Grade 03: Mathematics

In this unit, 'Numbers to 1000', you learn to read, write, order and compare numbers to 1000. Lessons are short and playful, with objects, pictures and talk. You see it, say it, then do it alone.

• Show it with objects or a picture: build or draw the idea in 'Numbers to 1000' before using symbols.
• Say the rule in your own words, then write one worked line, naming each step.
• Use it: read, write, order and compare numbers to 1000. Start with one easy question, then one with a real-life story.
• Check it: use a second method, estimate, or work backwards to test your answer.

Step by step.

1. Step 1, Read and write: 508 is five hundreds, no tens and eight ones. Write it in words as five hundred and eight. The zero in the tens place is a placeholder, so do not write 58.
2. Step 2, Expanded form: 364 = 300 + 60 + 4. Check by adding: 300 + 60 = 360, then 360 + 4 = 364. Break each number the same way to see which digit carries the most value.
3. Step 3, Compare 472 and 478: hundreds are both 4, tens are both 7, so compare ones: 2 is less than 8. So 472 < 478. Compare from the left, place by place, and stop at the first difference.
4. Step 4, Order 605, 650, 560, 506: hundreds are 6, 6, 5, 5. Of the two with 5 hundreds, 506 < 560. Of the two with 6, 605 < 650. Order: 506, 560, 605, 650.
5. Step 5, Count in 100s and 10s: from 275 count on by 100: 375, 475, 575. From 275 count back by 10: 265, 255, 245. Only the hundreds digit changes in the first, and only the tens in the second.
6. Step 6, Your turn: write 902 in expanded form and order 417, 471, 147, 714. Answer: 900 + 0 + 2; and the order is 147, 417, 471, 714.

Activity. About 20 to 30 minutes of class work, then one short practice task for home. Keep evidence: one page in your learning book.

Standard to meet. Read, write, order and compare numbers to 1000: at least 4 of 5 attempts correct, said or written, with one real example from home or school.

In this unit, 'Place value', you learn to show hundreds, tens and ones and round to the nearest ten. Lessons are short and playful, with objects, pictures and talk. You see it, say it, then do it alone.

• Show it with objects or a picture: build or draw the idea in 'Place value' before using symbols.
• Say the rule in your own words, then write one worked line, naming each step.
• Use it: show hundreds, tens and ones and round to the nearest ten. Start with one easy question, then one with a real-life story.
• Check it: use a second method, estimate, or work backwards to test your answer.

Step by step.

1. Step 1, Build 245: 2 hundreds blocks, 4 tens rods and 5 ones. Value: 200 + 40 + 5 = 245. The 4 is worth 40 because it sits in the tens place, not 4.
2. Step 2, Place value of a digit: in 837 the digit 3 is in the tens place, so its value is 30. The digit 8 has a value of 800. A digit's value depends on its position.
3. Step 3, Round 36 to the nearest ten: 36 lies between 30 and 40. The ones digit 6 is 5 or more, so round up to 40. The halfway point is 35, and 36 is past it.
4. Step 4, Round 83 to the nearest ten: the ones digit is 3, which is less than 5, so round down to 80. Check on a number line: 83 sits closer to 80 than 90, only 3 away.
5. Step 5, Round 475: the ones digit is exactly 5, so the rule rounds up to 480. Compare it with 474, which rounds down to 470. The digit 5 is the tipping point.
6. Step 6, Your turn: give the value of the 6 in 563 and round 148 and 152 to the nearest ten. Answer: the 6 is worth 60; 148 rounds to 150 and 152 rounds to 150.

Activity. About 20 to 30 minutes of class work, then one short practice task for home. Keep evidence: one page in your learning book.

Standard to meet. Show hundreds, tens and ones and round to the nearest ten: at least 4 of 5 attempts correct, said or written, with one real example from home or school.

In this unit, 'Addition', you learn to add up to three-digit numbers with carrying and solve word problems. Lessons are short and playful, with objects, pictures and talk. You see it, say it, then do it alone.

• Show it with objects or a picture: build or draw the idea in 'Addition' before using symbols.
• Say the rule in your own words, then write one worked line, naming each step.
• Use it: add up to three-digit numbers with carrying and solve word problems. Start with one easy question, then one with a real-life story.
• Check it: use a second method, estimate, or work backwards to test your answer.

Step by step.

1. Step 1, Set up 346 + 278 in columns with ones under ones, tens under tens and hundreds under hundreds. Estimate first: 350 + 280 = 630, so the answer should be about 630.
2. Step 2, Ones: 6 + 8 = 14, write 4 and carry 1 ten. Tens: 4 + 7 = 11, plus the carried 1 is 12, write 2 and carry 1 hundred. Keep the carries small and above the right column.
3. Step 3, Hundreds: 3 + 2 = 5, plus the carried 1 is 6. Reading across gives 624. This is close to the estimate of 630, so the answer is reasonable.
4. Step 4, Word problem: a school bought 325 red pens, 148 blue pens and 207 black pens. 325 + 148 = 473 (5 + 8 = 13, 2 + 4 + 1 = 7, 3 + 1 = 4). Then 473 + 207 = 680 pens.
5. Step 5, Check by reversing order: 207 + 148 = 355, and 355 + 325 = 680. Adding in a different order gives the same total, which confirms 680 is correct.
6. Step 6, Your turn: find 459 + 287 and give an estimate. Answer: 9 + 7 = 16, write 6 carry 1; 5 + 8 + 1 = 14, write 4 carry 1; 4 + 2 + 1 = 7. So 746; estimate 460 + 290 = 750.

Activity. About 20 to 30 minutes of class work, then one short practice task for home. Keep evidence: one page in your learning book.

Standard to meet. Add up to three-digit numbers with carrying and solve word problems: at least 4 of 5 attempts correct, said or written, with one real example from home or school.

In this unit, 'Subtraction', you learn to subtract up to three-digit numbers with borrowing and check by adding. Lessons are short and playful, with objects, pictures and talk. You see it, say it, then do it alone.

• Show it with objects or a picture: build or draw the idea in 'Subtraction' before using symbols.
• Say the rule in your own words, then write one worked line, naming each step.
• Use it: subtract up to three-digit numbers with borrowing and check by adding. Start with one easy question, then one with a real-life story.
• Check it: use a second method, estimate, or work backwards to test your answer.

Step by step.

1. Step 1, Set up 532 - 275 in columns and estimate: 530 - 280 = 250. The answer should be near 250. Always put the larger number on top.
2. Step 2, Ones: 2 is less than 5, so borrow from the tens. The 3 tens become 2 tens and the 2 ones become 12. 12 - 5 = 7. Write 7 in the ones place.
3. Step 3, Tens: now 2 is less than 7, so borrow from the hundreds. 5 hundreds become 4, and 2 tens become 12. 12 - 7 = 5. Hundreds: 4 - 2 = 2. The answer is 257.
4. Step 4, Check by adding: 257 + 275 = 532, since 7 + 5 = 12, write 2 carry 1; 5 + 7 + 1 = 13, write 3 carry 1; 2 + 2 + 1 = 5. This returns the start number 532.
5. Step 5, Word problem: a stadium holds 800 people and 463 seats are taken. 800 - 463 = 337, found by 799 - 463 = 336 and adding the 1 back. Check: 337 + 463 = 800.
6. Step 6, Your turn: find 614 - 358 and check by adding. Answer: 614 - 358 = 256, because 256 + 358 = 614 (6 + 8 = 14, 5 + 5 + 1 = 11, 2 + 3 + 1 = 6).

Activity. About 20 to 30 minutes of class work, then one short practice task for home. Keep evidence: one page in your learning book.

Standard to meet. Subtract up to three-digit numbers with borrowing and check by adding: at least 4 of 5 attempts correct, said or written, with one real example from home or school.

In this unit, 'Multiplication', you learn to use tables to 10, multiply a two-digit number by one digit. Lessons are short and playful, with objects, pictures and talk. You see it, say it, then do it alone.

• Show it with objects or a picture: build or draw the idea in 'Multiplication' before using symbols.
• Say the rule in your own words, then write one worked line, naming each step.
• Use it: use tables to 10, multiply a two-digit number by one digit. Start with one easy question, then one with a real-life story.
• Check it: use a second method, estimate, or work backwards to test your answer.

Step by step.

1. Step 1, Recall a table fact: 7 x 8 means 7 jumps of 8, which is 8, 16, 24, 32, 40, 48, 56. So 7 x 8 = 56. A finger trick for the nines: for 9 x 6 the tens digit is 6 - 1 = 5 and the digits add to 9, so the answer is 54.
2. Step 2, Swap the order: 6 x 4 = 24 and 4 x 6 = 24. Draw an array of 6 rows with 4 dots in each row, then turn the page. The same 24 dots appear. Knowing one fact gives you two, which halves the tables you must learn.
3. Step 3, Multiply a two-digit number by one digit by splitting it. To find 23 x 4, split 23 into 20 and 3. Then 20 x 4 = 80 and 3 x 4 = 12. Add the parts: 80 + 12 = 92. Check with repeated addition 23 + 23 + 23 + 23 = 92.
4. Step 4, Try 46 x 3 the same way. Split 46 into 40 and 6. Then 40 x 3 = 120 and 6 x 3 = 18. Add: 120 + 18 = 138. Notice the partial answers are tens and ones, so write them in neat columns before adding.
5. Step 5, Use the column method for 34 x 6. Multiply the ones first: 4 x 6 = 24, write 4 and carry 2 tens. Multiply the tens: 3 x 6 = 18, add the carried 2 to get 20 tens. So the answer is 204. Estimate 30 x 6 = 180 to check it is sensible.
6. Step 6, Your turn: a box holds 52 pencils and there are 5 boxes. How many pencils altogether? Split 52 into 50 and 2 and add the parts. Answer: 50 x 5 = 250 and 2 x 5 = 10, so 52 x 5 = 260 pencils.

Activity. About 20 to 30 minutes of class work, then one short practice task for home. Keep evidence: one page in your learning book.

Standard to meet. Use tables to 10, multiply a two-digit number by one digit: at least 4 of 5 attempts correct, said or written, with one real example from home or school.

In this unit, 'Division', you learn to divide as sharing and grouping, link to tables, with remainders. Lessons are short and playful, with objects, pictures and talk. You see it, say it, then do it alone.

• Show it with objects or a picture: build or draw the idea in 'Division' before using symbols.
• Say the rule in your own words, then write one worked line, naming each step.
• Use it: divide as sharing and grouping, link to tables, with remainders. Start with one easy question, then one with a real-life story.
• Check it: use a second method, estimate, or work backwards to test your answer.

Step by step.

1. Step 1, Divide as sharing: 24 stickers shared equally among 4 friends. Each gets 6, because 4 x 6 = 24. Write 24 / 4 = 6. Use the 4 times table to find the answer.
2. Step 2, Divide as grouping: how many bags of 3 can be made from 21 apples? Count in threes: 3, 6, 9, 12, 15, 18, 21 is 7 jumps. So 21 / 3 = 7 bags.
3. Step 3, Link to tables: if 8 x 5 = 40 then 40 / 5 = 8 and 40 / 8 = 5. One multiplication fact gives two division facts, which makes recall faster.
4. Step 4, Remainders: 29 / 4. The 4 times table reaches 28 at 4 x 7. So 29 = 4 x 7 + 1, which means 7 remainder 1. The remainder must always be smaller than 4.
5. Step 5, Word problem: 38 pupils go on a trip in cars that seat 5. 5 x 7 = 35 leaves 3 pupils, so 7 full cars and 3 more. Another car is needed, so 8 cars in all.
6. Step 6, Your turn: find 45 / 9 and 34 / 6. Answer: 45 / 9 = 5 since 9 x 5 = 45; and 34 / 6 = 5 remainder 4 since 6 x 5 = 30 and 34 - 30 = 4.

Activity. About 20 to 30 minutes of class work, then one short practice task for home. Keep evidence: one page in your learning book.

Standard to meet. Divide as sharing and grouping, link to tables, with remainders: at least 4 of 5 attempts correct, said or written, with one real example from home or school.

In this unit, 'Fractions', you learn to name, compare and add simple fractions of a whole and of a set. Lessons are short and playful, with objects, pictures and talk. You see it, say it, then do it alone.

• Show it with objects or a picture: build or draw the idea in 'Fractions' before using symbols.
• Say the rule in your own words, then write one worked line, naming each step.
• Use it: name, compare and add simple fractions of a whole and of a set. Start with one easy question, then one with a real-life story.
• Check it: use a second method, estimate, or work backwards to test your answer.

Step by step.

1. Step 1, Name a fraction: a pizza cut into 8 equal slices, 3 eaten. The denominator 8 says how many equal parts; the numerator 3 says how many are taken. So 3/8 was eaten and 5/8 is left.
2. Step 2, Compare with the same denominator: 3/8 and 5/8. Both are eighths, so the one with more parts is larger. 5/8 > 3/8. For same numerators, 1/2 is bigger than 1/4.
3. Step 3, Add fractions of a whole: 2/8 + 3/8. Same denominator, so add only the numerators: 2 + 3 = 5. The answer is 5/8. The denominator stays 8 because the parts are the same size.
4. Step 4, Fraction of a set: 3/4 of 12 marbles. Divide 12 into 4 equal groups of 3. One group is 1/4 = 3 marbles. Three groups is 3 x 3 = 9 marbles.
5. Step 5, Check: the 9 marbles taken plus the 3 left make 12, the whole set. Also 9 is less than 12 but more than half of 12 (6), which suits 3/4.
6. Step 6, Your turn: find 2/5 + 1/5 and 2/3 of 15. Answer: 2/5 + 1/5 = 3/5; and 15 / 3 = 5 per part, so 2/3 of 15 is 10.

Activity. About 20 to 30 minutes of class work, then one short practice task for home. Keep evidence: one page in your learning book.

Standard to meet. Name, compare and add simple fractions of a whole and of a set: at least 4 of 5 attempts correct, said or written, with one real example from home or school.

In this unit, 'Time', you learn to read clocks to the minute, use a.m. and p.m. and find elapsed time. Lessons are short and playful, with objects, pictures and talk. You see it, say it, then do it alone.

• Show it with objects or a picture: build or draw the idea in 'Time' before using symbols.
• Say the rule in your own words, then write one worked line, naming each step.
• Use it: read clocks to the minute, use a.m. and p.m. and find elapsed time. Start with one easy question, then one with a real-life story.
• Check it: use a second method, estimate, or work backwards to test your answer.

Step by step.

1. Step 1, Read to the minute: hour hand just past 7, minute hand 3 small marks past the 8. The 8 is 40 minutes, plus 3 is 43. The time is 7:43, which is 17 minutes to 8.
2. Step 2, a.m. and p.m.: a.m. is from midnight to noon, p.m. is from noon to midnight. A school bell at 8:15 in the morning is 8:15 a.m. A film at 8:15 in the evening is 8:15 p.m.
3. Step 3, Elapsed time: a lesson starts at 9:40 a.m. and ends at 10:25 a.m. From 9:40 to 10:00 is 20 minutes, then 25 more, total 45 minutes.
4. Step 4, Across noon: a bus leaves at 11:30 a.m. and arrives at 2:10 p.m. From 11:30 to 12:00 is 30 minutes; 12:00 to 2:00 is 2 hours; plus 10 minutes. Total 2 hours 40 minutes.
5. Step 5, Find the end time: a game starts at 4:50 p.m. and lasts 55 minutes. Add 10 minutes to reach 5:00, then 45 more, so it ends at 5:45 p.m. Check: 10 + 45 = 55.
6. Step 6, Your turn: how long from 10:35 a.m. to 11:20 a.m., and what time is 40 minutes after 3:45 p.m.? Answer: 45 minutes; and 4:25 p.m.

Activity. About 20 to 30 minutes of class work, then one short practice task for home. Keep evidence: one page in your learning book.

Standard to meet. Read clocks to the minute, use a.m. and p.m. and find elapsed time: at least 4 of 5 attempts correct, said or written, with one real example from home or school.

In this unit, 'Measurement', you learn to measure length, mass and capacity and convert between metric units. Lessons are short and playful, with objects, pictures and talk. You see it, say it, then do it alone.

• Show it with objects or a picture: build or draw the idea in 'Measurement' before using symbols.
• Say the rule in your own words, then write one worked line, naming each step.
• Use it: measure length, mass and capacity and convert between metric units. Start with one easy question, then one with a real-life story.
• Check it: use a second method, estimate, or work backwards to test your answer.

Step by step.

1. Step 1, Length in cm: a pencil from 0 to 17 on the ruler is 17 cm. A table is 2 m 40 cm long. Since 1 m = 100 cm, 2 m 40 cm = 200 + 40 = 240 cm.
2. Step 2, Convert km to m: a road is 3 km. 1 km = 1000 m, so 3 km = 3 x 1000 = 3000 m. To go back, 4500 m / 1000 = 4 remainder 500, so 4 km 500 m.
3. Step 3, Mass: a bag of flour is 2 kg 300 g. Convert to grams: 2 x 1000 = 2000, plus 300 is 2300 g. Two such bags weigh 2 x 2300 = 4600 g, or 4 kg 600 g.
4. Step 4, Capacity: a bottle holds 1 litre 500 ml, which is 1500 ml. A glass holds 250 ml. 1500 / 250 = 6, since 250 x 6 = 1500. So 6 glasses can be filled.
5. Step 5, Choose the unit: a coin's mass is in grams, a lorry's mass in tonnes, a spoon of medicine in millilitres and a swimming pool in litres. Pick a unit that gives a sensible number.
6. Step 6, Your turn: convert 3 m 25 cm to cm, and 2 litres 50 ml to ml. Answer: 325 cm, since 300 + 25; and 2050 ml, since 2000 + 50.

Activity. About 20 to 30 minutes of class work, then one short practice task for home. Keep evidence: one page in your learning book.

Standard to meet. Measure length, mass and capacity and convert between metric units: at least 4 of 5 attempts correct, said or written, with one real example from home or school.

In this unit, 'Geometry', you learn to name angles, lines and 2D and 3D shapes by their properties. Lessons are short and playful, with objects, pictures and talk. You see it, say it, then do it alone.

• Show it with objects or a picture: build or draw the idea in 'Geometry' before using symbols.
• Say the rule in your own words, then write one worked line, naming each step.
• Use it: name angles, lines and 2D and 3D shapes by their properties. Start with one easy question, then one with a real-life story.
• Check it: use a second method, estimate, or work backwards to test your answer.

Step by step.

1. Step 1, Name lines by how they relate. Parallel lines stay the same distance apart and never meet, like two rails of a train track. Perpendicular lines meet at a square corner. Intersecting lines cross. Find one example of each in your classroom.
2. Step 2, Name angles by size. A right angle is a square corner, 90 degrees, like the corner of a page. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line, which is 180 degrees.
3. Step 3, Name 2D shapes by their properties. A triangle has 3 sides, a rectangle has 4 sides and 4 right angles with opposite sides equal, a pentagon has 5 sides, a hexagon has 6 and an octagon has 8, like a stop sign.
4. Step 4, Name 3D shapes by faces, edges and corners. A cube has 6 square faces, 12 edges and 8 corners. A square-based pyramid has 5 faces, 8 edges and 5 corners. A cylinder has 2 flat circular faces and 1 curved face.
5. Step 5, Solve mystery descriptions. 'I have 4 equal sides and 4 right angles' is a square. 'I have 6 square faces' is a cube. 'I have 1 flat circular face, 1 curved face and 1 point' is a cone. Use the properties, not the picture.
6. Step 6, Your turn: name a flat shape with 5 sides, then say how many faces and edges a cuboid has, and what kind of angle is smaller than 90 degrees. Answer: a pentagon, a cuboid has 6 faces and 12 edges, and the angle is acute.

Activity. About 20 to 30 minutes of class work, then one short practice task for home. Keep evidence: one page in your learning book.

Standard to meet. Name angles, lines and 2D and 3D shapes by their properties: at least 4 of 5 attempts correct, said or written, with one real example from home or school.

In this unit, 'Patterns', you learn to continue and describe number and shape patterns. Lessons are short and playful, with objects, pictures and talk. You see it, say it, then do it alone.

• Show it with objects or a picture: build or draw the idea in 'Patterns' before using symbols.
• Say the rule in your own words, then write one worked line, naming each step.
• Use it: continue and describe number and shape patterns. Start with one easy question, then one with a real-life story.
• Check it: use a second method, estimate, or work backwards to test your answer.

Step by step.

1. Step 1, Continue a number pattern: 5, 10, 15, 20, __. Each term is 5 more than the one before. The next two are 25 and 30. Describe it as: start at 5 and add 5 each time.
2. Step 2, Decreasing pattern: 90, 80, 70, 60. The rule is subtract 10 each time. Continuing gives 50, 40. Check using the gap: 90 - 80 = 10, 80 - 70 = 10, so the rule is steady.
3. Step 3, Find the missing term: 4, 7, __, 13, 16. The gap is 3 each time (7 - 4 = 3, 16 - 13 = 3). The missing term is 7 + 3 = 10, and 10 + 3 = 13 confirms it.
4. Step 4, Shape pattern: triangle, square, square, triangle, square, square. The repeating unit is triangle, square, square, so the 7th shape is a triangle and the 9th is a square.
5. Step 5, Growing pattern with matchsticks: 1 square uses 4 sticks, 2 squares in a row use 7, 3 squares use 10. Each new square adds 3 sticks. So 4 squares use 13 sticks.
6. Step 6, Your turn: continue 3, 6, 9, 12 and find the 5th and 6th terms of 2, 5, 8, 11. Answer: next terms 15, 18; and the sequence adds 3, so 14 and 17.

Activity. About 20 to 30 minutes of class work, then one short practice task for home. Keep evidence: one page in your learning book.

Standard to meet. Continue and describe number and shape patterns: at least 4 of 5 attempts correct, said or written, with one real example from home or school.

In this unit, 'Money', you learn to add, subtract and give change in dirhams and fils. Lessons are short and playful, with objects, pictures and talk. You see it, say it, then do it alone.

• Show it with objects or a picture: build or draw the idea in 'Money' before using symbols.
• Say the rule in your own words, then write one worked line, naming each step.
• Use it: add, subtract and give change in dirhams and fils. Start with one easy question, then one with a real-life story.
• Check it: use a second method, estimate, or work backwards to test your answer.

Step by step.

1. Step 1, Write money: 2 dirhams 50 fils is written 2.50 dirhams. 100 fils = 1 dirham, so 250 fils = 2.50 dirhams. Always write two digits after the point.
2. Step 2, Add: a pen costs 3.75 and an eraser costs 1.50. Fils: 75 + 50 = 125, so write 25 and carry 1 dirham. Dirhams: 3 + 1 + 1 = 5. Total 5.25 dirhams.
3. Step 3, Subtract: you have 10.00 dirhams and spend 6.35. 10.00 - 6.35: change 3.65 because 6.35 + 3.65 = 10.00 (35 + 65 = 100 fils, 6 + 3 + 1 = 10).
4. Step 4, Give change by counting up: item costs 7.60, you pay 10.00. From 7.60 to 8.00 is 40 fils, then to 10.00 is 2 dirhams. Change is 2.40 dirhams.
5. Step 5, Multiply: 4 notebooks at 2.25 each. 4 x 2 = 8 dirhams, 4 x 25 fils = 100 fils = 1 dirham. Total 9.00 dirhams. Check with rounding, 4 x 2.25 is near 4 x 2 = 8.
6. Step 6, Your turn: find 4.80 + 2.45 and the change from 10.00 after buying a 7.30 snack. Answer: 7.25 dirhams; change is 2.70, since 7.30 + 2.70 = 10.00.

Activity. About 20 to 30 minutes of class work, then one short practice task for home. Keep evidence: one page in your learning book.

Standard to meet. Add, subtract and give change in dirhams and fils: at least 4 of 5 attempts correct, said or written, with one real example from home or school.

In this unit, 'Data handling', you learn to read and make tally charts, pictographs and bar graphs. Lessons are short and playful, with objects, pictures and talk. You see it, say it, then do it alone.

• Show it with objects or a picture: build or draw the idea in 'Data handling' before using symbols.
• Say the rule in your own words, then write one worked line, naming each step.
• Use it: read and make tally charts, pictographs and bar graphs. Start with one easy question, then one with a real-life story.
• Check it: use a second method, estimate, or work backwards to test your answer.

Step by step.

1. Step 1, Tally chart: favourite fruits of 20 pupils. Mark each vote with a stroke and bundle the fifth. Apples ||||, bananas |||| ||, mangoes |||. Counts are 4, 7 and 3.
2. Step 2, Check the total: 4 + 7 + 3 = 14, but we expect 20 pupils. So 6 more votes went to grapes. Adding the totals shows a missing group, a quick check for every tally chart.
3. Step 3, Pictograph: let each picture mean 2 pupils. Bananas have 7 votes, which is 3 pictures and a half picture. Half a picture means 1 pupil. So 3 x 2 + 1 = 7.
4. Step 4, Bar graph: scale the vertical axis 0 to 8 in steps of 1. Draw a bar to 4 for apples, 7 for bananas, 3 for mangoes, 6 for grapes. Give the graph a title and label both axes.
5. Step 5, Read the graph: bananas are the most popular and mangoes the least. The difference is 7 - 3 = 4 pupils. Total pupils are 4 + 7 + 3 + 6 = 20, which agrees.
6. Step 6, Your turn: using bars of 5, 9 and 2, how many more is the tallest than the shortest, and what is the total? Answer: 9 - 2 = 7 more, and the total is 5 + 9 + 2 = 16.

Activity. About 20 to 30 minutes of class work, then one short practice task for home. Keep evidence: one page in your learning book.

Standard to meet. Read and make tally charts, pictographs and bar graphs: at least 4 of 5 attempts correct, said or written, with one real example from home or school.

On the slide: L1 Basic · Count and name shapes

Notes: Count objects up to 20 and name a circle, square and triangle. Notes: give ten buttons and two trays; learners count aloud, move three across and say how many are left (7), then hunt the room for one shape of each kind.

On the slide: L2 Awareness · Add, subtract and measure

Notes: Add and subtract within 100 and measure a length with a ruler. Notes: work 46 + 27 = 73 on a number line, jumping 20 then 7; learners measure a pencil in centimetres and explain how they checked their answer a second way.

This course: Grade 03 Mathematics is at this level. Its units include Numbers to 1000; Place value; Addition; Subtraction and more.

On the slide: L3 Foundation · Fractions and decimals

Notes: Compare fractions and decimals and use the four operations with whole numbers. Notes: shade 3/4 and 6/8 on equal strips to show they match, then add 0.5 + 0.25 = 0.75 and write it as 75 per cent of one whole.

On the slide: L4 Practitioner · Equations and percentages

Notes: Solve one-step and two-step equations and percentage problems, showing each step. Notes: practice case is 3x + 5 = 20, so x = 5, checked by substituting back; then a 15 per cent discount on 400 leaves 340, because 400 x 0.85 = 340.

On the slide: L5 Specialist · Geometry, data and graphs

Notes: Use the right-angled triangle rule, the mean and a straight-line graph to solve a problem. Notes: legs of 6 and 8 give a longest side of 10; the data 4, 6, 6, 8, 11 have mean 7; plot y = 2x + 1 and read y = 7 at x = 3.

On the slide: L6 Advanced · Proof, calculus and algebra

Notes: Prove results and use calculus and matrices to model change. Notes: differentiate f(x) = x^3 - 3x to get 3x^2 - 3, so turning points sit at x = 1 and x = -1; the second derivative 6x shows a minimum then a maximum. Learners prove the square root of 2 is irrational.

On the slide: L7 Super expert · Research-level modelling

Notes: Formulate and defend a proof or statistical model, stating assumptions and limits. Notes: for 25 values with mean 50 and standard deviation 10, the standard error is 2 and a 95 per cent interval is about 45.9 to 54.1 (t = 2.064). Learners check residuals and write a referee-style critique.