From 12d95caf002cd0720c33fa47829dffaf0ce43c07 Mon Sep 17 00:00:00 2001 From: <> Date: Wed, 10 Jul 2024 14:32:24 -0700 Subject: [PATCH] Latest build deployed. --- Notes.html | 4 +- backmatter-1.html | 4 +- backmatter-2.html | 4 +- backmatter.html | 4 +- chap_five_apportionment.html | 4 +- chap_five_budget_deficit_debt.html | 4 +- chap_five_gerrymandering.html | 4 +- chap_five_popular_vote.html | 4 +- chap_five_review.html | 4 +- chap_five_voting_methods.html | 4 +- chap_four_contingency_tables.html | 4 +- chap_four_expected_value.html | 4 +- chap_four_review.html | 4 +- chap_four_theoretical_probability.html | 4 +- chap_one_arguments.html | 4 +- chap_one_fallacies.html | 4 +- chap_one_language_logic.html | 4 +- chap_one_logic_everyday_life.html | 4 +- chap_one_percents.html | 4 +- chap_one_problem_solving_percents.html | 134 +++++++++++++----- chap_one_proportional_reasoning.html | 4 +- chap_one_review.html | 4 +- chap_one_sets_venn.html | 4 +- chap_three_describing_data.html | 4 +- chap_three_measure_of_center.html | 4 +- chap_three_measure_of_variation.html | 4 +- chap_three_normal_model.html | 4 +- chap_three_review.html | 4 +- chap_three_statistical_process.html | 4 +- chap_two_income_taxes.html | 4 +- chap_two_intro_spreadsheet.html | 4 +- chap_two_loans.html | 4 +- chap_two_review.html | 4 +- chap_two_savings_plan.html | 4 +- chap_two_simple_compound.html | 4 +- democracy.html | 4 +- .../problem_solving/circle.png | Bin 0 -> 5268 bytes .../problem_solving/cylinder.png | Bin 0 -> 3263 bytes .../problem_solving/rectangle.png | Bin 0 -> 2058 bytes .../problem_solving/rectangular_box.png | Bin 0 -> 3833 bytes financial_math.html | 4 +- frontmatter-2.html | 4 +- frontmatter-3.html | 4 +- frontmatter-4.html | 4 +- frontmatter-5.html | 4 +- frontmatter-7.html | 4 +- frontmatter.html | 6 +- index.html | 2 +- knowl/xref/list-bottlecaps.html | 2 +- knowl/xref/list-breadcrumbs.html | 2 +- knowl/xref/list-carfree.html | 2 +- knowl/xref/list-chicken.html | 2 +- knowl/xref/list-filter.html | 2 +- knowl/xref/list-furnace.html | 2 +- language_logic_rules.html | 4 +- lunr-pretext-search-index.js | 69 ++++++--- probability.html | 4 +- root-1-2.html | 4 +- statistics.html | 4 +- 59 files changed, 249 insertions(+), 154 deletions(-) create mode 100644 external/images/language_logic_rules/problem_solving/circle.png create mode 100644 external/images/language_logic_rules/problem_solving/cylinder.png create mode 100644 external/images/language_logic_rules/problem_solving/rectangle.png create mode 100644 external/images/language_logic_rules/problem_solving/rectangular_box.png diff --git a/Notes.html b/Notes.html index 5df08cb..9adbd69 100644 --- a/Notes.html +++ b/Notes.html @@ -197,8 +197,8 @@

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  • 1.5.1 A Problem Solving Process
  • 1.5.2 Operation Sense
  • 1.5.3 Number Sense and Estimation
    • -
  • 1.5.4 Solving Problems with Geometry
    • -
  • 1.5.5 Solving Problems with Unit Conversions
    • +
  • 1.5.4 Solving Problems with Unit Conversions
    • +
  • 1.5.5 Solving Problems with Geometry
  • 1.5.6 Exercises
    diff --git a/backmatter-1.html b/backmatter-1.html index 51a8f07..5fb57c1 100644 --- a/backmatter-1.html +++ b/backmatter-1.html @@ -197,8 +197,8 @@

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  • 1.5.5 Solving Problems with Unit Conversions
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    diff --git a/chap_one_percents.html b/chap_one_percents.html index 279735f..beabb84 100644 --- a/chap_one_percents.html +++ b/chap_one_percents.html @@ -197,8 +197,8 @@

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  • 1.5.1 A Problem Solving Process
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    diff --git a/chap_one_problem_solving_percents.html b/chap_one_problem_solving_percents.html index 7d05fba..262d74d 100644 --- a/chap_one_problem_solving_percents.html +++ b/chap_one_problem_solving_percents.html @@ -197,8 +197,8 @@

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  • 1.5.1 A Problem Solving Process
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  • 1.5.5 Solving Problems with Unit Conversions
    • +
  • 1.5.4 Solving Problems with Unit Conversions
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  • 1.5.5 Solving Problems with Geometry
  • 1.5.6 Exercises
    @@ -564,8 +564,10 @@

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  • Use a problem solving process to solve a variety of real-world problems with trade-offs or more than one right answer
  • Identify which operation(s) to use in a problem and check for a reasonable answer
  • Estimate reasonable answers and give reasonable estimates for quantities needed to solve a problem
    • -
  • Solve problems that involve unit conversions
    • -
  • Solve problems that involve geometry
    • +
  • Solve problems that involve a combination of the four basic operations
    • +
  • Solve problems that involve percents, rates and/or proportions
    • +
  • Solve problems that involve unit conversions
    • +
  • Solve problems that involve geometry
    • Figure 1.5.1. Alternative Video Lesson

    Subsection 1.5.1 A Problem Solving Process @@ -776,32 +778,98 @@

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  • Without looking it up, we think it would be in the thousands or maybe ten-thousands. Of course it depends on the type and size of the fish, but we don’t think it would be in the hundred-thousands or millions.
    • Now that we have gone through an example using the problem solving process and talked about operations and number sense, we will continue with more mathematical tools to use in making decisions. We will focus the rest of this section on problem solving with percentages and absolute and relative change.

    -Subsection 1.5.4 Solving Problems with Geometry +Subsection 1.5.4 Solving Problems with Unit Conversions

    -
    -
    -

    +
    Many situations also require unit conversions. You can use your number and operation sense to know whether to multiply or divide or you can line up the units so they cancel out. Here are some unit conversions for reference.
    +

    Unit Conversions for Length.

    +
    +
    1 foot (ft) = 12 inches (in)
    1 mile (mi) = 5,280 feet (ft)
    1000 millimeters (mm) = 1 meter (m)
    1000 meters (m) = 1 kilometer (km)
    +
    1 yard (yd) = 3 feet (ft)
    2.54 centimeters (cm) = 1 inch (in)
    100 centimeters (cm) = 1 meter (m)
    +

    Unit Conversions for Weight and Mass.

    +
    +
    1 pound (lb) = 16 ounces (oz)
    1000 millgrams (mg) = 1 gram (g)
    1 kilogram (kg) = 2.2 pounds (on Earth)
    +
    1 ton = 2000 pounds (lbs)
    1000 grams (g) = 1 kilogram (kg)
    +

    Unit Conversions for Volume and Capacity.

    +
    +
    1 gallon (gal) = 4 quarts (qt)
    1 quart (qt) = 2 pints (pt)
    1 pint (pt) = 2 cups (c)
    1000 milliliters (ml) = 1 liter (L)
    +
    1 cup (c) = 8 fluid ounces (fl oz)
    1 cup (c) = 16 Tablespoons (T)
    1 Tablespoon (T) = 3 Teaspoons (t)
    +
    +
    Note: Fluid ounces are a capacity measurement for liquids. 1 fluid ounce weighs about 1 ounce for water only.

    Example 1.5.5.

    -
    -
    Solution.

    +
    +
    Solution.

    Example 1.5.6.

    -
    -
    Solution.

    -Subsection 1.5.5 Solving Problems with Unit Conversions +
    +
    Solution.

    +Subsection 1.5.5 Solving Problems with Geometry

    -
    -

    +

    Perimeter and Area.

    +
    +
    Rectangle
    Perimeter = \(2L + 2W\text{ units}\) +
    Area = \(L\cdot W\text{ units}^2\) +
    +
    Circle
    Circumference = \(2\pi r\text{ units}\) +
    Area = \(\pi r^2\text{ units}^2\) +
    +
    +
    +
    A rectangle with the width labeled W and the length labeled L.
    +
    A circle with the radius labeled r.
    +

    Volume.

    +
    +
    Rectangular Box
    Volume = \(L\cdot W\cdot H\text{ units}^3\) +
    +
    Cylinder
    Volume = \(\pi r^2 H\text{ units}^3\) +
    +
    +
    +
    A rectangular box with the width labeled W, length labeled L, and height labeled H
    +
    A cylinder with the radius labeled r and height labeled H
    +
    +

    Example 1.5.7.

    -
    -
    Solution.

    -Example 1.5.8. -

    -
    -
    Solution.

    +
    You need to replace the boards on your deck and you’d like to do it yourself to save money. You want to estimate how much you will need to save up for the wood.
    +
    Solution.
    +
    Step 1: We want to know how much the wood for the deck will cost. This will probably be in the thousands of dollars, possibly about $1000-2000, depending on the size of the deck and wood prices. In this context, estimates usually add 10% for parts of boards that don’t get used so we will do that as well.
    Step 2: We need to know the size and shape of the deck, the type of boards and cost per board. You measure your deck and it’s a 16 ft by 24 ft rectangle. Looking up prices online, you find 5/4-inch by 4-inch by 8-foot cedar deck boards for $11.99 each.
    Step 3: There are a few approaches we could take to this problem: 1) Go out to your deck and count the boards, 2) calculate the number of boards you will need using the area of the deck, or 3) calculate the area of the deck and find the approximate cost per square foot for deck boards.
    +
    Step 4: Option 3 seems like the most efficient approach so we will try that. The area of the deck is
    +
    +\begin{equation*} +16\text{ feet} \cdot 24\text{ feet} = 384\text{ feet}^2\text{.} +\end{equation*} +
    +
    To find the cost per square foot for decking boards, we could compute the area of the top of a single board, and then divide the cost by the area. Since the width of a board is 4 inches we also need to convert that into feet. So the area of a single board is
    +
    +\begin{equation*} +8\text{ feet}\cdot4\cancel{\mathrm{ inches}}\cdot\frac{1\text{ foot}}{12\cancel{\mathrm{ inches}}}=2.667\text{ ft}^2 +\end{equation*} +
    +
    The cost per square foot of one board is
    +
    +\begin{equation*} +\frac{\$11.99}{2.667\text{ ft}^2}\approx \$4.4957\text{ per square foot}\text{.} +\end{equation*} +
    +
    +
    This will allow us to estimate the material cost for the whole deck by multiplying
    +
    +\begin{equation*} +384\cancel{\mathrm{ feet}^2}\cdot\frac{\$4.4957}{\cancel{\mathrm{ feet}^2}}\approx\$1726.35\text{.} +\end{equation*} +
    +
    +
    Then we will add 10% to the cost. We can calculate the 10% and then add, or multiply by 1.10.
    +
    +\begin{equation*} +\$1726.35(1.10)\approx \$1898.99\text{.} +\end{equation*} +
    +
    Step 5: This answer is reasonable and fits with our original estimate. You should save up or set aside about $1900 for this project. This is just the cost of the wood and doesn’t include nails, screws or any foundation materials.
    +
    For confirmation with a second method, we could use option 2. We divide
    +

    Exercises 1.5.6 Exercises

    1.

    @@ -857,17 +925,17 @@

    Exercise Group.

    Use the problem solving process to solve these problems. For this set of questions, after you identify the information you need, click on the link in the question or go to Subsubsection 1.5.6.1 to find that information. The details may be imprecise; answer the question the best you can with the provided information. Document your steps and thinking.
    23.
    -
    You’re planning on making 6 meatloafs for a party. You go to the store to buy breadcrumbs, and see they are sold by the canister. How many canisters do you need to buy? Information: List 1.5.9 +
    You’re planning on making 6 meatloafs for a party. You go to the store to buy breadcrumbs, and see they are sold by the canister. How many canisters do you need to buy? Information: List 1.5.8
    24.
    -
    Your friend wants to cover their car in bottle caps, like in this picture. How many bottle caps are you going to need? Information: List 1.5.10 +
    Your friend wants to cover their car in bottle caps, like in this picture. How many bottle caps are you going to need? Information: List 1.5.9
    A car covered in metal bottle caps with a sun design.
    25.
    -
    You need to buy some chicken for dinner tonight. You found an ad showing that the store across town has it on sale for $2.99 a pound, which is cheaper than your usual neighborhood store, which sells it for $3.79 a pound. Is it worth the extra drive? Information: List 1.5.11 +
    You need to buy some chicken for dinner tonight. You found an ad showing that the store across town has it on sale for $2.99 a pound, which is cheaper than your usual neighborhood store, which sells it for $3.79 a pound. Is it worth the extra drive? Information: List 1.5.10
    26.
    -
    I have an old gas furnace, and am considering replacing it with a new, high efficiency model. Is upgrading worth it? Information: List 1.5.12 +
    I have an old gas furnace, and am considering replacing it with a new, high efficiency model. Is upgrading worth it? Information: List 1.5.11
    27.
    -
    Janine is considering buying a water filter and a reusable water bottle rather than buying bottled water. Will doing so save her money? Information: List 1.5.13 +
    Janine is considering buying a water filter and a reusable water bottle rather than buying bottled water. Will doing so save her money? Information: List 1.5.12
    28.
    -
    Marcus is considering going car-free to save money and be more environmentally friendly. Is this financially a good decision? Information: List 1.5.14 +
    Marcus is considering going car-free to save money and be more environmentally friendly. Is this financially a good decision? Information: List 1.5.13
    @@ -887,7 +955,7 @@

    Exercise Group.

    Subsubsection 1.5.6.1 Information for Problem Solving Problems

    -
    List 1.5.9. Breadcrumb Information
      +
      List 1.5.8. Breadcrumb Information
      • How much breadcrumbs does the recipe call for?
        • It calls for 1 and a half cups of breadcrumbs.
        @@ -917,7 +985,7 @@

        Exercise Group.

        Nutrition label for cannister of breadcrumbs; Serving size of 1/3 cup is 30g; Servings per container about 14; Amount per serving: 110 calories, 1.5 grams of fat.
      -
      List 1.5.10. Car and Bottle Cap Information
        +
        List 1.5.9. Car and Bottle Cap Information
        • What kind of car is that?
          • A 1993 Honda Accord.
          @@ -940,7 +1008,7 @@

          Exercise Group.

          • Caps are 1 inch in diameter.
        -
        List 1.5.11. Chicken Information
          +
          List 1.5.10. Chicken Information
          • How much chicken is needed?
            • Four pounds.
            @@ -965,7 +1033,7 @@

            Exercise Group.

            • About $3.69/gallon right now.
          -
          List 1.5.12. Furnace Information
            +
            List 1.5.11. Furnace Information
            • How efficient is the current furnace?
              • It is a 60% efficient furnace.
              @@ -994,7 +1062,7 @@

              Exercise Group.

              • Probably at least 15 years.
          -
          List 1.5.13. Water Filter Information
          +
          List 1.5.12. Water Filter Information
          • How much water does Janine drink in a day?
            • She normally drinks 3 bottles a day, each 16.9 ounces.
            @@ -1020,7 +1088,7 @@

            Exercise Group.

        -
        List 1.5.14. Car Information
        +
        List 1.5.13. Car Information
        -
        July 8, 2024
        +
        July 10, 2024