Lessons The mathematics of the primary school: counting on and back, the number between, doubles, making tens, tens and ones, skip counting, odd and even, places in a line, and word problems of joining, separating and comparing. Every problem is read into a world of things and counts, and Mova answers from that world.
The lessons course of Mova's primary school: 200 lessons, 644 sentences, each sentence with its syntax tree and pragmatics. Licence: CC BY-SA 4.0 (Mova corpus 0.4).
61 Counting on and counting back 4 sentences · To count on, start at the number you have and say the next numbers, one for each step forward. 62 The number just before, just after and in between 3 sentences · The number just after a number is one more; the number just before it is one less. 63 Doubles and near doubles 3 sentences · A double is a number added to itself: 7 + 7 = 14. 64 How many more to make a full ten 4 sentences · To find how many more make a round number, count on from what you have to that number. 65 Bundles of ten and loose ones 4 sentences · A bag of 10 is one ten. 66 How many more to have as many 3 sentences · Take the smaller amount away from the bigger amount. 67 Skip counting by twos, fives and tens 4 sentences · When every group has the same number, count by that number: by 2s for pairs, by 5s for hands, by 10s for tens. 68 Pairs and the one left alone 3 sentences · When things are put in pairs, every pair has 2. 69 Places in a line 3 sentences · In a line, first, second, third… tell the place counted from one end. 70 Number sense review: tens, ones and how many more 4 sentences · First find each amount: bags of 10 count as tens, loose ones as ones. 71 Some more join in: how many now 3 sentences · A story can start with some things and then more things join them. 72 Some more join in: how many came, how many at first 3 sentences · In a joining story we know two of three numbers: how many at first, how many came, how many at the end. 73 Some go away: how many are left 3 sentences · A story can start with some things and then some of them go away: given away, lost or sold. 74 Some go away: how many went, how many at first 3 sentences · In a story where some things go away we know two of three numbers: how many at first, how many went, how man… 75 Two parts and the whole 2 sentences · Sometimes nothing comes or goes: a group is simply made of two parts, like boys and girls in a class. 76 How many more, how many fewer 3 sentences · To compare two numbers, we ask how many more one has than the other. 77 More than, fewer than, less than 1 sentences · Read carefully who is compared to whom: «Sam has 9, that is 4 fewer than Lily» means Lily has 4 more, 9 + 4… 78 Two steps: some come, some go 3 sentences · Some stories have two changes: first some things come, then some go away, or the other way round. 79 A number we do not need 6 sentences · Some stories tell us a number that the question does not ask about. 80 Review: adding and taking away stories 5 sentences · Each story asks for one number that is missing: a start, a change, an end, a whole, a part or a difference. 81 Equal groups 3 sentences · When there are several groups and every group holds the same number, multiply to find how many in all. 82 Rows and columns 3 sentences · When things stand in rows and every row is the same length, they make an array. 83 Times as many 2 sentences · If Tom has 4 marbles and Ann has 3 times as many, Ann has 4 × 3 = 12 marbles. 84 Sharing equally 3 sentences · To share things equally means every one gets the same number. 85 How many groups 3 sentences · Sometimes we know how many go in each group and must find how many groups we can make. 86 When the remainder needs one more 3 sentences · When everyone or everything must fit, the ones left over still need a place, so we need one more group. 87 Only the full ones count 3 sentences · Sometimes only full groups count, and the ones left over are not enough for another group. 88 So many each day 2 sentences · To find how much in several days, multiply the amount for one day by the number of days. 89 Multiply, then add or take away 3 sentences · Some problems take two steps: first multiply to find the total of the equal groups, then add or take away. 90 Multiplying and dividing together 3 sentences · Many problems need both: first multiply to find the whole, then divide to share it. 91 Counting coins 3 sentences · A penny is worth 1 cent, a nickel 5 cents, a dime 10 cents and a quarter 25 cents. 92 Buying several things at one price 2 sentences · When every thing costs the same, the total cost is the price of one times the number of things. 93 The change from a payment 3 sentences · A dollar is 100 cents. 94 Saving every week for a price 2 sentences · If you save the same amount every week, the number of weeks is the price divided by the amount saved each we… 95 How many hours have passed 2 sentences · To find how long something lasts on the same day, count the hours from the start to the end: end minus start. 96 Hours and minutes 3 sentences · One hour has 60 minutes. 97 Days and weeks 3 sentences · One week has 7 days. 98 Metres and centimetres 3 sentences · One metre is 100 centimetres. 99 Kilograms and grams, litres and millilitres 3 sentences · One kilogram is 1000 grams, and one litre is 1000 millilitres. 100 Yards, feet and inches in two steps 3 sentences · One yard is 3 feet, and one foot is 12 inches. 101 One equal part of a set 3 sentences · A fraction like one third means: split the whole set into equal parts and take one part. 102 Several equal parts of a set 3 sentences · Two thirds means two of the three equal parts. 103 What is left after a part is used 2 sentences · Find the part first, then take it away from the whole. 104 Comparing a half with a smaller part 2 sentences · A half of a set is the biggest of these parts: a half of 12 is 6, a third of 12 is 4, a fourth of 12 is 3. 105 The perimeter of a rectangle 2 sentences · A rectangle has two long sides and two short sides: a rectangle 7 cm long and 3 cm wide has a perimeter of 7… 106 The area of a rectangle in square units 4 sentences · Area tells how many unit squares cover a shape. 107 A missing side from the perimeter or the area 2 sentences · A square has four equal sides, so one side is the perimeter divided by 4: a perimeter of 28 cm gives 28 ÷ 4… 108 Sides and corners of many shapes 2 sentences · A triangle has 3 sides and 3 corners, a square 4, a pentagon 5 and a hexagon 6: a flat shape has as many cor… 109 Faces, edges and corners of cubes 1 sentences · One cube has 6 + 12 + 8 = 26 faces, edges and corners together, so 3 cubes have 3 × 26 = 78. 110 Review: fractions and shapes together 3 sentences · Some problems need two steps: first the area of a rectangle, then a fraction of that area. 111 The price of one, then the price of many 3 sentences · When things cost the same each, first find the price of one: divide the total price by how many were bought. 112 Speed: how far in so many hours 4 sentences · Speed tells how far something goes in one hour: a car going 60 km each hour has a speed of 60 km an hour. 113 Ages: years ago, years from now 3 sentences · Everyone gets one year older each year, so in 5 years a child of 8 will be 8 + 5 = 13, and 3 years ago was 8… 114 A pattern day by day 2 sentences · When something grows by the same number each day, the first day has the start, and each later day adds the s… 115 For every few of one, so many of another 2 sentences · Find how many groups there are from the colour you know, then multiply for the other colour. 116 The average of a few scores 2 sentences · The average shares the total out evenly: add all the scores, then divide by how many scores there are. 117 Working backwards through two steps 3 sentences · To find how many there were at the start, begin at the end and undo each step in the opposite order. 118 Two steps and a number you do not need 6 sentences · Some stories give a number that does not help answer the question. 119 A story in three steps 4 sentences · A long story can be solved one step at a time: find one number, use it to find the next, then finish. 120 Mixed challenge: reasoning stories 4 sentences · Each story here is one of the kinds met before: a price per thing, a speed, ages, a pattern, a ratio, an ave… 121 Adding across ten 1 sentences · When two numbers together make more than ten, first fill up a ten, then add what is left. 122 Taking away across ten 2 sentences · When there are not enough ones to take away, first take away down to ten, then take away the rest from the t… 123 Counting in a repeating pattern 4 sentences · A pattern repeats the same group again and again. 124 How many more, how many fewer 2 sentences · To compare two numbers, match them one to one; what has no partner is the difference. 125 The missing number in a story 4 sentences · Sometimes a story hides one number: what there was at first, or how many were added or taken. 126 More by, fewer by 3 sentences · «7 more than» means add: 7 more than 20 is 20 + 7 = 27. 127 Stories in two steps 3 sentences · Some stories change a number twice. 128 Cuts, posts and floors: the gaps between 4 sentences · To cut a log into 4 pieces you need only 3 cuts: the last piece needs no cut. 129 Sisters and brothers 3 sentences · A girl does not count herself among her own sisters. 130 A staircase of cubes and handshakes 3 sentences · A staircase of 4 steps built of cubes has 1, 2, 3 and 4 cubes in its steps: 1 + 2 + 3 + 4 = 10 cubes. 131 The times table in stories 3 sentences · When there are several equal groups, multiply the number of groups by the number in one group. 132 Division: sharing and grouping 4 sentences · Division answers two questions. 133 So many times more, so many times fewer 1 sentences · So if Ann has 5 and that is 3 times fewer than Ben has, Ben has 5 × 3 = 15. 134 Metres and centimetres, dollars and cents 3 sentences · 1 metre is 100 centimetres, and 1 dollar is 100 cents. 135 Hours and minutes 3 sentences · 1 hour is 60 minutes, so 2 hours are 60 + 60 = 120 minutes. 136 Perimeter: all the way round a triangle 4 sentences · The perimeter of a shape is the length all the way round it: add the lengths of all its sides. 137 Brackets in a story: first the group, then the groups 5 sentences · Work out what is in brackets first. 138 The unknown number: equations as stories 4 sentences · An equation is a story with a missing number. 139 Cuts and pieces, posts and gaps 3 sentences · To cut a log into 5 pieces you need only 4 cuts: the last piece needs no cut of its own. 140 Ages that grow together: sum and difference 3 sentences · Each year both children get one year older, so the sum of two ages grows by 2 each year, and the difference… 141 Numbers to 1000: adding and taking away in stories 3 sentences · A number to 1000 has hundreds, tens and ones: 476 is 4 hundreds, 7 tens and 6 ones. 142 Multiplying by a one-digit number 3 sentences · To multiply a big number by a one-digit number, multiply the ones, the tens and the hundreds apart and add:… 143 Dividing by a one-digit number: how many can be bought 3 sentences · To divide a big number by a one-digit number, divide the hundreds, then the tens, then the ones: 576 ÷ 4: 5… 144 The price of one thing from the money paid and the change 2 sentences · If you paid with more money than the things cost, the change came back: what the things cost is the money gi… 145 What the remainder means: one more is needed 3 sentences · Dividing with a remainder gives full groups and some left over: 50 ÷ 8 = 6 remainder 2. 146 A rectangle's area from its perimeter 3 sentences · The perimeter of a rectangle is twice the length plus twice the width, so half the perimeter is length + wid… 147 Sum and multiple: two amounts from their total and «times as many» 3 sentences · If one amount is 3 times another, draw the smaller as 1 part and the bigger as 3 parts: together they are 1… 148 The area of a shape made of rectangles 4 sentences · An L-shaped figure can be seen in two ways: as two rectangles side by side, or as a big rectangle with a cor… 149 Sum and difference: two amounts from their total and their gap 3 sentences · If two amounts add up to a total and one is bigger by a difference, add the difference to the total: now bot… 150 A square cut into equal strips 3 sentences · When a square is cut by parallel cuts into equal strips, every strip is as long as the square's side, and it… 151 A fraction of a quantity 3 sentences · To find a fraction of a quantity, first find one equal part: divide by the number below the line. 152 The whole from its fraction 3 sentences · If we know how much a fraction of something is, we can find the whole. 153 How long it lasts: from one clock time to another 3 sentences · To find how long something lasts, count from the start time to the end time. 154 The calendar: days from one month into the next 2 sentences · April, June, September and November have 30 days; the other months have 31, except February. 155 Difference and multiple: how many times as many, and how many more 3 sentences · The difference is then 3 - 1 = 2 units. 156 Planting trees along a road, with a tree at both ends 2 sentences · When trees stand in a line with one at each end, there is always one more tree than there are gaps. 157 Planting trees: both ends, one end, no ends, and around a pond 7 sentences · First find the number of gaps: length ÷ distance. 158 Ages: in how many years will one be twice or three times as old 4 sentences · The difference between two ages never changes: every year both people get one year older. 159 The bar model: the whole from the part that is left, and from a difference 3 sentences · Draw the whole as a bar cut into equal units. 160 Olympiad: how many digits number the pages of a book 6 sentences · Pages 1 to 9 use one digit each: 9 digits. ← previous Languagenext → Medicine↑ back to the school This page in Markdown → https://md.mova.elamur.ai/free/en/corpora/school/lessons/