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Specific Competence: Students will be able to tell the difference between and use different kinds of numbers. These include: - Natural numbers (counting numbers like 1, 2, 3...) - Integers (whole numbers, positive, negative, or zero) - Prime numbers (numbers only divisible by 1 and themselves, like 2, 3, 5) - Square numbers (numbers you get by multiplying a whole number by itself, like 4, 9, 16) - Cube numbers (numbers you get by multiplying a whole number by itself three times, like 8, 27, 64) - Common factors (numbers that divide exactly into two or more numbers) - Common multiples (numbers that are multiples of two or more numbers) - Rational numbers (numbers that can be written as a simple fraction) - Irrational numbers (numbers that cannot be written as a simple fraction, like pi) - Reciprocals (1 divided by a number). Learning Activities: Students will practice: - Changing numbers written in words to digits and vice versa (e.g., 'six billion' to 6,000,000,000). - Breaking down a number into its prime factors (e.g., 72 = 2 × 2 × 2 × 3 × 3). - Finding the largest number that divides exactly into two or more numbers (Highest Common Factor or HCF). - Finding the smallest number that is a multiple of two or more numbers (Lowest Common Multiple or LCM). Expected Standard: Students will correctly identify and use different types of numbers, convert between number forms, and find factors and multiples.
Specific Competence: Students will understand and use the language, symbols, and Venn diagrams to describe groups of items called 'sets'. Learning Activities: Students will use set symbols such as: - n(A) for the number of items in set A. - A' for all items not in set A (complement). - A symbol for the 'universal set' (all possible items). - A ∪ B for items that are in set A OR set B (union). - A ∩ B for items that are in set A AND set B (intersection). - They will work with Venn diagrams that show up to two sets. - They will understand how sets are defined (e.g., A = {x: x is a natural number} means A is the set of all natural numbers). Expected Standard: Students will correctly use set language and symbols and show sets using Venn diagrams.
Specific Competence: Students will be able to calculate numbers involving squares, square roots, cubes, cube roots, and other powers and roots. Learning Activities: Students will: - Remember the squares of numbers from 1 to 15 and their square roots (e.g., know that the square root of 169 is 13). - Remember the cubes of 1, 2, 3, 4, 5, and 10 and their cube roots. - Solve problems like calculating 5 multiplied by 8 squared multiplied by 3 (5 × 8² × 3). Expected Standard: Students will correctly calculate squares, cubes, and their roots, and apply these skills to other powers and roots.
Specific Competence: Students will use the terms and symbols for proper fractions (numerator smaller than denominator), improper fractions (numerator larger than denominator), mixed numbers (whole number and a fraction), decimals, and percentages. They will recognize when these forms are equal and change between them. Learning Activities: Students will practice: - Writing fractions in their simplest form (e.g., 2/4 becomes 1/2). - Changing a fraction to a decimal, a decimal to a percentage, and so on. Expected Standard: Students will correctly use and change between fractions, decimals, and percentages, always writing fractions in their simplest form. (Note: Changing recurring decimals to fractions and vice versa is not required).
Specific Competence: Students will arrange amounts of things by their size (magnitude) and understand the symbols for: - Equals (=) - Not equals (≠) - Greater than (>) - Less than (<) - Greater than or equal to (⩾) - Less than or equal to (⩽) Learning Activities: Students will practice putting numbers or quantities in order from smallest to largest or largest to smallest. They will use the comparison symbols correctly to show relationships between numbers. Expected Standard: Students will correctly order different quantities and use comparison symbols.
Specific Competence: Students will use addition, subtraction, multiplication, and division for calculations with: - Integers (whole numbers, including negative ones). - Fractions. - Decimals. They will follow the correct order of operations (like doing multiplication before addition) and use brackets properly. Learning Activities: Students will solve problems that involve: - Negative numbers (e.g., -5 + 3). - Improper fractions (e.g., 7/4) and mixed numbers (e.g., 1 ¾). - Real-life situations, such as figuring out temperature changes. Expected Standard: Students will accurately perform all four basic operations on different types of numbers, following the correct order of operations.
Specific Competence: Students will understand and use powers (indices) where the exponent can be a positive whole number, zero, or a negative whole number. They will also understand and use the rules for working with these powers. Learning Activities: Students will practice: - Finding the value of a number raised to a negative power (e.g., 7⁻²). - Applying the rules of powers for multiplication (e.g., 2⁻³ × 2⁴), powers of powers (e.g., (2³) ²), and division (e.g., 2³ ÷ 2⁴). Expected Standard: Students will correctly work with positive, zero, and negative powers and apply the rules of powers.
Specific Competence: Students will use standard form (a way to write very large or very small numbers) which looks like A × 10ⁿ. In this form, n is a positive or negative whole number, and A is a number between 1 and less than 10. Students will change numbers into and out of standard form and do calculations with numbers in standard form. Learning Activities: Students will: - Write numbers like 6,000,000 in standard form (6 × 10⁶). - Change numbers from standard form back to their usual form. - Perform calculations like multiplying or dividing numbers given in standard form. Expected Standard: Students will correctly use standard form for numbers, convert between forms, and perform calculations. (Note: Students taking the 'Core' exam will only do calculations with standard form in Paper 3).
Specific Competence: Students will round numbers to a specific level of exactness (using decimal places or significant figures). They will make good guesses (estimates) for calculations involving numbers, amounts, and measurements. They will round their answers to a sensible level of exactness for the problem. Learning Activities: Students will practice: - Rounding numbers (e.g., rounding 5764 to the nearest thousand, which is 6000). - Rounding numbers to a certain number of decimal places or significant figures. - Estimating the answer to a calculation by first rounding each number in the problem (e.g., estimating (9.79 × 0.765) / 41.3 by rounding each number to 1 significant figure). Expected Standard: Students will accurately round numbers and make good estimates for calculations.
Specific Competence: Students will state the highest and lowest possible values (upper and lower bounds) for data that has been rounded to a certain exactness. Learning Activities: Students will practice finding the upper bound of a measurement (e.g., if a length is measured to the nearest metre, they will find the largest possible value it could be). Expected Standard: Students will correctly find the highest and lowest possible values for rounded measurements. (Note: Students are not expected to find the bounds of answers to calculations that used rounded data).
Specific Competence: Students will use addition, subtraction, multiplication, and division for calculations. This includes working with whole numbers, fractions, and decimals. They will also correctly follow the order of operations and use brackets. Learning Activities: Work with negative numbers, improper fractions, and mixed numbers. Solve problems from real-life situations, such as changes in temperature. Expected Standard: Students will correctly perform calculations with different types of numbers and apply these operations in practical scenarios.
Specific Competence: Use addition, subtraction, multiplication, and division to solve problems. Learning Activities: You will work with whole numbers, fractions (including those with bigger tops than bottoms, and mixed numbers like 1 and a half), and decimal numbers. You will learn the correct order to do calculations (like doing multiplication before addition) and how to use brackets. You will solve problems that include negative numbers and real-life examples, such as changes in temperature. Expected Standard: You must use all four operations correctly with different kinds of numbers. You also need to understand the right order for doing calculations and using brackets.
Specific Competence: Understand what powers (also called indices) are and how to use them. This includes powers that are positive, zero, or negative whole numbers. Learn the rules for working with powers. Learning Activities: You will find the value of a number when it's raised to a power, for example, 7⁻² (7 to the power of negative 2). You will solve problems where you combine powers, such as 2⁻³ multiplied by 2⁴, or (2³)², or 2³ divided by 2⁴. Expected Standard: You need to know what powers mean. You must also know how to use the rules for multiplying powers, dividing powers, and raising a power to another power.
Specific Competence: Use standard form, which is a way to write very big or very small numbers (like A × 10ⁿ). Here, 'n' is a whole number (it can be positive or negative), and 'A' is a number between 1 and less than 10. You will change numbers into standard form and back again. You will also do calculations with numbers written in standard form. Learning Activities: You will change very large or very small numbers into standard form (for example, 3,000,000 becomes 3 × 10⁶) and then change them back again. You will also add, subtract, multiply, and divide numbers that are written in standard form. Expected Standard: You should be able to write numbers in standard form and use it for calculations. For some tests (Paper 3), students taking the core exam are expected to do calculations with standard form.
Specific Competence: Round numbers to a specific level of accuracy, like to a certain number of decimal places or significant figures. Make educated guesses (estimates) for answers to calculations that involve numbers, amounts, and measurements. Round your final answers in a way that makes sense for the problem. Learning Activities: You will practice rounding numbers to a certain number of decimal places or significant figures. For instance, round 5764 to the nearest thousand. You will also estimate the answer to a calculation by rounding each number first (for example, estimate (9.79 × 0.765) / 41.3 by rounding each number to 1 significant figure). Expected Standard: You must know how to round numbers. You should also use rounding to make good estimates for calculations.
Specific Competence: Find the highest and lowest possible values (called upper and lower bounds) for a number that has been rounded to a certain accuracy. Learning Activities: You will find the range of values that an original measurement could have been before it was rounded. For example, if a length is measured to the nearest metre, you will find its upper bound (the largest possible original value). Expected Standard: You need to understand how rounding changes the true value of a number. You must be able to state the highest and lowest possible values (bounds) for a measurement that has been rounded. You are not expected to find the bounds for the answers to calculations where the original numbers were already rounded.
Specific Competence: Understand and use ratios and proportion. Learning Activities: You will write ratios in their simplest form (for example, 20:30:40 simplifies to 2:3:4). You will share a total amount into parts based on a given ratio. You will use ratios to solve real-life problems, such as changing amounts in recipes, using map scales, or figuring out which product offers the best value when you shop. Expected Standard: You must be able to make ratios simpler. You should also be able to share amounts using a ratio and use ratios to solve real-life problems.
Specific Competence: Use common ways to measure how one thing changes compared to another (rates). Apply different types of rates. Solve problems about average speed. Learning Activities: You will calculate using things like hourly pay, how much one currency is worth in another (exchange rates), how fast liquids move (flow rates), and how much fuel a car uses (fuel consumption). You will also calculate with pressure, density (how much 'stuff' is in a space), and how many people live in an area (population density). You will calculate average speed, for example, if a cyclist travels 45 kilometres in 3 hours and 45 minutes. Expected Standard: You need to understand different kinds of rates and solve problems with them. You must know the formula that links speed, distance, and time. Formulas for pressure and density will be given in the question if you need them. You will see symbols like m/s (metres per second) and g/cm³ (grams per cubic centimetre).
Specific Competence: Calculate a percentage of a given amount. Show one amount as a percentage of another. Work out how much something has gone up or down in percentage. Calculate simple interest and compound interest. Learning Activities: You will find a percentage of a certain amount. You will turn one amount into a percentage of another. You will calculate how much something has increased or decreased in percentage terms, like changes in prices or populations. You will also calculate simple interest (interest only on the original amount) and compound interest (interest on the original amount plus any interest already earned). This includes problems about money you put down (deposits), price reductions (discounts), how much money you make or lose (profit and loss), how much you earn, and percentages that are more than 100%. Expected Standard: You must be able to do many different types of percentage calculations. Formulas for interest are not given, so you are expected to know them or work them out.
Specific Competence: Use a calculator well and efficiently. Put numbers into the calculator correctly. Understand what the numbers on the calculator screen mean. Learning Activities: You will learn how to use a calculator's features in the best way. You will enter numbers and calculations correctly. You will understand that you should not round numbers while you are doing a calculation; only round the final answer. You will understand what the calculator shows you in real-life situations. For example, knowing that 4.8 in money means $4.80, or 3.25 in time means 3 hours and 15 minutes. You will also learn to enter time correctly, like 2 hours 30 minutes as 2.5 hours. Expected Standard: You should be good at using a calculator for maths problems. You should also be able to understand what the calculator shows you in real-life situations.
Specific Competence: Do calculations with time. Change between different units of time (like seconds to minutes). Use both the 24-hour and 12-hour clock. Read clocks and timetables. Learning Activities: You will calculate using seconds, minutes, hours, days, weeks, months, and years. You will understand how these units relate to each other (for example, 1 year equals 365 days). You will change times between the 24-hour clock (for example, 0315 for 3:15 a.m. and 1515 for 3:15 p.m.) and the 12-hour clock. You will solve problems that involve different time zones, local times, and how much time has passed. Expected Standard: You need to be good at doing time calculations, changing between time units, and reading time information from different places.
Specific Competence: Do calculations with money. Change money from one currency to another. Learning Activities: You will add, subtract, multiply, and divide amounts of money. You will also change money from one currency to another using exchange rates (how much one type of money is worth compared to another). Expected Standard: You must be able to do money calculations and change between different currencies correctly.
Specific Competence: Understand that letters can stand for numbers. Put numbers into algebraic expressions and formulas. Learning Activities: Use letters to represent unknown numbers. Replace letters with given numbers in algebraic statements and rules. Expected Standard: Students can use letters for numbers and correctly substitute numbers into algebraic expressions and formulas.
Specific Competence: Simplify algebraic expressions by combining similar terms. Expand products of algebraic expressions. Factorise expressions by taking out common factors. Learning Activities: Combine terms like '2a' and '5a'. Multiply out brackets, including multiplying two brackets together (e.g., (2x+1)(x-4)). Find common parts in an expression and put them outside brackets (e.g., 9x² + 15xy = 3x(3x+5y)). Expected Standard: Students can simplify, expand, and factorise algebraic expressions correctly.
Specific Competence: Understand and use powers (indices) that are positive, zero, or negative. Apply the rules for working with indices. Learning Activities: Work with numbers and letters raised to powers (e.g., x squared, x to the power of zero, x to the power of negative one). Apply rules for multiplying, dividing, and raising powers to other powers. Solve simple equations involving powers (e.g., 2^x = 32). Expected Standard: Students can use positive, zero, and negative indices and apply the rules of indices correctly.
Specific Competence: Create simple algebraic expressions, equations, and formulas. Solve linear equations with one unknown. Solve two linear equations at the same time (simultaneous equations) with two unknowns. Rearrange simple formulas to make a different letter the subject. Learning Activities: Write algebraic statements from word problems. Find the value of 'x' in equations like 3x+4=10. Solve systems of two equations with two variables. Change the subject of a formula (e.g., from A=bh to h=A/b). Expected Standard: Students can construct, solve, and rearrange equations and formulas.
Specific Competence: Show and understand inequalities, including how to represent them on a number line. Learning Activities: Draw inequalities like x > 3 or -3 <= x < 1 on a number line, using open circles for 'less than' or 'greater than' and closed circles for 'less than or equal to' or 'greater than or equal to'. Expected Standard: Students can correctly represent and interpret inequalities on a number line.
Specific Competence: Continue number patterns. Find the rule that describes how numbers change in a sequence. Find and use the 'nth term' for linear, simple quadratic, and simple cubic sequences. Learning Activities: Identify the next numbers in a given sequence (e.g., 1, 3, 6, 10, 15, ...). Work out the rule for how to get from one term to the next. Find a general formula (nth term) to find any number in the sequence for linear (e.g., 2, 5, 8, 11...), simple quadratic (e.g., 2, 5, 10, 17...), and simple cubic sequences. Expected Standard: Students can continue sequences, recognise patterns, and find the nth term for different types of sequences.
Specific Competence: Use and understand graphs that show real-life situations, such as travel graphs and conversion graphs. Draw graphs using given information. Learning Activities: Read information from graphs showing distance over time (travel graphs) or how one unit converts to another (conversion graphs). Plot points and draw graphs from a set of data. Understand that the steepness (gradient) of a straight line graph shows a rate of change (e.g., speed). Expected Standard: Students can effectively use and create graphs to understand and represent real-world situations.
Specific Competence: Create tables of values, draw, recognise, sketch, and understand graphs for linear (ax+b), quadratic (±x²+ax+b), and reciprocal (a/x) functions. Solve related equations by looking at graphs, including finding where graphs cross the x-axis (roots) or where two graphs meet. Learning Activities: Make a list of (x, y) pairs for different functions. Plot these points to draw graphs of straight lines, U-shaped curves (parabolas), and curves like y=a/x. Quickly draw the general shape of linear and quadratic graphs. Find the solutions to equations by identifying where a graph crosses the x-axis or where two graphs intersect. Expected Standard: Students can draw, sketch, interpret, and use graphs of linear, quadratic, and reciprocal functions to solve equations.
Specific Competence: Understand and use coordinates, draw straight-line graphs, find the steepness (gradient) of a line, write the equation of a line, and work with parallel lines. Learning Activities: Students will: * Plot points on a graph using two numbers (Cartesian coordinates). * Draw straight-line graphs when given an equation (like y = 2x + 3) or a table of values. * Find how steep a straight line is (its gradient) directly from a graph. * Work out the equation of a straight line (in the form y = mx + c) from its graph or from given information. * Find the gradient and equation of a straight line that runs next to another line (parallel). Expected Standard: Students will clearly understand and use coordinates, accurately draw and interpret graphs of straight lines, find the steepness and equation for straight lines, including lines that are parallel, and write equations in a simple form.
Specific Competence: Understand and use the correct names for points, lines, angles, and various 2D and 3D shapes. Learning Activities: Students will: * Learn and use words like point, line, parallel (lines that never meet), perpendicular (lines that meet at a right angle), right angle, acute (small) angle, obtuse (large) angle, reflex (very large) angle. * Learn names for different triangles (e.g., equilateral, isosceles), four-sided shapes (e.g., square, rectangle, rhombus), and shapes with many sides (polygons like pentagon, hexagon). * Understand terms related to circles (e.g., centre, radius, diameter, circumference) and simple 3D shapes (e.g., cube, cylinder, pyramid, sphere). Expected Standard: Students will accurately use and explain the specific words for points, lines, angles, different 2D shapes (triangles, quadrilaterals, polygons, circles), and common 3D solids.
Specific Competence: Measure and draw lines and angles, build (construct) triangles, and work with flat patterns (nets) of 3D shapes. Learning Activities: Students will: * Use a ruler to measure and draw lines and angles accurately. * Draw a triangle using only a ruler and a pair of compasses when given the lengths of all its sides. * Draw flat patterns (nets) for 3D shapes like cubes, boxes (cuboids), prisms, and pyramids. * Use measurements from these nets to calculate the space inside (volume) and the total outside area (surface area) of the 3D shapes. Expected Standard: Students will accurately measure and draw geometric figures, construct triangles precisely using specific tools, and correctly draw and understand nets of common 3D shapes.
Specific Competence: Draw and understand drawings that are scaled down or up, and use three-figure bearings to show direction. Learning Activities: Students will: * Create and read drawings where real-world objects or distances are shown smaller or larger using a specific scale. * Figure out real distances from scale drawings. * Use three-figure bearings (numbers from 000° to 360°, measured clockwise from North) to describe directions between points. * Understand the main compass directions: North, East, South, West. Expected Standard: Students will accurately draw and interpret scale drawings, and correctly use and calculate three-figure bearings, understanding the main compass directions.
Specific Competence: Calculate the lengths of sides in shapes that are similar (look the same but are different sizes). Learning Activities: Students will: * Identify shapes that have the same shape but different sizes (similar shapes). * Understand the 'scale factor,' which is the number you multiply by to go from one similar shape's length to another's. * Use this scale factor to find missing lengths in similar figures. Expected Standard: Students will correctly calculate unknown side lengths in similar two-dimensional shapes by using the scale factor.
Specific Competence: Find line symmetry and rotational symmetry in flat (two-dimensional) shapes. Learning Activities: Students will: * Identify lines of symmetry (where you can fold a shape so both halves match) in shapes like triangles, quadrilaterals, and polygons. * Determine how many times a shape looks the same as it is turned around a central point (order of rotational symmetry). Expected Standard: Students will accurately recognise and describe line symmetry and the order of rotational symmetry for different two-dimensional shapes.
Specific Competence: Calculate unknown angles using rules about how angles behave. Learning Activities: Students will: * Apply rules such as: angles around a point add up to 360°, angles on a straight line add up to 180°, opposite angles where two lines cross are equal. * Use the rule that angles inside a triangle add up to 180° and inside a four-sided shape (quadrilateral) add up to 360°. * Calculate angles formed by parallel lines (lines that never meet), such as corresponding angles (same position), alternate angles (opposite sides inside), and co-interior angles (same side inside, add to 180°). * Know and use rules for angles inside and outside regular polygons (shapes with all equal sides and angles). Expected Standard: Students will accurately calculate unknown angles in diagrams, providing clear reasons using the correct mathematical words for angles related to points, straight lines, shapes (triangles, quadrilaterals, polygons), and parallel lines.
Specific Competence: Students will be able to find unknown angles within circles. They will also be able to explain their answers using specific rules about circles. Learning Activities: Students will practice calculating angles in diagrams involving semicircles, tangents, and radii. They will learn and apply specific rules like "an angle in a semicircle is 90 degrees" and "the angle where a tangent touches a radius is 90 degrees." Expected Standard: Students must correctly calculate angles and clearly state the specific circle rule they used to get their answer.
Specific Competence: Students will be able to use standard metric units for weight, length, flat space (area), solid space (volume), and how much a container can hold (capacity). They will also be able to change these measurements into larger or smaller units. Learning Activities: Students will practice identifying and using units like millimeters (mm), centimeters (cm), meters (m), kilometers (km), square centimeters (cm²), cubic meters (m³), milliliters (ml), liters (l), grams (g), and kilograms (kg). They will practice converting between these units, for example, from cm² to m² or m³ to liters. Expected Standard: Students must accurately convert between different metric units in real-life problems.
Specific Competence: Students will be able to calculate the distance around (perimeter) and the flat space inside (area) of rectangles, triangles, parallelograms, and trapeziums. Learning Activities: Students will solve problems to find the perimeter and area of these basic 2D shapes. They will need to remember the formulas for these calculations, except for the area of a triangle, which will be provided. Expected Standard: Students must correctly calculate perimeters and areas for the given shapes, using the right formulas.
Specific Competence: Students will be able to calculate the distance around (circumference) and the flat space inside (area) of a full circle. They will also calculate the length of a curved part of a circle (arc) and the area of a slice of a circle (sector). Learning Activities: Students will work on problems involving circles and parts of circles. They will use given formulas to find circumference, area, arc length, and sector area, where the sector angle divides 360 degrees evenly. Expected Standard: Students must correctly perform calculations for circles, arcs, and sectors. Their answers might be asked for using the symbol π (pi).
Specific Competence: Students will be able to calculate the total flat space on the outside (surface area) and the total space taken up by (volume) common 3D shapes. These shapes include cuboids, prisms, cylinders, spheres, pyramids, and cones. Learning Activities: Students will solve problems to find the surface area and volume of various 3D objects. They will use formulas provided for specific parts like the curved surface area of a cylinder or the volume of a sphere. A prism is any solid with the same shape all the way through. Expected Standard: Students must accurately calculate surface areas and volumes for the specified 3D shapes, using the provided formulas. Answers might be asked for using the symbol π (pi).
Specific Competence: Students will be able to calculate the perimeter and area of shapes made by joining simpler shapes or using only parts of shapes. They will also calculate the surface area and volume of 3D objects made by joining simpler solids or using parts of solids. Learning Activities: Students will learn to break down complex 2D and 3D figures into simpler parts. They will then calculate the perimeter, area, surface area, or volume of these compound or partial shapes. For example, finding the volume of half of a sphere. Expected Standard: Students must correctly calculate measurements for complex 2D and 3D shapes, including those made from combined or partial figures. Answers might be asked for using the symbol π (pi).
Specific Competence: Students will learn to use a special rule called Pythagoras' theorem and other tools (sine, cosine, tangent) to figure out missing lengths and angles in triangles that have a perfect square corner (right-angled triangles). They will also solve real-life problems using these tools. Learning Activities: Students will learn how to use Pythagoras' theorem to find a missing side when two sides of a right-angled triangle are known. They will practice using sine, cosine, and tangent (which are ways to compare the sides of a right-angled triangle) to find missing angles or sides. They will solve problems that combine these methods, including those that involve directions (called bearings). Expected Standard: Students will correctly use Pythagoras' theorem and the sine, cosine, and tangent tools in their calculations. They will solve real-world problems accurately, giving angle answers in degrees, rounded to one decimal place.
Specific Competence: Students will learn to recognise, explain, and draw four ways to move or change shapes: reflection, rotation, enlargement, and translation. They will also understand how to use vectors to describe a translation. Learning Activities: Students will practice flipping shapes over a line (reflection), turning shapes around a point (rotation by 90-degree steps), making shapes bigger or smaller from a central point (enlargement), and sliding shapes in a specific direction (translation). For translation, they will use a special arrow called a vector to show the movement. Expected Standard: Students will correctly identify, describe, and draw reflections, rotations, enlargements, and translations. They will accurately use vectors to show how shapes are translated.
Specific Competence: Students will understand the probability scale from 0 to 1. They will calculate the chance of a single event happening. They will know that the chance of an event not happening is 1 minus the chance of it happening. Learning Activities: Students will learn using notes and examples. They will solve problems that use information from tables, graphs, or Venn diagrams (limited to two sets). For example, if the chance a counter is blue is 0.8, students will find the chance it is not blue. Expected Standard: Students do not need to use special probability symbols. They should give probabilities as fractions, decimals, or percentages. Venn diagrams used for problems will only have two groups.
Specific Competence: Students will understand that relative frequency is a way to guess how likely an event is. They will calculate expected frequencies. Learning Activities: Students will learn using notes and examples. For example, they will use results from spinner experiments to guess the chance of a certain outcome. They will use probability to guess an expected value from a larger group. Expected Standard: Students will understand what "fair," "biased," and "random" mean.
Specific Competence: Students will calculate the chance of two or more events happening together. Learning Activities: Students will learn using notes and examples. They will use sample space diagrams, Venn diagrams, and tree diagrams to find these chances. Expected Standard: Combined events will only involve putting things back after picking them (with replacement). Venn diagrams will only have two groups. In tree diagrams, the results will be written at the end of the branches, and the chances will be written next to the branches.
Specific Competence: Students will sort and arrange statistical data into tables. Learning Activities: Students will learn using notes and examples. They will use tally tables and two-way tables. Expected Standard: Data should be organized clearly and correctly.
Specific Competence: Students will read, understand, and draw conclusions from tables and statistical diagrams. They will compare different sets of data using tables, graphs, and statistical calculations. They will understand the limits of drawing conclusions from given data. Learning Activities: Students will learn using notes and examples. For example, they will compare average values and ranges between two sets of data. Expected Standard: Conclusions drawn should be reasonable and supported by the data.
Specific Competence: Students will calculate the mean (average), median (middle value), mode (most common value), and range (difference between highest and lowest) for individual data. They will know when to use each of these measures. Learning Activities: Students will learn using notes and examples. Expected Standard: Data will be given as a list or in a frequency table, but not in groups (e.g., not "10-20", "21-30").
Specific Competence: Students will draw and understand different types of charts and diagrams. Learning Activities: Students will learn using notes and examples. They will draw and understand: (a) bar charts, (b) pie charts, (c) pictograms, (d) stem-and-leaf diagrams, and (e) simple frequency distributions. This includes stacked and side-by-side bar charts. Expected Standard: Stem-and-leaf diagrams must have data in order and include a key to explain what the numbers mean.
Specific Competence: Students will draw and understand scatter diagrams. They will understand what positive, negative, and no correlation mean (how two things relate). They will draw, understand, and use a straight line that best fits the data. Learning Activities: Students will learn using notes and examples. Expected Standard: Plotted points should be clearly marked, for example, as small crosses (×). A line of best fit must be a single straight line drawn by looking at the data. It should go across all the data points. It does not need to touch every point, but there should be roughly an equal number of points on both sides of the line along its whole length.
