Expresswala Academy Mathematics Tuition
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Classes 6-8

Primary Years

Mathematics for Classes 6 to 8: decimals and roots, real numbers, equations, exponents, plane geometry and mensuration.

Primary Years is where the number line fills in. Decimals come first, then squares and square roots, then cubes and cube roots. Real numbers and their properties gather all of that into one idea.

Only then does the programme move on. Simple equations with real numbers, exponents, arithmetic applications, plane geometry and mensuration each lean on what came before.

Both CBSE and the Andhra Pradesh state syllabus are covered, so a child from either stream can join.

Who is this for?

This is for a child in Classes 6 to 8, at the point where numbers stop being whole and friendly. Decimals arrive, then square and cube roots, and with them the first irrational numbers a child ever meets. It suits the child who can follow a method faithfully and still cannot say what it is for.

What students learn

  • Calculate with decimals, and say what makes a number irrational.
  • Recognise the common perfect squares on sight, and find a square root without guessing.
  • Move between a cube and its root as readily as between a square and its own.
  • Use the properties of real numbers to check working, not only to describe it.
  • Solve an equation with real numbers and test the answer against the question asked.
  • Write an unwieldy number as a power, and simplify it.
  • Decide which arithmetic method a worded problem needs, instead of trying each in turn.
  • Set out a geometrical argument in ordered steps, with the reason for each.
  • Find perimeter, area and volume, and know which one the question wants.

By the end of this programme

  • Treat any real number, whole or decimal or root, as an ordinary thing to calculate with.
  • Read a worded problem, set up an equation from it, and solve it.
  • Choose an arithmetic method deliberately rather than by trial.
  • Work through a geometry or mensuration question with the reasoning written out.
  • See from regular assessment which topics are secure and which still need work.

How the programme runs

Classes run live online over Zoom, in batches of up to ten students, and in person at our Poranki centre.

At this stage a child will often understand the method perfectly and still repeat the same slip in every question. Spotting that takes someone watching the working rather than the answer. A batch of ten online is small enough to allow that.

Time is set aside for doubts, so a question left from an earlier chapter can still be asked. A free demo class can be booked on this website, by phone, or on WhatsApp at +91 90599 12593.

Tests and assessment

Assessment is regular, and its purpose is to catch a weak topic while it is still small. How we teach →

Practice at home

Practice is expected between classes, set on the chapter in hand. The free downloadable worksheets on this site carry the same material further for a child who wants more of it.

Courses in this programme

6 lessons

Decimals and Introduction to Irrational Numbers

A first course in decimals, taught with rupees and paise, a ruler and weights in grams: place value, reading and writing decimals, adding, subtracting, multiplying, dividing, and which fractions give a decimal that stops.

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5 lessons

Real Numbers and Their Properties

Learn what the real numbers are and how they behave: the six sets of numbers and how they nest, where the irrationals sit, the four operations with roots such as 2√3, and the closure, commutative, associative, identity and inverse properties.

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