Grade 01: Mathematics

In this unit, 'Numbers to 20', you learn to count, read, write and order numbers to 20. 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 20' before using symbols.
• Say the rule in your own words, then write one worked line, naming each step.
• Use it: count, read, write and order numbers to 20. 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, Count a group: draw 14 stars in two rows, 10 in the top row and 4 in the bottom. Touch each star once and say 1, 2, 3 up to 14, moving each touched star aside so none is counted twice.
2. Step 2, Write the number: 14 is one ten and four ones, so write 1 then 4. Say it aloud as fourteen. Compare with 41, which has the digits swapped but means four tens and one one, a much bigger number.
3. Step 3, Order numbers: put 9, 17, 12 and 5 in order from smallest to biggest. Look at each on a number line from 0 to 20. The order is 5, 9, 12, 17, because each one sits further right.
4. Step 4, Find the missing number: in the pattern 11, 12, __, 14, 15 count on from 12. The next count word is thirteen, so the gap is 13. Check by counting the whole row again from 11 to 15.
5. Step 5, Compare two numbers: which is more, 16 or 19? Count to 16 first, then keep going 17, 18, 19. Since 19 comes later in the count, 19 is more than 16, and 16 is less than 19.
6. Step 6, Your turn: draw 18 dots and write the number. Then put 7, 20, 13 and 2 in order from smallest to biggest. Answer: 18 is one ten and eight ones, and the order is 2, 7, 13, 20.

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. Count, read, write and order numbers to 20: at least 4 of 5 attempts correct, said or written, with one real example from home or school.

In this unit, 'Numbers to 100', you learn to count in ones and tens, read and write numbers to 100, tens and ones. 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 100' before using symbols.
• Say the rule in your own words, then write one worked line, naming each step.
• Use it: count in ones and tens, read and write numbers to 100, tens and ones. 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, Count in tens: touch ten-sticks one at a time and say 10, 20, 30, 40, 50. Five sticks of ten make 50. Each jump adds one whole ten, so the ones digit stays 0 every time.
2. Step 2, Tens and ones: show 3 ten-sticks and 7 loose cubes. Three tens are 30, and 7 more makes 37. Write 3 in the tens place and 7 in the ones place, and say thirty-seven.
3. Step 3, Read a number: 64 has a 6 in the tens place and a 4 in the ones place. So it is 6 tens and 4 ones, which is 60 and 4. Draw 6 sticks and 4 cubes to prove it.
4. Step 4, Count on from a number: start at 47 and count on ones: 48, 49, 50. After 49 the ones run out, so we make a new ten and the number becomes 50. Then 51, 52 follow.
5. Step 5, Check on a hundred square: find 58 in the row that runs from 51 to 60. One step right gives 59, and one step down gives 68, which is ten more. This confirms that moving down a row adds a ten.
6. Step 6, Your turn: show 52 with sticks and cubes, then say how many tens and ones. Count on from 96 to 100. Answer: 52 is 5 tens and 2 ones, and the count is 97, 98, 99, 100.

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. Count in ones and tens, read and write numbers to 100, tens and ones: at least 4 of 5 attempts correct, said or written, with one real example from home or school.

In this unit, 'Adding within 20', you learn to add using objects, number lines and number bonds to 10. 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 'Adding within 20' before using symbols.
• Say the rule in your own words, then write one worked line, naming each step.
• Use it: add using objects, number lines and number bonds to 10. 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, Add with objects: 6 red counters and 5 blue counters. Push them together and count all: 6, then 7, 8, 9, 10, 11. So 6 + 5 = 11. Writing it as a sentence helps: six and five make eleven.
2. Step 2, Count on with a number line: for 8 + 4 start on 8 and hop 4 times: 9, 10, 11, 12. Land on 12, so 8 + 4 = 12. Keep the bigger number in your head and count only the small one.
3. Step 3, Use number bonds to 10: 7 + 5. Split 5 into 3 and 2. Since 7 + 3 = 10, add the remaining 2 to get 12. So 7 + 5 = 12. Bonds to 10 make big sums easy.
4. Step 4, Check with doubles: 6 + 6 = 12 is a double. Then 6 + 7 is one more than the double, which is 13. A different route lets you confirm the earlier answers are sensible.
5. Step 5, Word problem: Amal has 9 marbles and wins 6 more. 9 + 6: make 10 with 1 from the 6, leaving 5, so 10 + 5 = 15. Write the answer with words: Amal has 15 marbles.
6. Step 6, Your turn: find 8 + 7 using a bond to 10, and 9 + 3 on a number line. Answer: 8 + 2 = 10, then 5 more gives 15; and 9 hop 3 lands on 12.

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 using objects, number lines and number bonds to 10: at least 4 of 5 attempts correct, said or written, with one real example from home or school.

In this unit, 'Taking away within 20', you learn to subtract using objects and number lines, and link adding with taking away. 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 'Taking away within 20' before using symbols.
• Say the rule in your own words, then write one worked line, naming each step.
• Use it: subtract using objects and number lines, and link adding with taking away. 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, Take away objects: 12 cubes, remove 5. Cross out five cubes and count the rest: 7 are left. So 12 - 5 = 7. Say it as: twelve take away five leaves seven.
2. Step 2, Count back on a number line: for 15 - 4 start on 15 and hop back 4: 14, 13, 12, 11. You land on 11, so 15 - 4 = 11. Count the hops, not the start number.
3. Step 3, Link to adding: since 11 + 4 = 15, then 15 - 4 = 11 must be true. Write the fact family: 4 + 11 = 15, 11 + 4 = 15, 15 - 4 = 11, 15 - 11 = 4. These four go together.
4. Step 4, Subtract using ten: 14 - 6. Take away 4 to reach 10, then take away the other 2 to get 8. So 14 - 6 = 8. Check by adding: 8 + 6 = 14, which matches the start.
5. Step 5, Word problem: there are 13 birds on a wall and 7 fly off. Work 13 - 7: 13 - 3 = 10, then 10 - 4 = 6. Answer: 6 birds are left. Check: 6 + 7 = 13.
6. Step 6, Your turn: solve 16 - 9 and write its fact family. Answer: 16 - 6 = 10, then 10 - 3 = 7, so 16 - 9 = 7. The family is 9 + 7 = 16, 7 + 9 = 16, 16 - 9 = 7, 16 - 7 = 9.

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 using objects and number lines, and link adding with taking away: at least 4 of 5 attempts correct, said or written, with one real example from home or school.

In this unit, 'Shapes around us', you learn to name and sort flat and solid shapes by their features. 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 'Shapes around us' before using symbols.
• Say the rule in your own words, then write one worked line, naming each step.
• Use it: name and sort flat and solid shapes by their features. 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 flat shapes: a clock face is a circle with one curved side and no corners. A book cover is a rectangle with 4 sides and 4 corners. A sandwich cut corner to corner makes a triangle with 3 sides.
2. Step 2, Count sides and corners: a square has 4 equal sides and 4 corners. A rectangle also has 4 sides, but two are long and two are short. Tap each side and say the count to be sure.
3. Step 3, Name solid shapes: a ball is a sphere, a tin of beans is a cylinder, a dice is a cube, and a party hat is a cone. Solids can be held and have faces you can feel.
4. Step 4, Sort by a feature: put a ball, a dice, a tin and a box in two groups, can roll and cannot roll. Ball and tin roll. Dice and box have flat faces only, so they do not roll.
5. Step 5, Find shapes in a face: a cube has 6 flat faces and every face is a square. Trace around one face of a dice on paper and you draw a square with 4 equal sides.
6. Step 6, Your turn: name the shape of a coin, a cereal box and a football, and say which of them roll. Answer: circle (flat face of a cylinder), cuboid, sphere. The coin and football roll; the box does not.

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 and sort flat and solid shapes by their features: at least 4 of 5 attempts correct, said or written, with one real example from home or school.

In this unit, 'Length and weight', you learn to compare and order objects by length and weight using everyday words. 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 'Length and weight' before using symbols.
• Say the rule in your own words, then write one worked line, naming each step.
• Use it: compare and order objects by length and weight using everyday words. 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, Compare length: lay a pencil and a crayon with their left ends on the same line. The pencil sticks out further, so the pencil is longer and the crayon is shorter. Starting at the same line is the key.
2. Step 2, Order three objects: a ribbon, a straw and a toothpick. Line them up from one edge. The order from shortest to longest is toothpick, straw, ribbon. Say: the ribbon is the longest of the three.
3. Step 3, Measure with cubes: a book is 9 cubes long and a cup is 4 cubes tall. Because 9 is more than 4, the book is longer than the cup is tall. Count with no gaps and no overlaps.
4. Step 4, Compare weight: hold a bag of rice in one hand and a feather in the other. The rice feels heavier and the feather lighter. A balance tips down on the heavy side, which confirms it.
5. Step 5, Order by weight: a pumpkin, an apple and a grape. Put them on a balance two at a time. The order from lightest to heaviest is grape, apple, pumpkin. Use words heavier and lighter.
6. Step 6, Your turn: a rope is 12 cubes long and a stick is 8 cubes long. Which is longer, and by how many cubes? Answer: the rope is longer by 4 cubes, since 12 - 8 = 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. Compare and order objects by length and weight using everyday words: 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 tell time to the hour and half hour and order the days of the week. 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: tell time to the hour and half hour and order the days of the week. 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 o'clock: the short hour hand points to 3 and the long minute hand points to 12. That is 3 o'clock. When the minute hand is on 12, we say o'clock and read only the hour hand.
2. Step 2, Read half past: the minute hand points to 6 and the hour hand is between 4 and 5. That is half past 4, written 4:30. Half past means the long hand has gone half way round.
3. Step 3, Show a time: to show half past 7 draw the minute hand on 6. Draw the hour hand halfway between 7 and 8. Check that the long hand points down, since half past always points down.
4. Step 4, Order the days: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday. Seven days in a week. If today is Tuesday, tomorrow is Wednesday and yesterday was Monday.
5. Step 5, Day after problem: today is Thursday. Two days later is Saturday, since Friday is one and Saturday is two. Check by counting on the fingers: Friday, Saturday. Answer: Saturday.
6. Step 6, Your turn: what time is it when the hour hand is on 9 and the minute hand on 12? And what day comes after Friday? Answer: 9 o'clock, and the day after Friday is Saturday.

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. Tell time to the hour and half hour and order the days of the week: 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 name coins and notes and make small amounts. 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: name coins and notes and make small amounts. 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 the coins: use a coin with the number 1, one with 5 and one with 10. Say the value of each: one, five, ten. Larger number does not always mean bigger coin, so read the number.
2. Step 2, Make 7 with coins: use one 5 coin and two 1 coins. Count: 5, then 6, 7. So 5 + 1 + 1 = 7. Start with the largest coin and count on with the smaller ones.
3. Step 3, Make 10 two ways: one 10 coin, or two 5 coins. Both give 10 because 5 + 5 = 10. Different coins can make the same amount, and you can use fewer coins with larger values.
4. Step 4, Count a handful: a 10 coin, a 5 coin and three 1 coins. Count 10, 15, 16, 17, 18. The total is 18. Counting the biggest first keeps your count quick and correct.
5. Step 5, Shop problem: a pencil costs 6 and you pay with a 10 coin. Count up from 6 to 10: that is 4 more. So the change is 4. Check: 6 + 4 = 10.
6. Step 6, Your turn: make 12 using only 5 and 1 coins, then find change from 10 for a sticker costing 3. Answer: two 5 coins and two 1 coins make 12; change is 7 since 3 + 7 = 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 coins and notes and make small amounts: at least 4 of 5 attempts correct, said or written, with one real example from home or school.

In this unit, 'Patterns and sorting', you learn to continue and make patterns and sort by one rule. 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 and sorting' before using symbols.
• Say the rule in your own words, then write one worked line, naming each step.
• Use it: continue and make patterns and sort by one rule. 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 colour pattern: red, blue, red, blue, red, __. The unit that repeats is red, blue. After red comes blue, so the next one is blue. Read the whole pattern aloud twice.
2. Step 2, Find the repeating unit: circle, circle, square, circle, circle, square. The unit is circle, circle, square, three shapes long. Next you draw circle, circle, square again to extend it.
3. Step 3, Number pattern: 2, 4, 6, 8, __. Each number is 2 more than the one before. So the next is 8 + 2 = 10. Say the rule in a sentence: add 2 each time.
4. Step 4, Make a pattern: use claps and stamps. Clap, clap, stamp, clap, clap, stamp is an AAB pattern. Show it with blocks: yellow, yellow, green, yellow, yellow, green.
5. Step 5, Sort by one rule: buttons, 5 red and 3 blue. Sort by colour into two groups. Count each group: 5 and 3. There are 2 more red than blue, as 5 - 3 = 2.
6. Step 6, Your turn: continue star, heart, heart, star, heart, heart, __, __ and sort 4 big and 6 small balls by size. Answer: star, heart; and the groups have 4 big and 6 small, so 2 more small.

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 make patterns and sort by one rule: 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.

This course: Grade 01 Mathematics is at this level. Its units include Numbers to 20; Numbers to 100; Adding within 20; Taking away within 20 and more.

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.

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.