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Problem Solving & Math Models Flashcards

Problem Solving & Math Models Flashcards
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Estimation

Finding an approximate answer to a problem, but not the exact answer/value

Shown using equal sign with wavy lines

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Analogies Principle

A problem solving principle that involves using comparisons to describe unfamiliar concepts

Example: explaining a parallelogram as a slanted rectangle

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Splitting Hairs Principle

A problem solving principle that states that two things that are similar may not be the same (details are important)

Example: 2 right triangles with the same angles may have different side lengths

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Order Principle

A problem solving principle that states that order matters when solving problems

Example: finding the median of a data set requires putting the values in ascending or descending order

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Counterexample Principle

A problem solving principle that involves disproving a statement using a single example

Example: 'right-handed people always bat right-handed' is disproven by one that bats left-handed

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Always Principle

A problem solving principle that states that there are certain things that are always true

Example: a whole number multiplied by an even number will always be even

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13 cards in set

Flashcard Content Overview

The flashcards in this set review mathematical problem solving and modelling. Included are problem solving principles, as well as cards on mathematical modelling, how to estimate, and how to solve multi-step word problems.

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Always Principle

A problem solving principle that states that there are certain things that are always true

Example: a whole number multiplied by an even number will always be even

Counterexample Principle

A problem solving principle that involves disproving a statement using a single example

Example: 'right-handed people always bat right-handed' is disproven by one that bats left-handed

Order Principle

A problem solving principle that states that order matters when solving problems

Example: finding the median of a data set requires putting the values in ascending or descending order

Splitting Hairs Principle

A problem solving principle that states that two things that are similar may not be the same (details are important)

Example: 2 right triangles with the same angles may have different side lengths

Analogies Principle

A problem solving principle that involves using comparisons to describe unfamiliar concepts

Example: explaining a parallelogram as a slanted rectangle

Estimation

Finding an approximate answer to a problem, but not the exact answer/value

Shown using equal sign with wavy lines

Find the estimated total spent on 5 shirts that were $5.05 each.

Round to nearest dollar: $5

$5 * 5 = $25

Steps for Solving Word Problems

1. Visualize problem for understanding; determine what you are trying to solve

2. Write equations that will enable the problem to be solved

3. Solve

A farmer sells 5 cartons of eggs on each weekday day, and 10 cartons of eggs each weekend day. Find the number of cartons of eggs sold that week.

Monday-Friday: 5 cartons * 5 days = 25 cartons

Saturday and Sunday: 10 cartons * 2 = 20 cartons

25 + 20 = 45 cartons of eggs

At the beginning of the week, a store had 60 shirts, 40 pants, and 20 hats. At the end of the week, there were 10 items left. 3 were pants, and 3 were hats. Find the number of shirts that were sold.

10 items left = 3 pants + 3 hats + x shirts

x = 4 shirts remaining

60 shirts at start - y shirts sold = 4 shirts remaining

y = 56 shirts sold

At the beginning of the week, a store had 60 shirts, 40 pants, and 20 hats. At the end of the week, there were 10 items left. Find the amount of money earned if all items cost $15 each.

60 shirts + 40 pants + 20 hats = 120 items

120 items - 10 items left = 110 items sold

110 items * $15 = $1,650.00 earned

Modelling

The process of representing scenarios with examples

Mathematical Model

A formula that is used to represent a real-world problem

Represent phenomena in ideal (perfect) conditions, so not always 100% accurate

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