B7.1.2 · Strand 1, sub-strand 2

Number Operations

Powers of 10, mental strategies, the four operations with whole numbers and decimals, and indices.

1. Lesson 1 · B7.1.2.1.1 · about 45 min

   Multiplying and Dividing by Powers of 10

   Shopkeepers, bankers and engineers multiply and divide by 10, 100 and 1,000 all day long, usually in their heads. In this lesson you will discover the simple rule behind it: the digits slide across the place value chart while the decimal point stays still. You will also connect benchmark fractions such as $\frac{1}{2}$, $\frac{1}{4}$ and $\frac{1}{10}$ to their decimals and percentages.

2. Lesson 2 · B7.1.2.1.2 · about 45 min

   Mental Mathematics Strategies and Number Properties

   Good mental mathematicians are not people who calculate faster — they are people who change a hard sum into an easy one before they start. In this lesson you will learn halving and doubling, the distributive property and other number properties that let you work out sums like 28 × 5, 18 × 6 and 8 × 99 in your head.

3. Lesson 3 · B7.1.2.1.3 · about 45 min

   Using Mental Strategies to Solve Word Problems

   Real-life maths rarely arrives as "7 × 8 = ?". It comes as a question in words: the price of a dozen eggs, the time until the school bus arrives, how many pieces you can cut from a string. In this lesson you will learn to spot the operation hidden in the words, then use quick mental strategies to answer — the way you would in a mental maths quiz.

4. Lesson 4 · B7.1.2.2.1 · about 50 min

   Adding and Subtracting Whole Numbers and Decimals

   Every receipt at the market, every MoMo balance and every football attendance figure involves adding and subtracting. In this lesson you will use expanded form (partitioning) to see exactly what happens to each place value, then use the column method confidently with carrying, exchanging and decimal points.

5. Lesson 5 · B7.1.2.2.2 · about 60 min

   Multiplying and Dividing by 1- and 2-Digit Numbers

   How many 64 kg bags will a cocoa cooperative fill? What do 48 bags of rice cost at GH₵365 each? Questions like these need multiplication and division of big numbers. In this lesson you will multiply by partitioning, by the place value (column) method and by the lattice method, divide by short and long division, and use divisibility tests to know in advance whether a division will work out exactly.

6. Lesson 6 · B7.1.2.2.3 · about 60 min

   Solving Story Problems with Decimals

   Kilograms of meat, metres of cloth, litres of fuel and cedis and pesewas are all decimals. In this lesson you will bring together everything you know about adding, subtracting, multiplying and dividing to solve story problems — including problems from tables — and you will learn to write your own story problems too.

7. Lesson 7 · B7.1.2.3.1 · about 40 min

   Repeated Factors and Powers

   When the same number is multiplied again and again, the answer grows very fast, and writing it out becomes tiring. In this lesson you will build repeated factors with bottle tops, learn the short way of writing them as a power such as $2^{5}$, and name the base and the index.

8. Lesson 8 · B7.1.2.3.2 · about 45 min

   Writing Numbers as Powers and Products of Powers

   Numbers like 32, 81 and 1,000 hide repeated factors inside them. In this lesson you will break a number into equal factors, write it as a power such as $3^{4}$, and write bigger numbers as a product of powers such as $2^{3} \times 3^{2}$. This skill is the key to finding HCF and LCM and to simplifying fractions quickly.

9. Lesson 9 · B7.1.2.3.3 · about 40 min

   The Zero Index: Why Any Number to the Power 0 Is 1

   What could $5^{0}$ mean, when you cannot write 5 as a factor zero times? In this lesson you will discover, using patterns and division of powers, that any natural number raised to the power 0 equals 1. You will then use this fact, together with the rule for dividing powers, to simplify expressions.

10. Lesson 10 · B7.1.2.3.4 · about 45 min

    Finding the Value of a Number in Index Form

    A power such as $5^{3}$ is a short way of writing a number, but what number is it? In this lesson you will expand powers into repeated factors, multiply them step by step (with smart shortcuts), and evaluate expressions such as $2^{3} \times 3^{2}$ and $2^{4} + 3^{3} - 5^{0}$. You will also use powers to find areas of square plots and volumes of cube-shaped tanks.

11. Lesson 11 · B7.1.2.3.5 · about 50 min

    Finding the HCF Using Prime Factors in Index Form

    How wide should you cut strips of cloth so that nothing is wasted? How many equal parcels can you make from two different heaps of oranges? These are Highest Common Factor (HCF) questions. In this lesson you will write numbers as products of prime powers and use them to find the HCF quickly, even for large numbers, and you will see how the same idea gives the LCM.