2 5math Laws
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The document discusses various mathematical properties including: - Commutative and associative properties of addition and multiplication which allow changing the order or grouping of terms. - Identity properties which show that adding or multiplying a number by its identity (0 for addition, 1 for multiplication) does not change the number. - The opposite property which involves changing all addition signs to subtraction or multiplying the entire expression by -1. - The distributive property which allows multiplying a number by the terms inside parentheses. - Properties of equality including reflexive, symmetric, transitive, and substitution properties which define when expressions can be said to be equal.
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Ben harvested 73 eggplant and 94 pieces of okra, for a total of 73 + 94 = 167 pieces of vegetables harvested. The associative property of addition states that changing the grouping of the addends does not change the sum, as shown in examples such as (4 + 3) + 5 = 4 + (3 + 5).
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This document reviews probability and statistics concepts from Algebra I Chapter 4.3. It discusses experimental versus theoretical probability and provides examples of calculating probability using fractions, decimals, and percentages. Sample spaces and probability trees are presented for coin flips, rolling dice, and drawing colored buttons from a bag. Calculating theoretical probability is defined as the number of favorable outcomes divided by the total number of possible outcomes.
4 5b Histograms
The document discusses histograms and how they are used to organize and summarize data. Histograms divide a continuous range of data into bins of equal size to display the frequency distribution. They show the frequency of data values within each discrete interval. The document provides an example of students measuring the density of an unknown liquid and creating a histogram to analyze the results. It outlines the steps to organize the density data values, determine the appropriate bin ranges, count the data into groups, and interpret the frequency table and histogram created.
4 1 Proportions
The document provides examples of using proportions to solve various math problems involving ratios, fractions, rates, and geometric similarities. It includes word problems about book sales, fertilizer amounts, heights and shadows, and finding missing values in proportions. The examples demonstrate setting up and solving proportions to find unknown quantities.
4[1].4central Tendencies
The document discusses employee absences and how statistics can be used to analyze absence data. It notes that 40% of illness-related absences occur on Mondays and Fridays, potentially reducing workplace effectiveness. It asks how a boss would feel about this statistic and notes that only 2/5 of absences occur at the start and end of the work week. The document also provides an overview of measures of central tendency, including mean, median, mode, and range.
4[.5a Box Whiskers
The document provides instructions for building a box and whiskers plot. It explains that box and whisker plots use the median, quartiles, minimum and maximum values of a dataset. The instructions say to line up the numbers, find the median of the top and bottom halves, and note the minimum and maximum. A number line is drawn and boxes are placed around the middle values with whiskers extending to the minimum and maximum to complete the plot. An example is provided of calculating the values for a box and whiskers plot from a dataset.
4.5a Box Whiskers
This document provides instructions for building a box and whiskers plot. It explains that you should line up and find the median of the numbers, note the minimum and maximum values, and build the plot with a box covering the middle three quartiles and whiskers extending from the box. An example number line is given that could be used as a pattern for the box and whiskers plot, along with instructions to find the minimum, maximum, median, and first and third quartiles.
4.4central Tendencies
The document discusses employee absences and productivity. It notes that 40% of illness-related absences occur on Mondays and Fridays, reducing workplace effectiveness. It asks how a boss would feel about this statistic and notes that only 2/5 of absences occur at the start and end of the work week. The document also provides an overview of measures of central tendency, including mean, median, mode, and range.
3 3two Step Equations
This document provides instructions and examples for solving two-step equations. It explains that the two steps are: 1) add or subtract on both sides, and 2) multiply or divide on both sides. It then provides examples of solving equations using these two steps, showing the process of isolating the variable and using the inverse operation. Finally, it gives some practice problems for the reader to solve two-step equations.
2 3 Subtract Integers
1) Subtracting real numbers is the same as adding the opposite (negative) number.
2) To subtract, change the operation to addition and change the sign of the number being subtracted.
3) For example, 4 - 5 would become 4 + (-5), where -5 is the opposite (negative) of 5.
2 4mult Pos By Neg
The document discusses multiplication and division of integers. It explains that:
- When multiplying integers, the sign of the product depends on the number of negative factors. An even number of negatives gives a positive product, and an odd number gives a negative product.
- Division of integers can be performed by rewriting it as multiplication using the reciprocal of the second factor.
- Fractions and their reciprocals are also discussed as ways to rewrite division of fractions as multiplication.
2 2bpos Neg Fractionss
This document discusses adding and subtracting positive and negative integers without calculators. It provides warm up problems asking students to add opposites and lists problems from the textbook for students to work on, including problems subtracting odd integers from pages 47 and 71 of the textbook.
2 2 Pos Neg Numbers
This document discusses adding positive and negative numbers. It begins with warm up questions asking students to find sums and differences without calculators. It then reviews homework answers from the previous day. The document explains how to add positive and negative numbers using colored buttons as an example. It shows -7 + 4 equals 3 negatives. In 3 sentences or less.
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