Course

Junior Algebra: the bridge to O-level

Name: Junior Algebra: the bridge to O-level
Price: 1199 BDT

Algebra your child can see before they see a letter. A balance weighs an unknown, a machine hides a rule, and every idea starts as something you can move, not a line of symbols.

42 lessons3h 49mEnglish

What you'll learn

Find an unknown weight by balancing, and explain why a level beam proves equality
Share a total fairly between identical unknowns, the concrete root of dividing to solve
Test a candidate rule against every input-output pair before trusting it
Reject a rule using one counterexample, the concrete root of a proof
Solve a one-step or two-step equation by undoing operations in reverse order
Evaluate an expression at a chosen x, and explain why an expression has many values but an equation has one
Expand a single bracket, and explain why the multiplier reaches every term inside it
Tell apart a sequence that adds a constant jump from one that multiplies by a constant factor
Find the linear rule an + b behind a growing pattern, checked against a hidden step
Place and move along negative numbers, treating addition and subtraction as movement
Test whether a point satisfies an inequality, and tell a strict bound from an inclusive one
Plot a coordinate pair in any of the four quadrants, reading x before y
Substitute a chosen x into a linear rule to find the point it produces on a grid

Requirements

Comfortable adding and subtracting whole numbers
Has met multiplication as repeated groups, e.g. from times tables

Course content

42 lessons · 3h 49m

What's hiding? Unknowns without letters

Weighing a sealed bucket on a balance and testing a rule against every input, before any letter appears. The unknown is a real number found by balancing, not a symbol to fear.

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A mystery number

Weigh a sealed bucket by adding unit weights until the scale is level.

Preview6m 2.

Two buckets, the same weight

Two identical buckets share the total weight equally.

Preview6m

A heavier mystery

Balancing works the same way for a larger hidden number.

A machine that hides its rule

A rule has to fit every input and output, not just the first one.

The trap of one good guess

A rule that matches once can still fail the next pair.

Check what you know

Three questions on balancing buckets and testing a rule.

Balancing equations

The sealed bucket becomes the letter x, and balancing becomes solving. Undo one operation at a time, always keeping both sides equal, working up from one step to two.

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The bucket becomes x

The same balance idea, now written as x + 3 = 8.

Preview6m 2.

Remove the same from both sides

Changing one side alone tips the scale, so both sides change together.

Preview6m

Sharing between two xs

2x = 10 is the two-bucket idea from before, written in symbols.

Two moves, not one

Undo the addition before the multiplication, the newest layer first.

Predict before you slide

Solve on paper first, then use the scale only to confirm.

Check what you know

Three questions on solving one-step and two-step equations.

Expressions and brackets

Plugging a number into an expression, then discovering that a bracket multiplies everything inside it, not just the first term. The two totals a bracket produces stay separate until the very end.

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Plugging in a number

Evaluate 3x + 2 at a chosen x, multiply before you add.

Preview6m 2.

One expression, many values

Unlike an equation, an expression has a different value for every x.

Preview6m

A bracket means repeat

3(x + 2) is three whole copies of the group x + 2.

Two totals, not one

A bracket multiplies every term inside it, which 3x + 2 does not.

Expand it yourself

Work out both totals on paper, then check them against the strip.

Check what you know

Three questions on plugging in values and expanding a bracket.

Patterns and rules

Sequences that grow by adding the same jump versus multiplying by the same factor, then a tile pattern whose rule turns out to be an + b, the same shape as 3x + 2 in a growing picture instead of a bucket.

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Spot the step

A sequence that adds the same jump every time.

Preview6m 2.

Doubling is different

Multiplying by the same factor grows much faster than adding.

Preview6m

From pattern to formula

A growing tile pattern has the same shape as an + b.

The hidden step proves it

A rule must also match a step you cannot see yet.

A rate in real life

Savings growing at a steady weekly rate follow the same an + b shape.

Check what you know

Three questions on sequences and finding a rule.

Negatives and inequalities

Numbers below zero as real positions on the line, addition and subtraction as movement along it, then an inequality as a whole shaded region with a circle that is either open or filled at each boundary.

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Below zero

A negative number is a real position left of zero, not a small number.

Preview6m 2.

Moving along the line

Addition moves right, subtraction moves left, even across zero.

Preview6m

Which side of the line?

x > 3 is a whole shaded region, and its open circle excludes 3 itself.

The boundary counts too

x ≥ 3 fills in the circle at 3, including the boundary this time.

Trapped between two numbers

Two bounds shade a strip between them, each with its own circle.

Check what you know

Three questions on negative numbers and reading an inequality.

Coordinates and simple graphs

Reading a coordinate pair as across then up, extending into all four quadrants, then closing the loop back to substitution: a rule turns a chosen x into a y, and the pair names one point on the grid.

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Across, then up

A coordinate pair moves across first, then up, in a fixed order.

Preview6m 2.

All four quadrants

A negative x moves left, a negative y moves down, read separately.

Preview6m

A point from a rule

Substitute x into y = 2x + 1, then plot the pair it produces.

A different point, same rule

A negative x fed into the same rule lands in a different quadrant.

Predict before you drag

Work out the point on paper, then confirm it on the grid.

Check what you know

Three questions on reading coordinates and plotting from a rule.

About the creator

8bitlesson

Cambridge O Level, A Level and university courses, taught through interactive labs.

Mentora builds the sciences and mathematics as things you can move rather than videos you watch. Cambridge O Level and A Level mathematics, physics, chemistry and accounting, a primary mathematics track, and first-year university computer science. Every lesson works a real exam question end to end.