--- title: Lessons — a course of Mova's primary school, with trees and pragmatics · page 2 description: 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 --- [Mova](https://md.mova.elamur.ai/free/en/) · [this page in HTML](https://mova.elamur.ai/free/en/corpora/school/lessons/page/2/) [home](https://md.mova.elamur.ai/free/en/) / [corpora](https://md.mova.elamur.ai/free/en/corpora/) / [school](https://md.mova.elamur.ai/free/en/corpora/school/) / Lessons # Lessons · page 2 [1](https://md.mova.elamur.ai/free/en/corpora/school/lessons/) **2** - [161](https://md.mova.elamur.ai/free/en/corpora/school/lessons/161-multiplying-big-numbers/) — Multiplying bigger numbers in stories — 3 sentences · When there are many equal groups, multiply the number of groups by the size of one group, even when both are… - [162](https://md.mova.elamur.ai/free/en/corpora/school/lessons/162-dividing-big-numbers/) — Dividing bigger numbers in stories — 3 sentences · Dividing tells how many equal groups there are, or how many go into each group, when the total is large. - [163](https://md.mova.elamur.ai/free/en/corpora/school/lessons/163-meeting-and-moving-apart/) — Moving towards each other and moving apart — 3 sentences · When two travellers move towards each other, the gap between them shrinks by both their speeds together ever… - [164](https://md.mova.elamur.ai/free/en/corpora/school/lessons/164-catching-up/) — Catching up — 4 sentences · When a faster traveller chases a slower one going the same way, the gap shrinks by the difference of the spe… - [165](https://md.mova.elamur.ai/free/en/corpora/school/lessons/165-working-together/) — Working together — 3 sentences · When two teams work at the same time, their work for one day adds up: what both do together in a day is the… - [166](https://md.mova.elamur.ai/free/en/corpora/school/lessons/166-chickens-and-rabbits/) — Chickens and rabbits: heads and legs — 4 sentences · Suppose every animal were a chicken: then there would be 2 legs for each head. - [167](https://md.mova.elamur.ai/free/en/corpora/school/lessons/167-heads-and-legs-in-disguise/) — Chickens and rabbits in disguise: wheels, tickets, boats — 3 sentences · Any story with two kinds of things, a total count and a total of something else, is a chickens and rabbits p… - [168](https://md.mova.elamur.ai/free/en/corpora/school/lessons/168-the-missing-score/) — The score that makes the average — 3 sentences · An average of 80 over 4 tests means the 4 marks add up to 4 × 80 = 320. - [169](https://md.mova.elamur.ai/free/en/corpora/school/lessons/169-a-team-joins-later/) — Working alone first, then together — 3 sentences · When one team starts alone and the other joins later, first take away the work done alone, then share the re… - [170](https://md.mova.elamur.ai/free/en/corpora/school/lessons/170-the-dog-between-two-walkers/) — The dog that runs back and forth — 4 sentences · Do not follow each trip of the dog: only ask how long it runs. - [171](https://md.mova.elamur.ai/free/en/corpora/school/lessons/171-unknown-on-both-sides/) — The unknown on both sides of a story — 3 sentences · Sometimes the unknown number appears twice: 3 bags and 5 more weigh as much as 1 bag and 21 more. - [172](https://md.mova.elamur.ai/free/en/corpora/school/lessons/172-backwards-three-steps/) — Working backwards through three steps — 3 sentences · To find the start, begin with what is left at the end and undo the steps one by one, from the last to the fi… - [173](https://md.mova.elamur.ai/free/en/corpora/school/lessons/173-fractions-of-the-rest/) — A part, then a part of the rest — 2 sentences · A ribbon is 60 cm. 1/3 is cut off: 60 / 3 = 20 cm, and 40 cm remain. - [174](https://md.mova.elamur.ai/free/en/corpora/school/lessons/174-surplus-and-shortage/) — Too many or too few: surplus and shortage — 5 sentences · If each child gets 3 pencils, 5 are left over; if each gets 4, 2 are missing. - [175](https://md.mova.elamur.ai/free/en/corpora/school/lessons/175-venn-neither/) — Two circles: both and neither — 5 sentences · Draw two overlapping circles. - [176](https://md.mova.elamur.ai/free/en/corpora/school/lessons/176-which-row/) — Which row? Steps that grow by the same number — 4 sentences · When each row has the same number more than the row before, row N has the first row plus N - 1 steps. - [177](https://md.mova.elamur.ai/free/en/corpora/school/lessons/177-sum-of-rows/) — Adding all the rows — 4 sentences · When rows grow by the same number, pair the first row with the last, the second with the one before the last… - [178](https://md.mova.elamur.ai/free/en/corpora/school/lessons/178-days-of-the-week/) — Days of the week after many days — 5 sentences · Number the days of the week: Monday is 1, Tuesday 2, …, Sunday 7. - [179](https://md.mova.elamur.ai/free/en/corpora/school/lessons/179-venn-both/) — Two circles: how many are in both? — 3 sentences · Those who are in at least one circle are the whole group without those in neither circle. - [180](https://md.mova.elamur.ai/free/en/corpora/school/lessons/180-digits-on-pages/) — Olympiad puzzle: how many pages from the digits? — 5 sentences · Numbering pages from 1: pages 1 to 9 use 9 digits, pages 10 to 99 are 90 pages of 2 digits, 180 digits; toge… - [181](https://md.mova.elamur.ai/free/en/corpora/school/lessons/181-pigeonhole-same-colour/) — Sure of several of the same colour — 3 sentences · To be sure of something, think of the unluckiest draw: it takes as many as it can without the wish coming tr… - [182](https://md.mova.elamur.ai/free/en/corpora/school/lessons/182-pigeonhole-both-colours/) — Sure of one of each of two colours — 4 sentences · To be sure of a red one and a blue one, imagine the worst luck: all the others come first, and of red and bl… - [183](https://md.mova.elamur.ai/free/en/corpora/school/lessons/183-odd-numbers-in-a-range/) — How many odd numbers in a range — 3 sentences · Odd and even numbers take turns, so in a range about half of the numbers are odd; the ends decide whether it… - [184](https://md.mova.elamur.ai/free/en/corpora/school/lessons/184-digit-sum-count/) — Two-digit numbers with a given digit sum — 4 sentences · A two-digit number has a tens digit from 1 to 9 and a ones digit from 0 to 9; count the numbers by trying ea… - [185](https://md.mova.elamur.ai/free/en/corpora/school/lessons/185-cuts-and-pieces/) — Cuts and pieces — 3 sentences · Cutting a log or a ribbon into pieces always takes one cut fewer than the number of pieces: the last piece n… - [186](https://md.mova.elamur.ai/free/en/corpora/school/lessons/186-balance-pans/) — Balancing the scales — 6 sentences · When the scales balance, both pans weigh the same. - [187](https://md.mova.elamur.ai/free/en/corpora/school/lessons/187-together-again-lcm/) — When together again — 4 sentences · Two things that repeat meet again at the smallest number that is a multiple of both repeat times. - [188](https://md.mova.elamur.ai/free/en/corpora/school/lessons/188-longest-equal-pieces-gcd/) — The longest equal pieces — 2 sentences · To cut two lengths into equal pieces with nothing left, the piece must divide both lengths; the longest such… - [189](https://md.mova.elamur.ai/free/en/corpora/school/lessons/189-boat-crossings/) — Crossing the river with one boat — 4 sentences · The boat cannot cross empty, so after every trip across except the last one somebody must row it back. - [190](https://md.mova.elamur.ai/free/en/corpora/school/lessons/190-number-riddles/) — Who am I? Number riddles — 4 sentences · A riddle about a two-digit number gives facts about its digits; find the digits from the facts and put them… - [191](https://md.mova.elamur.ai/free/en/corpora/school/lessons/191-comparison-model/) — The comparison model: times as many, and the total — 3 sentences · Draw the smaller amount as one bar, a unit. - [192](https://md.mova.elamur.ai/free/en/corpora/school/lessons/192-three-parts/) — A whole in three parts — 5 sentences · When a whole is made of three parts, the parts add up to the whole. - [193](https://md.mova.elamur.ai/free/en/corpora/school/lessons/193-change-after-shopping/) — Change after buying several things — 4 sentences · First find what each kind of thing costs in all: the price of one times how many. - [194](https://md.mova.elamur.ai/free/en/corpora/school/lessons/194-adding-hours-and-minutes/) — Adding hours and minutes — 4 sentences · Add the hours to the hours and the minutes to the minutes. - [195](https://md.mova.elamur.ai/free/en/corpora/school/lessons/195-metres-and-centimetres/) — Metres and centimetres in several steps — 3 sentences · One metre is 100 centimetres. - [196](https://md.mova.elamur.ai/free/en/corpora/school/lessons/196-before-and-after/) — Before and after: giving to make equal — 5 sentences · When one child gives things to another, the total stays the same. - [197](https://md.mova.elamur.ai/free/en/corpora/school/lessons/197-area-of-an-l-shape/) — The area of an L-shape — 4 sentences · An L-shape is a rectangle with one corner missing. - [198](https://md.mova.elamur.ai/free/en/corpora/school/lessons/198-two-exchanges/) — Exam 1: two exchanges — 3 sentences · If A then has 3 times as many as B, the gap is 2 of B's units: one unit is 24 ÷ 2 = 12. - [199](https://md.mova.elamur.ai/free/en/corpora/school/lessons/199-too-many-or-too-few/) — Exam 2: some left over, some missing — 4 sentences · Sharing p each leaves some over; sharing q each leaves some missing. - [200](https://md.mova.elamur.ai/free/en/corpora/school/lessons/200-heads-and-a-difference-of-legs/) — Exam 3: heads, and a difference of legs — 5 sentences · Chickens have 2 legs, rabbits 4. - [201](https://md.mova.elamur.ai/free/en/corpora/school/lessons/201-legs-on-insects-and-spiders/) — Legs on insects and spiders — 3 sentences · Every insect has 6 legs: ants, beetles, bees, ladybirds and grasshoppers all walk on 6 legs. - [202](https://md.mova.elamur.ai/free/en/corpora/school/lessons/202-legs-on-four-legged-animals/) — Legs on four-legged animals — 3 sentences · Dogs, cats, mice, lions, giraffes, horses, tortoises and lizards each walk on 4 legs. - [203](https://md.mova.elamur.ai/free/en/corpora/school/lessons/203-legs-on-birds-and-animals-with-none/) — Legs on birds, and animals with none — 3 sentences · Every bird has 2 legs: chickens, ducks, penguins, owls and parrots stand on 2 legs. - [204](https://md.mova.elamur.ai/free/en/corpora/school/lessons/204-wings-and-legs/) — Wings on birds and on insects — 3 sentences · A bird has 2 wings: ducks, owls, chickens and every other bird. - [205](https://md.mova.elamur.ai/free/en/corpora/school/lessons/205-legs-on-a-mixed-farm/) — Legs on a mixed farm — 3 sentences · On a farm, cows, pigs, sheep and goats walk on 4 legs, while chickens and ducks stand on 2. - [206](https://md.mova.elamur.ai/free/en/corpora/school/lessons/206-horseshoes/) — Hooves and horseshoes — 3 sentences · A horse has 4 legs, and each leg ends in a hoof, so a horse has 4 hooves. - [207](https://md.mova.elamur.ai/free/en/corpora/school/lessons/207-fingers-and-toes/) — Fingers and toes — 4 sentences · A person has 2 hands with 5 fingers each, so 10 fingers, and 2 feet with 5 toes each, so 10 toes. - [208](https://md.mova.elamur.ai/free/en/corpora/school/lessons/208-eyes-ears-and-hands/) — Eyes, ears and hands — 3 sentences · Every person has 2 eyes, 2 ears and 2 hands, but only 1 nose. - [209](https://md.mova.elamur.ai/free/en/corpora/school/lessons/209-people-and-animals-together/) — People and animals together — 3 sentences · A person walks on 2 legs, while a dog, a cat or a sheep walks on 4. - [210](https://md.mova.elamur.ai/free/en/corpora/school/lessons/210-counting-back-from-legs-and-wheels/) — Counting back from heads and legs, cycles and wheels — 4 sentences · Cows have 4 legs and chickens 2. - [211](https://md.mova.elamur.ai/free/en/corpora/school/lessons/211-teeth-of-grown-ups-and-children/) — Teeth of grown-ups and children — 3 sentences · A young child with all the first teeth, the milk teeth, has 20 of them. - [212](https://md.mova.elamur.ai/free/en/corpora/school/lessons/212-pairs-and-odd-socks/) — Pairs and odd socks — 3 sentences · A pair is two things that go together: a pair of socks is 2 socks, a pair of shoes is 2 shoes. - [213](https://md.mova.elamur.ai/free/en/corpora/school/lessons/213-a-pair-for-each-person/) — A pair for each person — 3 sentences · Each person has two feet and two hands, so each person wears a pair: 2 shoes, 2 boots, 2 gloves. - [214](https://md.mova.elamur.ai/free/en/corpora/school/lessons/214-sleeves-in-the-wash/) — Sleeves in the wash — 2 sentences · A sweater, a coat, a shirt with long sleeves — each has 2 sleeves, one for each arm. - [215](https://md.mova.elamur.ai/free/en/corpora/school/lessons/215-clean-socks-for-a-week/) — Clean socks for a week — 4 sentences · A week has 7 days. - [216](https://md.mova.elamur.ai/free/en/corpora/school/lessons/216-legs-on-tables-and-chairs/) — Legs on tables and chairs — 3 sentences · An ordinary chair stands on 4 legs, and an ordinary table stands on 4 legs too. - [217](https://md.mova.elamur.ai/free/en/corpora/school/lessons/217-corners-of-bunting-flags/) — Corners of bunting flags — 3 sentences · A triangle has 3 corners and 3 sides; a square and a rectangle each have 4 corners and 4 sides. - [218](https://md.mova.elamur.ai/free/en/corpora/school/lessons/218-fence-around-a-square/) — Fence around a square — 3 sentences · A square has 4 sides, and all 4 sides are the same length. - [219](https://md.mova.elamur.ai/free/en/corpora/school/lessons/219-wheels-on-cycles/) — Wheels on cycles — 4 sentences · A unicycle has 1 wheel, a bicycle has 2 and a tricycle has 3: «uni» means one, «bi» two, «tri» three. - [220](https://md.mova.elamur.ai/free/en/corpora/school/lessons/220-riders-on-tandems-and-bicycles/) — Riders on tandems and bicycles — 3 sentences · A tandem is a bicycle made for two: it has 2 seats, one behind the other, and 2 wheels like an ordinary bicy… - [221](https://md.mova.elamur.ai/free/en/corpora/school/lessons/221-days-and-weeks/) — Days and weeks — 3 sentences · A week has 7 days, from Monday to Sunday, and then the next week begins. - [222](https://md.mova.elamur.ai/free/en/corpora/school/lessons/222-fortnights/) — Fortnights and school weeks — 3 sentences · A fortnight is two weeks, so it is 14 days. - [223](https://md.mova.elamur.ai/free/en/corpora/school/lessons/223-days-in-the-months/) — Days in the months — 3 sentences · January, March, May, July, August, October and December have 31 days; April, June, September and November ha… - [224](https://md.mova.elamur.ai/free/en/corpora/school/lessons/224-years-and-months/) — Years, decades and seasons — 3 sentences · A year has 12 months, 4 seasons of 3 months each, and 52 weeks and a day or two; a decade is 10 years and a… - [225](https://md.mova.elamur.ai/free/en/corpora/school/lessons/225-hours-and-minutes/) — Hours, minutes and seconds — 4 sentences · An hour has 60 minutes and a minute has 60 seconds; a day has 24 hours. - [226](https://md.mova.elamur.ai/free/en/corpora/school/lessons/226-how-long-on-the-clock/) — How long it takes on the clock — 3 sentences · To find how long something lasts, count on from the start time to the next o'clock, then on to the end time. - [227](https://md.mova.elamur.ai/free/en/corpora/school/lessons/227-every-day-for-weeks/) — Every day for a week — 3 sentences · Something that happens every day happens 7 times in a week, because a week has 7 days. - [228](https://md.mova.elamur.ai/free/en/corpora/school/lessons/228-counting-in-the-classroom/) — Counting in the classroom — 3 sentences · When children are put into groups, tables or boats, nobody may be left out: a smaller last group still needs… - [229](https://md.mova.elamur.ai/free/en/corpora/school/lessons/229-the-school-week/) — The school week — 3 sentences · A school week has 5 school days, Monday to Friday. - [230](https://md.mova.elamur.ai/free/en/corpora/school/lessons/230-letters-colours-and-points/) — Letters, colours and points — 5 sentences · The English alphabet has 26 letters. - [231](https://md.mova.elamur.ai/free/en/corpora/school/lessons/231-players-in-a-team/) — Players in a team — 3 sentences · Every sport has its own number of players in a team, and you are expected to know it: a soccer team and a cr… - [232](https://md.mova.elamur.ai/free/en/corpora/school/lessons/232-teams-of-rugby-and-other-football/) — Teams of rugby and other football — 2 sentences · A rugby union team has 15 players on the pitch, and so does a Gaelic football team and a hurling team (rugby… - [233](https://md.mova.elamur.ai/free/en/corpora/school/lessons/233-making-teams/) — Making teams — 3 sentences · A volleyball team has 6 players on the court. - [234](https://md.mova.elamur.ai/free/en/corpora/school/lessons/234-points-in-a-game/) — Points in a game — 3 sentences · In basketball a basket scored from inside the line is worth 2 points, a three-pointer 3 points and a free th… - [235](https://md.mova.elamur.ai/free/en/corpora/school/lessons/235-overs-holes-frames-and-halves/) — Overs, holes, frames and halves — 3 sentences · In cricket an over is 6 balls bowled by one bowler. - [236](https://md.mova.elamur.ai/free/en/corpora/school/lessons/236-dice/) — Dice — 3 sentences · An ordinary die has 6 faces with 1, 2, 3, 4, 5 and 6 dots. - [237](https://md.mova.elamur.ai/free/en/corpora/school/lessons/237-a-deck-of-cards/) — A deck of cards — 3 sentences · A full deck of playing cards, without the jokers, has 52 cards: 4 suits of 13. - [238](https://md.mova.elamur.ai/free/en/corpora/school/lessons/238-board-games/) — Board games — 3 sentences · A chess game starts with 32 pieces on the board, 16 white and 16 black. - [239](https://md.mova.elamur.ai/free/en/corpora/school/lessons/239-toys-rows-and-groups/) — Toys, rows and groups — 3 sentences · Things set out in equal rows are counted by multiplying: rows × how many in each row. - [240](https://md.mova.elamur.ai/free/en/corpora/school/lessons/240-us-coins/) — US coins — 3 sentences · In the United States a penny is 1 cent, a nickel 5 cents, a dime 10 cents and a quarter 25 cents; 100 cents… - [241](https://md.mova.elamur.ai/free/en/corpora/school/lessons/241-paying-with-us-coins/) — Paying with US coins — 3 sentences · In the United States a dollar is worth 100 cents, and a quarter is worth 25 cents, so 4 quarters make a doll… - [242](https://md.mova.elamur.ai/free/en/corpora/school/lessons/242-canadian-coins/) — Canadian coins — 3 sentences · In Canada the one-dollar coin is called a loonie, because it has a loon on it, and the two-dollar coin is ca… - [243](https://md.mova.elamur.ai/free/en/corpora/school/lessons/243-british-coins-and-notes/) — British coins and notes — 3 sentences · In Britain a pound is worth 100 pence, written 100p, and a five-pound note is often called a fiver. - [244](https://md.mova.elamur.ai/free/en/corpora/school/lessons/244-australian-new-zealand-and-irish-money/) — Australian, New Zealand and Irish money — 3 sentences · A price like $4.50 means 4 dollars and 50 cents, which is 450 cents. - [245](https://md.mova.elamur.ai/free/en/corpora/school/lessons/245-shopping-sums/) — Shopping sums — 3 sentences · A six-pack holds 6 cans, and a dollar is worth 100 cents. - [246](https://md.mova.elamur.ai/free/en/corpora/school/lessons/246-best-buys-and-offers/) — Best buys and offers — 3 sentences · A dozen is 12 things, and a dollar is worth 100 cents. - [247](https://md.mova.elamur.ai/free/en/corpora/school/lessons/247-metres-centimetres-and-millimetres/) — Metres, centimetres and millimetres — 3 sentences · A metre is 100 centimetres, and a centimetre is 10 millimetres. - [248](https://md.mova.elamur.ai/free/en/corpora/school/lessons/248-feet-inches-yards-pounds-and-stone/) — Feet, inches, yards, pounds and stone — 3 sentences · A foot is 12 inches. - [249](https://md.mova.elamur.ai/free/en/corpora/school/lessons/249-weight-and-volume-in-the-kitchen/) — Weight and volume in the kitchen — 3 sentences · A litre is 1000 millilitres, and a kilogram is 1000 grams. - [250](https://md.mova.elamur.ai/free/en/corpora/school/lessons/250-distances-out-and-about/) — Distances out and about — 4 sentences · A kilometre is 1000 metres. - [251](https://md.mova.elamur.ai/free/en/corpora/school/lessons/251-dozens-and-spoonfuls/) — Dozens and spoonfuls — 4 sentences · A dozen is 12. - [252](https://md.mova.elamur.ai/free/en/corpora/school/lessons/252-recipes-and-sandwiches/) — Recipes and sandwiches — 3 sentences · A sandwich is made from 2 slices of bread with the filling in between. - [253](https://md.mova.elamur.ai/free/en/corpora/school/lessons/253-laying-the-table/) — Laying the table — 3 sentences · When a table is laid, every person gets a knife, a fork and a spoon: 3 pieces of cutlery for each person. - [254](https://md.mova.elamur.ai/free/en/corpora/school/lessons/254-pizzas-for-a-crowd/) — Pizzas and cakes for a crowd — 3 sentences · A large pizza is cut into 8 slices. - [255](https://md.mova.elamur.ai/free/en/corpora/school/lessons/255-return-tickets/) — Getting everyone there — 2 sentences · A return ticket takes you there and brings you back: it is 2 journeys. - [256](https://md.mova.elamur.ai/free/en/corpora/school/lessons/256-birthday-candles/) — Candles and party bags — 3 sentences · A birthday cake has one candle for every year: a child turning 7 gets 7 candles. - [257](https://md.mova.elamur.ai/free/en/corpora/school/lessons/257-cups-of-juice/) — Party costs, drinks and time — 4 sentences · A litre is 1000 millilitres (ml). - [258](https://md.mova.elamur.ai/free/en/corpora/school/lessons/258-cups-and-plates-for-the-guests/) — Seating and serving the guests — 3 sentences · At a party every person at the table gets one cup and one plate: that is 2 things for each person. - [259](https://md.mova.elamur.ai/free/en/corpora/school/lessons/259-laying-the-party-table/) — Laying the party table — 3 sentences · A table laid in full gives every person 5 things: a plate, a knife, a fork, a spoon and a glass. - [260](https://md.mova.elamur.ai/free/en/corpora/school/lessons/260-loaves-for-the-sandwiches/) — Planning the whole party — 4 sentences · A sandwich takes 2 slices of bread. 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