and then figures out how much States, 80 persons per square mile, larger than the material she will need. She charges the following 8. Core Skill 1; Core Skill 4; Number Core Skill 2; Number Core Skill 3; Number Core Skill 5.
A doctor orders Ceclor elixir for a child who weighs 9.3 kg. The child must receive 25 mg of the drug for each kilogram of body weight. The ter in the body of a 160-pound runner? Here are hospital pharmacy stocks Ceclor elixir in a con- • A typical soda can holds 12 fluid ounces.
• 16 ounces (one pint) of water weighs one (a) Estimate the answer mentally. (Suggestion: approximate the child’s weight as 10 kg.) A liquid weed-killer comes in four different (b) Compute the answer to the nearest tenth of a kinds of bottles. The accompanying table gives information about the concentration, size, and price of the bottles. The “concentration” refers The distance traveled by a freely falling ob- to the percent of “active ingredient” in the bot- ject dropped from rest is given by the formula tle. The rest of the liquid in the bottle is water.
s = 1 g t2. Here s is the distance fallen, g is a For example, bottle B contains (0.18)(32) = 5.76 constant representing the earth’s surface gravity, fl. oz. of active ingredient and 32 − 5.76 = 26.24 and t is the duration of time over which the ob- ject falls. If s has units of meters and t has units Weed killer comes in four different kinds of of seconds, what must be the units of g? If we interpret g as a rate of change, what sort of quan- tity is changing with time? What does this mean about the speed of a freely falling object? 10. Core Skill 2; Equations Core Skill 3.
The ideal gas law is a mathematical relation- ship that describes the pressure, volume, and tem- perature of an ideal gas in thermal equilibrium: (a) Rank the four bottles in order of how good a buy each represents. State what criterion you In the ideal gas law, p stands for pressure, V stands for volume, n is the number of moles of (b) Suppose a job calls for a total of 12 fl. oz. of gas, R is a constant equal to 0.0821 L·atm , and active ingredient. How much would you need T stands for temperature measured in the Kelvin to spend if you bought Type A bottles? Type B bottles? Type C bottles? Type D bottles? (a) Find the temperature of 0.520 mol of argon gas occupying a volume of 4.25 L at a pres- A table in a construction manual lists the “k-values” of different building materials. The k- (b) If the volume stays the same as in (a), but the value measures how easily heat flows through a pressure drops by half, then what must have material. The k-value of concrete is given as The construction manual gives the following example problem illustrating the k-value: be lost through a 100 ft2 concrete wall 6 inches thick over a 12 hour period, if the Check out the Runner’s World calculation. Are there really about 120 soda cans’ worth of wa- Your friend Anders doesn’t know much aboutconstruction—or about heat loss—yet he wasable to get the answer, 28 BTUs, just by thinkingabout units. How did he get the answer? shows the relationship between distance traveledand time for a different train (Train A, Train B,and Train C).
Which train was traveling fastest during the interval of time shown? Justify your answer.
42!). "
3. Charles A. Dana Center. (2009). Algebra I Assessments (2nd ed.). Austin: Author.
8. Adapted from Ready or Not: Creating a High School Diploma That Counts. Achieve copyright 10. Adapted from Ready or Not: Creating a High School Diploma That Counts. Achieve copyright


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