OpenStem

@openstem · Joined Jul 2026

7420 public items8 groups

Note~285 words · 1 min

The one rule Proportional means y is always the same multiple of x. That's it. Test a table: divide every row Work out y ÷ x for each row and compare. Here k = 4, so the rule is y = 4x. Test an equation: look for extras Test a graph: two ch

Mathematics

Mathematics · L2 · Proportional Relationships

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Note~306 words · 2 min

Raw data is unreadable Data arrives in whatever order it was collected: not sorted, not counted, not organised. Before you can say anything about it you have to organise it, and the two simplest tools are a frequency table and a dot plot. T

Mathematics

Mathematics · L2 · Data Displays: Dot Plots & Frequency Tables

@openstem

Note~178 words · 1 min

Pair things up Every whole number is either odd or even, and pairing is the way to find out which. 6 blocks make exactly 3 pairs, so 6 is even. 5 blocks make 2 pairs and one lonely block, so 5 is odd. The last-digit shortcut Pairing up 138

Mathematics

Mathematics · L1 · Odd & Even Numbers

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Note~203 words · 1 min

Two kinds of pattern A pattern follows a rule you can predict. There are two kinds you'll meet constantly. Repeating patterns A repeating pattern uses a small group, called the core, over and over in the same order. Growing patterns A growi

Mathematics

Mathematics · L1 · Patterns: Repeating & Growing

@openstem

Note~165 words · 1 min

Numbers have two jobs The words, 1st to 10th In a race The runner who is 1st crossed before everyone. The runner who is 4th crossed after three others. Those words describe a SPOT, not a count. Both at once A queue can be described both way

Mathematics

Mathematics · L1 · Ordinal Numbers & Ordering

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Note~212 words · 1 min

Folding to find symmetry A shape has symmetry if an imaginary line splits it so both halves match exactly, like a mirror image. That line is a line of symmetry. The test is folding. If both halves land perfectly on top of each other, that's

Mathematics

Mathematics · L1 · Symmetry & Reflection

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Note~192 words · 1 min

Doubling Doubling makes a number twice as big. The easy way is to add it to itself: double 4 is 4 + 4 = 8. A doubles fact is just an addition where both numbers match, like 6 + 6. Learn 6 + 6 = 12 and you've learned double 6 as well; they'r

Mathematics

Mathematics · L1 · Doubling & Halving

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Note~191 words · 1 min

What a number line is A straight line with numbers marked at equal spaces, in order from smallest to biggest. Every whole number has its own spot, and numbers close together on the line are close together in value. To place 24 on a line fro

Mathematics

Mathematics · L1 · Number Lines & Rounding to Ten

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Note~172 words · 1 min

Fractions of a group, not a shape You already know a fraction can be part of ONE whole thing, like half a pizza. It can also be part of a GROUP of separate objects: half a bag of marbles, a third of a pile of stickers. Sharing into equal gr

Mathematics

Mathematics · L1 · Fractions of a Group

@openstem

Note~214 words · 1 min

Flat shapes A 2D shape is flat: it has length and width but no thickness, so you can draw one on paper. Describe any of them with two numbers: how many sides, and how many corners. Sorting shapes Square or rectangle? Ask one more question:

Mathematics

Mathematics · L1 · 2D Shapes & Their Attributes

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Note~225 words · 1 min

Equal parts, or no fraction at all A whole is one complete thing: one pizza, one square, one apple. Cut it up and the pieces only count as fractions if they're all exactly the same size. Naming the parts In 1/4, the bottom number says how m

Mathematics

Mathematics · L1 · Equal Parts: Halves, Thirds & Quarters

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Note~221 words · 1 min

How much a container holds Capacity is how much fits inside: water, sand, rice, anything pourable. A bucket has a large capacity, a teacup a small one. Compare two containers by asking: does this one hold more, less, or the same? Measuring

Mathematics

Mathematics · L1 · Capacity & Volume: More, Less or Same

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Note~243 words · 1 min

Comparing without measuring Long before a ruler, you can tell which of two things is longer just by lining them up carefully. That's called direct comparison. Place them side by side with one end lined up EXACTLY together, like two pencils

Mathematics

Mathematics · L1 · Comparing Length: Longer, Shorter, Taller

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Note~212 words · 1 min

Three numbers, four facts A fact family is three numbers linked by adding and subtracting. From those three you can write four true number sentences: two additions and two subtractions. Take 4, 5 and 9. Since 4 + 5 = 9, three more facts com

Mathematics

Mathematics · L1 · Fact Families & Related Facts

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Note~203 words · 1 min

A good guess, on purpose Sometimes you don't need the exact number. Estimating means looking at a group and deciding ABOUT how many there are, without counting each one. Benchmark numbers A benchmark is a number you know well by sight. Pict

Mathematics

Mathematics · L1 · Estimating & Benchmark Numbers

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Note~231 words · 1 min

Two groups, one question Some word problems describe two groups and then ask you to compare them. The clue words are "how many more" and "how many fewer". Sam has 8 stickers, Ana has 5. How many more does Sam have? There are two amounts, an

Mathematics

Mathematics · L1 · Comparison Word Problems: More & Fewer

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Note~176 words · 1 min

Words that show order When something happens in steps, like getting dressed or telling a story, special words show the order: first, next, then, after that, and last. Before and after These describe how two events relate. If socks come befo

Mathematics

Mathematics · L1 · Sequencing Events: First, Next, Last

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Note~178 words · 1 min

Four coins to know Penny, nickel, dime and quarter. Before you can add coins or make change, you need to look at one and know instantly which it is and what it's worth. Colour first, then size The penny is the only copper-coloured one, so i

Mathematics

Mathematics · L1 · Coin Recognition & Values

@openstem

Note~87 words · 1 min

One idea, three costumes A fraction, a decimal and a percent all answer the same question: how much of the whole? How to switch between them

Mathematics

Mathematics · L2 · Fractions, Decimals, and Percents

@openstem

Note~213 words · 1 min

Pick the chart that fits the question A graph turns numbers into a picture. The wrong picture hides the pattern. Every graph needs three things Reading a scatter plot Each dot is one thing measured twice. No line is drawn for you. Look at t

Mathematics

Mathematics · L2 · Reading and Making Graphs

@openstem

Note~185 words · 1 min

Same bottom number? Add the tops Equal denominators mean the pieces are already the same size, so you can just combine them. Different bottoms? Make them match first Different denominators mean different piece sizes. You can't add halves to

Mathematics

Mathematics · L2 · Adding & Subtracting Fractions

@openstem

Note~219 words · 1 min

Same value, three looks Switching between the three is what lets you compare a test score, a price tag and a discount in your head. Fraction to percent Percent of a number Turn the percent into a decimal, then multiply. That's the whole met

Mathematics

Mathematics · L2 · Decimals & Percents

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Note~259 words · 1 min

One rulebook, so everyone gets the same answer Without an agreed order, the same expression would have several defensible answers. PEMDAS is the agreement. Why order changes the answer Take 3 + 4 × 2. Now one with an exponent, 5 + (6 − 2)²:

Mathematics

Mathematics · L2 · Order of Operations

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Note~246 words · 1 min

An exponent is a counter It counts how many copies of the base get multiplied together. Squares and cubes Square roots undo squaring A root asks squaring's question backwards: what times itself gives this? Estimating a root that isn't exact

Mathematics

Mathematics · L2 · Exponents & Square Roots

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Note~270 words · 1 min

Two routes to the same answers Every quadratic is ax² + bx + c = 0. You have two tools. 1. Factoring Split it into two brackets, then set each bracket to zero. 2. The quadratic formula The bit under the root, b² − 4ac, is the discriminant.

Mathematics

Mathematics · L3 · Factoring & the Quadratic Formula

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Note~138 words · 1 min

One identity to remember It falls straight out of the unit circle, where every point satisfies x² + y² = 1. Using it Know one of sin θ or cos θ and you can get the other. Given sin θ = 3/5 in the first quadrant: Two identities you get for f

Mathematics

Mathematics · L3 · Key Trig Identities & the Pythagorean Identity

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Note~170 words · 1 min

Two kinds of sequence Arithmetic sequences Note the (n − 1): the first term hasn't had d added to it yet. Sum of the first n terms: Geometric sequences Why geometric growth feels different Arithmetic sequences trace a straight line. Geometr

Mathematics

Mathematics · L3 · Sequences & Series

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Note~78 words · 1 min

The normal distribution Heights, exam scores, measurement errors: lots of measurements cluster around a middle value and taper off evenly on both sides. That shape has a name and an equation.

Mathematics

Mathematics · L3 · The Bell Curve

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Note~304 words · 2 min

A system is two conditions at once Two equations, same variables. A solution has to satisfy BOTH. Each equation is a line. The solution is where they cross, so solving algebraically just finds that crossing point without drawing. Substituti

Mathematics

Mathematics · L3 · Systems of Linear Equations

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Note~380 words · 2 min

Add, subtract, multiply Degree and leading term The leading term decides the shape. Everything else just nudges it. Slide a below: the bigger |a|, the tighter the parabola, and a negative a turns it over. On a wide enough view, x² buries an

Mathematics

Mathematics · L3 · Polynomial Operations & Factoring

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