Calculators
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The document discusses how to use a calculator effectively by following the proper order of operations. It explains that calculators may give different answers depending on the order terms are entered due to differences in how calculators evaluate expressions. The proper order of operations is BODMAS: Brackets, Orders (Exponents), Division, Multiplication, Addition, Subtraction. Examples are provided to illustrate the importance of the order of operations and using brackets to evaluate multi-step calculations correctly on a calculator.
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1. The document discusses adding and subtracting negative numbers using examples with biscuits. It explains that subtracting a negative number is the same as adding a positive number, and vice versa.
2. Quick rules are provided for subtracting or adding to negative numbers. When subtracting from a negative number, add the numbers and place a minus sign in front of the answer. When adding to a negative number, subtract the numbers and use the same sign as the larger number.
3. A method is described for calculating a string of additions and subtractions by separating the numbers into "add" and "subtract" totals and finding the difference between the totals.
Quicker maths
This is the ultimate set of game-changer, the nuclear bomb of calculations, the Best, Just follow the rules and beat the computer
The ultimate tricks to speed up your Calculating Power
4 lesson 1 4 order of operations
The document provides definitions and examples for key terms related to order of operations, including numerical expression, evaluate, sum, difference, product, factor, and quotient. It gives the order of operations as parentheses, exponents, multiplication/division from left to right, and addition/subtraction from left to right. An example problem is worked through step-by-step to demonstrate applying the order of operations. Additional practice problems are provided for students to evaluate.
Mathematical Equations
This document discusses mathematical equations and variables. It explains that a variable can represent any quantity that can change value in an equation. Common variables are x and y. The document also covers order of operations using PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) to determine the proper sequence to evaluate terms in an equation. Following PEMDAS is important as it tells us the order to follow when an equation contains multiple operations. An example problem demonstrates applying PEMDAS to solve an equation step-by-step.
Decimal Numbers Part 3
1. The document discusses multiplying decimal numbers, including multiplying decimals by whole numbers, decimals by decimals, and decimals by 10, 100, and 1,000.
2. Key rules covered are counting decimal places to determine the product's decimal placement and moving the decimal over when multiplying by powers of 10.
3. Examples provide step-by-step workings of multiplying decimals using partial products and placing the decimal point correctly in the final product.
April 12
The document provides information and examples about solving quadratic equations by completing the square. It begins with reviewing solving quadratics by factoring, graphing, and square roots. Then it introduces completing the square as a fourth method. Examples are provided to show how to identify the value to add inside the square and rewrite the equation in factored form. Students are assigned practice problems in pairs to work through applying this new method.
Times tables; NIED, Okahandja - Advisory teachers - October 2013
This document provides information and strategies for teaching times tables to students. It discusses times tables as repeated addition and structured multiplication. It then presents various hands-on materials and activities teachers can use to help students learn and memorize their times tables, including containers for counting objects, tiles, memory games, relation sheets, and times table squares. Teachers are encouraged to make these low-cost materials themselves and try them out to discover how they can best be used for mathematics instruction in their classrooms.
Lesson 10
The document outlines objectives for a math lesson including equations of lines, rational denominators, and completing the square. It provides examples of different types of lines and rational/irrational numbers. It then lists problems for finding equations of lines, simplifying expressions with rational denominators, and solving equations by completing the square.
Unit 9 review (6th grade)
The document provides guidance and examples for solving various math problems involving simplifying expressions and equations, combining like terms, using formulas, and writing and solving equations to represent word problems. It includes step-by-step instructions, examples to practice, and checks for understanding.
2.3 subtraction real numbers 1
This document discusses subtracting rational numbers. It states that subtraction is the same as adding the opposite. To subtract, change the subtraction operation to addition and change the sign of the number behind the subtraction sign. Examples are provided such as -5 - (-3) = -5 + 3 = -2. The document also provides examples of subtracting fractions and decimals. Students are assigned practice problems subtracting rational numbers.
Ch 01
1. The document discusses factors that affect the world's environment like population growth and provides population data from 1950 to 2050 in 10-year intervals.
2. It asks which 10-year period saw the largest increase in population and which saw the largest percentage increase.
3. The chapter aims to refresh skills working with numbers expressed as fractions, decimals, percentages, and indexes and applying them to real-life situations.
Msm1 fl ch01_03
The document provides a lesson on evaluating numerical expressions using the order of operations. It includes examples of simplifying expressions with addition, subtraction, multiplication, division and exponents. It also has examples of word problems involving amounts of money spent on items. The lesson concludes with a quiz to assess understanding of simplifying expressions and applying the order of operations.
Similar to Calculators (20)
Times tables; NIED, Okahandja - Advisory teachers - October 2013
Times tables; NIED, Okahandja - Advisory teachers - October 2013
More from Terry Golden
Reflections rotations translations
1. The document discusses different types of geometric transformations including reflections, rotations, and translations.
2. A reflection produces a mirror image of an object across a line or plane. Corresponding points on the object and its reflection are equidistant from the line/plane of reflection.
3. A rotation turns an object around a fixed point by a specified angle and direction. To perform a rotation, one traces the object onto tracing paper and rotates the paper around the given point by the required angle and direction.
Probability exclusive
The document discusses mutually exclusive outcomes and probability. It provides examples of tossing a coin, where the outcomes of heads and tails are mutually exclusive and must add up to 1. It also gives an example of drawing balls from a bag containing red, blue and green balls, where the probabilities of drawing red and blue balls add up to 12/14, making the probability of drawing a green ball 2/14 or 1/7.
Powers
This document provides an explanation of powers and indices. It discusses how indices can be used to represent repeated multiplication, such as 22 representing 2 x 2 and 23 representing 2 x 2 x 2. It also explains that indices can be used in combination with each other and other mathematical functions. The document provides examples of calculating values of formulas when given specific values for variables. It notes that indices only apply to the previous number and brackets can be used to keep workings clear. Values substituted can be positive, negative, decimals or fractions.
Percentages
This document explains how to convert fractions to percentages in 3 main steps:
1) Convert the fraction to a decimal by dividing the numerator by the denominator. Then multiply the decimal by 100 to get the percentage.
2) Think of 100 as the denominator of an equivalent fraction. Find the equivalent fraction by setting 100 as the denominator.
3) Directly convert the fraction to a percentage by multiplying the fraction by 100 and simplifying. This skips converting to a decimal first.
Worked examples are provided to demonstrate both converting through decimals and directly to percentages.
Grouping data stem and leaf diagrams
This document explains how to represent math test score data for 30 students using a stem and leaf diagram. [1] The test scores ranged from 40 to 81 and are grouped into the 40s, 50s, 60s, 70s, and 80s. [2] The stem represents the tens place value and the leaves are the units that follow each ten. [3] The modal score is in the 60-69 group and the median score is 63.
Grouping data discrete
This document discusses grouping discrete data and calculating statistics like the mode, mean, and frequency. It provides an example of grouping the number of goals scored in soccer matches to find the mode of 3 goals. Another example calculates the mean shoe size from a survey by tallying shoe sizes into a frequency table and dividing the total by the number of participants.
Graphs 3
This graph shows Joe's trip to the local shop over time. It shows that Joe walked at a steady pace as the distance from his home to the shop increased linearly over 15 minutes. Then the distance remained the same as he spent more time at the shop before returning home. The graph uses distance from home on the y-axis and time on the x-axis to tell the story of Joe's shopping trip.
Fractions multiplicatin
To multiply fractions:
1) Multiply the numerators together to get the new numerator
2) Multiply the denominators together to get the new denominator
3) Simplify the resulting fraction if possible by cancelling common factors in the numerator and denominator.
Drawing triangles
This document provides instructions for drawing different types of triangles based on given information:
1. When given one angle and the lengths of two sides, use a protractor and ruler to draw the triangle.
2. When given the measures of two angles and the length of one side, construct the triangle using a protractor and ruler.
3. When given the lengths of all three sides but no angles, use a compass and ruler to draw the triangle.
Drawing polygons
The document discusses drawing regular polygons by dividing a circle into equal parts. It explains that 360 degrees is commonly used because it has many factors, making it easy to divide a circle evenly. Drawing regular polygons involves dividing the circle by the number of sides of the desired polygon shape. An example is then given of how to draw a regular pentagon by dividing the circle into 72 degree segments since 360 divided by 5 is 72.
Correlation
The document discusses scatter diagrams and correlation. It explains positive and negative correlation, and how to draw a line of best fit on a scatter plot to show the relationship between two variables. It provides examples of perfect, strong, and weak correlation, and discusses using the line of best fit to estimate values.
Compound measures
The document discusses compound measures like speed, density, and population density. Speed is the distance traveled over time. Density is the mass of an object divided by its volume. Population density is the number of people in an area divided by the total land area. These compound measures combine two or more simple measures to represent a single value.
Circles diameter
1. The document discusses circles and the relationships between their circumference, diameter, and radius. It provides examples of measuring circular objects and calculating circumference from diameter and vice versa.
2. The key relationship discussed is that the ratio of a circle's circumference to its diameter is a constant called pi (π), approximately 3.14.
3. Examples are given of calculating circumference from diameter and radius using the formulas C = πd and C = 2πr.
More from Terry Golden (13)
Calculators
- 1. October 4, 2012 Using a calculator effectively Next
- 2. Explanation October 4, 2012 If you perform the calculation 2 + 4 × 3 on a calculator, you may get the answer 18, or the answer 14. This is because the calculation may be performed according to the order in which the numbers are typed in, so 2 + 4 × 3 = 18 More Next
- 3. Explanation October 4, 2012 If you perform the calculation 2 + 4 × 3 on a calculator, you may get the answer 18, or the answer 14. This is because the calculation may be performed according to the order in which the letters are typed in, so 2 + 4 × 3 = 18 or your calculator may follow the rules of maths, and do the multiplication first, so 2 + (4 × 3) = 14 More Next
- 4. Explanation October 4, 2012 When you see a sum involving more than one calculation, it has do be done in a particular order. Remembering the word BODMAS may help you… This means that the order you perform the operations in a calculation is always rackets. rders of, or pOwer. ivide. ultiply. dd. ubtract. More Next
- 5. Example October 4, 2012 It is very important to learn which way the calculator you are using works. On your calculator, press the buttons in this order.. 1 + 2 × 4 = Did you get the incorrect answer 12, or the correct answer, 9? How might you change the following sequence, to make sure that you got the correct answer? 3 − 2 × 6 = There are various ways, but one is to add brackets. 3 − ( 2 × 6 ) = -9 More Next
- 6. Explanation October 4, 2012 Powers can be found using the buttons x 2 or x y or sometimes x The root of a number can be found using the buttons or x or sometimes Roots should be considered “powers”, or “orders of” in the BODMAS sequence. You may find it useful to use the memory of your calculator. Familiarise yourself with the memory buttons. You may use STO and RCL or M+ and MR More Next
- 7. Practise October 4, 2012 Use your calculator to work out the following… 3² 9 64 8 -2 ² 4 121 11 3² 2 (10– 4) (-1.4 × -4.3) + (-5.2 × 2) -4.38 12.1 5.2 – 4.3 + 11.2 2.86 × 62 d.p. -3.9 + 1.4 -2 to -0.05 4.6 ² – 2.4 ² 26.92 4.6 ³ – 2.1 ⁴ 116.7841 -1.4 × 3 5 8.2 ² to ² 9.60+ 52 d.p. (2.9238.328 3.1 ³ + 6.4 – ) More Next End