Search & glossary

Every rule and concept in Grade 5, with its definition and a link to the lesson that teaches it. Search by term, by idea, or by lesson title.

Glossary (45)

"Of" means times: $\tfrac34$ of something is $\tfrac34 \times$ that thing.; Multiplying Fractions › Word Problems
Bigger or smaller?: Multiplying by a number greater than $1$ gives more than you started with; multiplying by a number less than $1$ gives less; multiplying by exactly $1$ changes nothing.; Multiplying Fractions › Multiplying as Scaling
Chain the steps: To go from hours to seconds, go through minutes: $1$ h $= 60$ min $= 60\times60 = 3600$ s.; Converting Units › Two-Step Conversions
Convert first: Turn mixed numbers into improper fractions before multiplying: $1\tfrac12 = \tfrac32$ .; Multiplying Fractions › Mixed Numbers and Whole Numbers
Convert first, then compute: Before adding, subtracting, dividing or comparing, put every measurement into the same unit.; Converting Units › Word Problems
Directions on a map: On a coordinate map, east and west change the $x$ -coordinate (east adds, west subtracts); north and south change the $y$ -coordinate (north adds, south subtracts).; The Coordinate Plane › Word Problems
Filling things up: Volume answers "how much fits inside?".; Volume › Word Problems
In plain terms: Multiply as if the points were not there, then count how many decimal places the two numbers had together and put the point back that far from the right.; Decimal Operations › In Plain Terms & More Examples
In plain terms: Multiply the top numbers together and the bottom numbers together, then simplify.; Multiplying Fractions › In Plain Terms & More Examples
In plain terms: Volume counts the unit cubes that fill a box: multiply length by width by height.; Volume › In Plain Terms & More Examples
In plain terms: An ordered pair $(x, y)$ means go across $x$ first, then up $y$ .; The Coordinate Plane › In Plain Terms & More Examples
In plain terms: Do brackets first, then multiplication and division, and only then addition and subtraction — working left to right within each step.; Order of Operations › In Plain Terms & More Examples
In plain terms: Changing to a smaller unit needs more of them, so multiply; changing to a bigger unit needs fewer, so divide.; Converting Units › In Plain Terms & More Examples
In plain terms: Multiplying by $10^n$ slides every digit $n$ places to the left; the digits stay the same, only their value grows.; Powers of Ten › In Plain Terms & More Examples
Inside out: With brackets inside parentheses, work from the innermost group outward.; Order of Operations › Nested Grouping
It gets smaller: Multiplying by a fraction less than $1$ makes the result smaller — surprising at first, but taking part of something gives less than you started with.; Multiplying Fractions › Why Straight Across Works
Layers again: The number of cubes in one layer is the area of the base, $B$ .; Volume › Base Area Times Height
Line up the points: Write the numbers in columns with the decimal points lined up, fill empty places with zeros, then add or subtract place by place from the right, regrouping just as with whole numbers.; Decimal Operations › Adding and Subtracting Decimals
Make the divisor whole: To divide by a decimal, move the point in BOTH numbers the same number of places until the divisor is whole.; Decimal Operations › Dividing Decimals
Not powers of ten: In U.S.; Converting Units › Customary Units
Partners share a step: Multiplication and division are partners: do them in the order they appear, from left to right.; Order of Operations › Ties Go Left to Right
Pull the tens aside: To multiply whole numbers that end in zeros, multiply the front digits, then attach all the zeros from both numbers: $40 \times 300 = 4 \times 3 \times 10 \times 100 = 12 \times 1000 = 12{,}000$ .; Powers of Ten › Patterns in the Zeros
Reading a proof: Do not read a proof the way you read a rule.; Decimal Operations › Why It Works
Reading a proof: Do not read a proof the way you read a rule.; Multiplying Fractions › Why It Works
Reading a proof: Do not read a proof the way you read a rule.; Volume › Why It Works
Reading a proof: Do not read a proof the way you read a rule.; The Coordinate Plane › Why It Works
Reading a proof: Do not read a proof the way you read a rule.; Order of Operations › Why It Works
Reading a proof: Do not read a proof the way you read a rule.; Converting Units › Why It Works
Reading a proof: Do not read a proof the way you read a rule.; Powers of Ten › Why It Works
Same $x$ or same $y$: Two points with the same $y$ lie on a horizontal line; the distance between them is the difference of the $x$ -coordinates.; The Coordinate Plane › Distances and Shapes
Sanity check: $2.4$ is close to $2$ , so the answer should be near $6$ — and $7.2$ is.; Decimal Operations › Counting Decimal Places
Shift right: Dividing by $10^n$ moves every digit $n$ places to the right.; Powers of Ten › Dividing by Powers of Ten
Split, then add: An L-shaped solid is two boxes glued together.; Volume › Solids Made of Two Boxes
The Big Idea: Multiply as if the points were not there, then put the point back.; Decimal Operations › Counting Decimal Places
The Big Idea: Multiplying fractions means taking a part of a part.; Multiplying Fractions › Why Straight Across Works
The Big Idea: Volume counts the unit cubes that fill a solid.; Volume › Counting Cubes
The Big Idea: An ordered pair $(x, y)$ is a set of directions from the origin: go across $x$ , then up $y$ .; The Coordinate Plane › Across Then Up
The Big Idea: Without a rule, $2 + 3 \times 4$ could be $20$ or $14$ .; Order of Operations › The Agreed Order
The Big Idea: Going to a smaller unit means you need more of them, so multiply.; Converting Units › Multiply or Divide?
The Big Idea: Multiplying by $10^n$ moves every digit $n$ places to the left.; Powers of Ten › Shifting Places
The formula: For a rectangular box, $V = l \times w \times h$ , measured in cubic units.; Volume › Counting Cubes
Two rules, one graph: Two number patterns can be paired up term by term to make ordered pairs.; The Coordinate Plane › Patterns and Graphs
Which operation?: Finding the total of several equal amounts means multiply.; Decimal Operations › Word Problems
Why scientists write powers of ten: Very large and very small numbers are easier to read as a number between $1$ and $10$ times a power of ten: $384{,}000 = 3.84 \times 10^5$ .; Powers of Ten › Word Problems
Words into symbols: Sum means add, difference means subtract, product means multiply, quotient means divide.; Order of Operations › Writing Expressions