Search & glossary

Every rule and concept in Grade 6, with its definition and a link to the lesson that teaches it. Search by term, by idea, or by lesson title.

Glossary (69)

Area in stories: Area problems ask how much surface: paint, carpet, fabric, soil.; Area of Triangles › Word Problems
Base area times height: Any prism's volume is (area of the base shape) $\times$ (length).; Surface Area and Volume › Triangular Prisms and Fractional Edges
Between the grid lines: Coordinates do not have to be whole numbers.; Quadrants › Fractions and Decimals on the Plane
Convert, flip the second, multiply: Change mixed numbers to improper fractions, keep the first, flip the divisor, multiply.; Dividing Fractions › Mixed Numbers and Whole Numbers
Count the same things together: Like terms have exactly the same letter part, like $4a$ and $2a$ .; Expressions › Combining Like Terms
Cut and slide: A parallelogram is a rectangle with a triangle moved from one end to the other: area $= bh$ .; Area of Triangles › Parallelograms and Trapezoids
Discounts, tax and tips: A discount is a percent of the original price, taken off.; Percent › Word Problems
Easy pieces: A few percents are easy: $50\%$ is half, $25\%$ is a quarter, $10\%$ is dividing by $10$ , and $1\%$ is dividing by $100$ .; Percent › Benchmark Percents
Equivalent ratios make a line: Plot each column of a ratio table as a point $(x, y)$ .; Ratios and Rates › Graphing Ratios
Even-sized sets: With an even count there is no single middle value, so the median is the average of the two middle numbers.; Statistics › Two Kinds of Middle
Every value, or grouped values: A dot plot shows every value.; Statistics › Dot Plots and Histograms
Expand or pull out: $3(x + 4) = 3x + 12$ by distributing.; Expressions › Distributing and Factoring
Flip a sign: Reflecting across the $x$ -axis changes the sign of $y$ ; across the $y$ -axis changes the sign of $x$ .; Quadrants › Reflections and Distances
Four steps: One-Step Equations › Word Problems
Greater, or farther?: "Which number is greater?" and "which number is farther from zero?" are different questions.; Absolute Value › Comparing with Absolute Value
Half-unit cubes: A cube with edges $\tfrac12$ unit has volume $\tfrac12 \times \tfrac12 \times \tfrac12 = \tfrac18$ : eight of them fill one unit cube.; Surface Area and Volume › Volume with Fractional Edges
How far and how much: Absolute value answers questions about size without direction: how far below sea level, how much is owed, how big a change was.; Absolute Value › Word Problems
In plain terms: A ratio compares two amounts.; Ratios and Rates › In Plain Terms & More Examples
In plain terms: A percent is a fraction out of $100$ .; Percent › In Plain Terms & More Examples
In plain terms: To divide by a fraction, flip it (its reciprocal) and multiply.; Dividing Fractions › In Plain Terms & More Examples
In plain terms: Negatives are the numbers left of zero.; Negative Numbers › In Plain Terms & More Examples
In plain terms: Absolute value is distance from zero, so it is never negative — just drop the sign.; Absolute Value › In Plain Terms & More Examples
In plain terms: A letter stands for a number.; Expressions › In Plain Terms & More Examples
In plain terms: Undo whatever was done to the letter using the opposite operation — an inverse operation — doing the same thing to both sides so the balance holds (the properties of equality).; One-Step Equations › In Plain Terms & More Examples
In plain terms: A triangle is half a rectangle with the same base and height, so its area is $\tfrac{1}{2} \times \text{base} \times \text{height}$ .; Area of Triangles › In Plain Terms & More Examples
In plain terms: Volume fills the inside (cubic units); surface area covers the outside (square units) — add the areas of all six faces.; Surface Area and Volume › In Plain Terms & More Examples
In plain terms: The mean shares the total out equally; the median is the middle value once the numbers are in order.; Statistics › In Plain Terms & More Examples
In plain terms: The signs of $x$ and $y$ tell you the quadrant: quadrants are numbered anticlockwise from the top right.; Quadrants › In Plain Terms & More Examples
Many answers at once: An inequality like $x > 3$ has many solutions: every number greater than $3$ .; One-Step Equations › Inequalities
Maps in four quadrants: Put the origin at a landmark, like the town square.; Quadrants › Word Problems
Mean times count is the total: If $n$ values have mean $m$ , their total is $n \times m$ .; Statistics › Working Backwards
Negatives in the world: Below zero, below sea level, owing money, losing points: each has a zero and two directions.; Negative Numbers › Word Problems
Outliers move the mean: One extreme value drags the mean but leaves the median alone.; Statistics › Which Average? And the Range
Phrases into expressions: More than and increased by add; less than and decreased by subtract; times and of multiply.; Expressions › Writing Expressions
Rates: A rate compares two different kinds of quantity: kilometres per hour, dollars per kilogram, minutes per kilometre.; Ratios and Rates › Word Problems
Read the base and height off the grid: When one side of a triangle lies along a grid line, the base is a difference of coordinates along that line, and the height is how far the third corner is from it.; Area of Triangles › Triangles on the Coordinate Grid
Reading a proof: Do not read a proof the way you read a rule.; Ratios and Rates › Why It Works
Reading a proof: Do not read a proof the way you read a rule.; Percent › Why It Works
Reading a proof: Do not read a proof the way you read a rule.; Dividing Fractions › Why It Works
Reading a proof: Do not read a proof the way you read a rule.; Negative Numbers › Why It Works
Reading a proof: Do not read a proof the way you read a rule.; Absolute Value › Why It Works
Reading a proof: Do not read a proof the way you read a rule.; Expressions › Why It Works
Reading a proof: Do not read a proof the way you read a rule.; One-Step Equations › Why It Works
Reading a proof: Do not read a proof the way you read a rule.; Area of Triangles › Why It Works
Reading a proof: Do not read a proof the way you read a rule.; Surface Area and Volume › Why It Works
Reading a proof: Do not read a proof the way you read a rule.; Statistics › Why It Works
Reading a proof: Do not read a proof the way you read a rule.; Quadrants › Why It Works
Same moves, uglier numbers: To undo multiplication by a fraction, multiply by its reciprocal.; One-Step Equations › Equations with Fractions and Decimals
Same pieces, divide the counts: When two fractions have the same denominator, dividing them is dividing the tops: $\tfrac68 \div \tfrac18 = 6 \div 1 = 6$ .; Dividing Fractions › Common Denominators Also Work
Scale the pair: A ratio table multiplies both numbers by the same factor row by row.; Ratios and Rates › Ratio Tables and Unit Rates
Subtract, then take the size: The distance between $a$ and $b$ on the number line is $|a - b|$ .; Absolute Value › Distance Between Numbers
Take away a debt: Subtracting a negative is the same as adding its opposite: $a - (-b) = a + b$ .; Negative Numbers › Subtracting a Negative
The Big Idea: A ratio compares two amounts.; Ratios and Rates › Rates as Ratios
The Big Idea: “Percent” literally means per hundred, so $p\%$ is the fraction $\dfrac{p}{100}$ .; Percent › Percent Means Out of 100
The Big Idea: Dividing asks “how many of these fit?” Dividing by $\dfrac{c}{d}$ is the same as multiplying by $\dfrac{d}{c}$ , because that undoes the division.; Dividing Fractions › Why Flip and Multiply
The Big Idea: Negative numbers continue the number line to the left of zero.; Negative Numbers › Both Sides of Zero
The Big Idea: $|x|$ is how far $x$ is from zero, ignoring direction.; Absolute Value › Distance Is Never Negative
The Big Idea: A letter holds a number we have not chosen yet.; Expressions › Substituting a Value
The Big Idea: An equation is a balance.; One-Step Equations › Keep the Balance
The Big Idea: Any triangle is exactly half of a rectangle with the same base and height — that is where the $\dfrac{1}{2}$ in the formula comes from.; Area of Triangles › Where the Half Comes From
The Big Idea: Volume fills the inside (cubic units).; Surface Area and Volume › Two Different Measures
The Big Idea: The mean shares the total out equally.; Statistics › Two Kinds of Middle
The Big Idea: The axes cut the plane into four quadrants, numbered anticlockwise from the top right.; Quadrants › Reading the Signs
The formula: Area $= \dfrac{1}{2}bh$ , where $h$ is measured perpendicular to the base, not along a slanted side.; Area of Triangles › Where the Half Comes From
The pattern: I is $(+,+)$ , II is $(-,+)$ , III is $(-,-)$ , IV is $(+,-)$ .; Quadrants › Reading the Signs
The sign rule: Same signs give a positive; different signs give a negative.; Negative Numbers › Multiplying and Dividing
Three questions, one equation: $\text{part} = \text{percent}\times\text{whole}$ .; Percent › Finding the Whole and the Percent
Two questions division answers: Division can ask how many groups?; Dividing Fractions › Word Problems
Wrap or fill?: Wrapping, painting and covering ask for surface area (square units).; Surface Area and Volume › Word Problems