Leapfrog

📺ITV Schools

companyATV

started19th Sep 1978

ended26th Jun 1979

last rpt3rd Jul 1981

3 school years

episodes28

duration15 mins

subject 📐MathematicsMathematics

age rangeAge 7-9

languageenIn English

5 images from Leapfrog

currentsequence: ; ### size: ### Leapfrog: ITV junior mathsPrevious series: Figure It Out Next series: Basic Maths

Leapfrog is an ITV schools TV series from the 1970s and 1980s, covering Mathematics for primary school pupils.

A maths series in which presenters in the studio carry out investigations and tell stories, interspersed with animations, real-world films and location footage, providing a bank of eye-catching experiences to help children understand concepts of number, shape and measure. So far so ordinary, like the ITV schools maths series which preceeded it (Figure It Out) and followed it (Basic Maths, Junior Maths and Video Maths). But Leapfrog was a very unusual series, and proved simply too unorthodox for many of the teachers who tried to use it.

Presenters Anni Domingo, Fred Harris and Sheelagh Gilbey

The presenters were Fred Harris (who also presented all of the ITV maths programmes mentioned above, plus many others), Sheelagh Gilbey and Anni Domingo, while Sylveste McCoy (sic) appeared in films shot on location, often playing a character called Bert who was trying to overcome large-scale mathematical problems. The presenters often did not speak to each other or the viewers, and long sections of the programmes would pass with only music or ambient sound being heard.

Leapfrog was structured as a magazine programme, with typically six or seven distinct items covered in each 15-minute episode. The episodes, unusually for a maths schools programme, were not themed around a particular topic (except in the summer term), themes simply flowed and developed throughout the series. Some of the items were revisited throughout the series and built up into sequences so that they did not make much sense when seen once, but became clear over the course of the school year.

In the autumn term there were repeated sequences showing Bert out of doors with two piles of regularly sized logs, trying to lay them down in two rows of exactly the same length, as well as regular items showing the complements of a number being worked out with fingers and thumbs - obviously this was most straightforward when showing the complements-in-10 such as 3 and 7, but some fingers could be painted blue and tied up with ribbon to show that they "don't count", so that the complements in lower numbers could also be shown. There were also regular animations showing a shape and its mirror image intersecting each other, with the intersections creating lots of different shapes.

There were more intersection animations in the spring term, but whereas they were achieved by straight translation in the autumn term, in the spring the shapes rotated around each other, creating different intersections. The spring term also showed the presenters counting using a 'tens table', with 100, 200 etc on the top row and "hundred" written at the end, "and" at the start of the middle row followed by 10, 20 etc and "-ty" at the end, and 1, 2 etc on the bottom row. By tapping a different place in each row, three-digit numbers could be identified. There was also a number line which could be used to move forward and backward using strips of card cut into exact sizes such as 3 units or 5 units.

Sylveste McCoy as Bert

Bert, having succeeded in his logging task at the end of the autumn term, spent the spring term trying to create patterns of carpet tiles, of which he had different amounts in three separate colours. At first he attempts to fit them all together in a tessellation, then later tries different regular patterns. The spring term also featured serialised extracts from Norman Juster's The Phantom Tollbooth, about a boy called Milo's adventures in a strange world full of fantastic mathematics.

Another of Norman Juster's works, The Dot and the Line, was serialised in the summer term. The summer also featured simple algebraic statements, with numbers replaced by a box or a triangle. This work was begun in the final episode of the spring term, and the algebra did not have to be solved, just to have suitable numbers found by trial and error. Pegboards were used occasionally in the spring term, and geoboards (like pegboards, but with all the pegs already in place so that rubber bands can be stretched between them) were used in the summer term to explore shapes. In the summer term there was a definite theme to each episode, with features on each of the numbers 5, 4, 3, 2, 1 and 0 (although these occupied only a portion of each episode) and special programmes devoted entirely to themes of growth and circles.

The programmes were extremely visual in nature and took advantage of many television tricks, especially overlaying the presenters on top of other images. When the complements identified by fingers and thumbs were displayed as numerals it was not by typing the numbers on the screen, but by having two of the presenters overlayed on top of the film, running onto the screen carrying large, colourful numbers and holding them up.

Mirror fun - an example of the visual effects used in the series as a tiny Fred Harris is superimposed on the table in front of Sheelagh Gilbey

Why 'Leapfrog'?

The name 'Leapfrogs' was already being used by the group of well-respected maths teachers who wrote the programmes and advised on the content - Ray Hemmings, Derick Last, Leo Rogers, David Sturgess and Dick Tahta. They published books, cassettes and other aids for maths teachers.

In the case of both the teachers' group and the television programme the name was chosen firstly as a neutral describing word or catchphrase. More importantly, the rules of the children's playground game of leapfrog were seen as representative of the series' approach to maths: a game played simply for the enjoyment of the children taking part, all sharing the experience with no winners or losers.

Critical Response

Leapfrog was innovatory in the development of mathematics on schools television, but it was not judged to be a great success at the time.

Stylistically the programmes were aimed at pupils who had grown up with television and enjoyed the colourful, unusual images they were shown. Teachers, on the other hand, often didn't know what to do with it. The long silent, or at least speech-free, portions of each programme were designed to be filled in by the teacher talking with the class about what was happening, but when teachers were not expecting this, or couldn't fill up all of the time, or simply found it hard to reconcile the unrelated sequences in each episode, the classroom experience of watching the episodes could turn into uncomfortable silence.

An evaluation report on the series identified "undoubted polarisation in the primary school between those who feel (Leapfrog) to be an excellent series and those who feel it has no redeeming qualities." The generally negative response from teachers lead to a steady loss of viewers.

The final episode of the series was shown to a group of 11-year-old children as part of an IBA Research Fellowship, alongside episodes of its contemporaries Maths-in-a-Box, It's Maths and others. The children were asked to judge how they felt the series would work for its intended audience of eight- and nine-year-olds. Many thought that it would be "too easy" due to its choice of topics and repetition of those topics, whilst at the same time "too confusing" in its presentation.

They were enthusiastic about the visual style...

"It has nice colours. The way the camera made the people small is nice."

...but not about the lack of explanation in the presentation style:

"They should explain what they are doing. I think it is a bit boring because it is so easy."

"You feel as though they don't want to talk about it to you."

After three years on the air Leapfrog was replaced by a new series called Basic Maths. This shared many of the production team of Leapfrog as well as the presenter Fred Harris, and it reproduced many of the items from its predecessor, even using some of the same film sequences. However Basic Maths was much more orthodox in style, with proper presenters actually talking to the viewer and episodes based on a common theme, and it proved to be more successful.

Episodes

Quick episode list

#	Title	Broadcast
1.	Programme 1	19 Sep 1978
2.	Programme 2	26 Sep 1978
3.	Programme 3	3 Oct 1978
4.	Programme 4	10 Oct 1978
5.	Programme 5	17 Oct 1978
6.	Programme 6	24 Oct 1978
7.	Programme 7	7 Nov 1978
8.	Programme 8	14 Nov 1978
9.	Programme 9	21 Nov 1978
10.	Programme 10	28 Nov 1978
11.	Programme 11	16 Jan 1979
12.	Programme 12	23 Jan 1979
13.	Programme 13	30 Jan 1979
14.	Programme 14	6 Feb 1979
15.	Programme 15	13 Feb 1979
16.	Programme 16	27 Feb 1979
17.	Programme 17	6 Mar 1979
18.	Programme 18	13 Mar 1979
19.	Programme 19	20 Mar 1979
20.	Programme 20	27 Mar 1979
21.	Programme 21 (Number 5)	1 May 1979
22.	Programme 22 (Growth)	8 May 1979
23.	Programme 23 (Number 4)	15 May 1979
24.	Programme 24 (Number 3)	22 May 1979
25.	Programme 25 (Number 2)	5 Jun 1979
26.	Programme 26 (Circles)	12 Jun 1979
27.	Programme 27 (Number 1)	19 Jun 1979
28.	Programme 28 (Number 0)	26 Jun 1979

The following guide to all 28 episodes is based mainly on the descriptions given in the teacher's notes.

Num	Title	Broadcast
1.	Programme 1	19 Sep 1978
	A shape and its mirror image intersect to music fingers and thumbs are used to count complements the movement of a sparkler is seen in the darkened studio six counters form pairs, but a seventh counter spoils things patterns are formed from squares of card Fred and Sheelagh play Make Seven, in which they have to guess how many objects to add to the other player's collection to make seven exactly.
2.	Programme 2	26 Sep 1978
	Another game of Make Seven fingers and thumbs make complements-in-ten seven counters split into groups of 3 & 4 and 5 & 2 a light in the dark studio is revealed to be a cat playing a violin two isosceles triangles intersect four squares of card are arrenged into patterns in different ways Bert begins laying out logs and finds that four of one type of log are as long as three of another type Fred has different sizes of chocolate logs in the studio.
3.	Programme 3	3 Oct 1978
	Card squares are arranged to make patterns with all sides touching a light is attached to a ball that is thrown around the darkened studio two circles intersect fingers and thumbs are again used to count complements-in-ten twelve counters are grouped in different ways Bert tries to make equal rows from a new pile of logs, but they are different sizes.
4.	Programme 4	10 Oct 1978
	Bert begins to set down two rows of logs complements are shown using fingers and thumbs, and also a pair of numbers separated by a comma five card squares are arranged with their sides touching to create pentominoes the Roman mosaic floor at Woodchester is reconstructed a light is attached to a football rattle in the darkened studio twenty-five dots are arranged in twos, then threes, then fours, each time with one left over, then finally they are arranged in fives Bert is still trying to create equal rows of logs - the logs are 53 and 41 units long, and he has along way to go!
5.	Programme 5	17 Oct 1978
	Different ways of showing all of the complements-in-ten animated mathematical equations distort into different equations the complements-in-ten are changed to make complements-in-100 film of balloons and bubbles there are a large number of counters on screen, which arrange themselves into groups to make it easier to count them a light moving around the darkened studio is revealed to be attached to a dancer's hand Bert is still struggling to make his rows of logs equal the presenters play a card game like snap where they have to call out the sum of two consecutive cards of the same colour two squares intersect the presenters use blocks of wood and paint to print intersecting square patterns.
6.	Programme 6	24 Oct 1978
	A stencil is used to make a wave pattern, which is incorporated into different drawings waves are shown in different real-world situations Bert creates complements-in-nine with his fingers (one of his thumbs "doesn't count") a rhythmic animation shows counting on an abacus in base 4 two ring shapes intersect Bert is still working on his rows of logs Rangoli patterns are shown and the presenters discuss how to create them.
7.	Programme 7	7 Nov 1978
	Bert is still adding more logs to his rows the presenters use thin blocks to create patterns of lines, and similar patterns are shown in the real world four fingers & thumbs don't count, so complements-in-six are created a mirror is moved around some drawings to create different shapes and even words the abacus counts up in base three Sheelagh tells a fairy tale in which a princess will marry whomever can tell whether the King has more sheep or cows.
8.	Programme 8	14 Nov 1978
	Fred lies down and is covered with a striped sheet, and the stripes form lines around his body fingers and thumbs form complements-in-10, but each digit is named -ty (such as "four-ty") to make complements-in-100 a mirror is held against different animated drawings to demonstrate symmetry the abacus counts in base five Bert finally gets his two lines of logs to be equal length a group of people count from one to ten in different languages.
9.	Programme 9	21 Nov 1978
	The presenters experiment with shadow puppets and try to guess objects from their shadows they tell a story about a man who hired a mule but did not hire its shadow fingers are again named "-ty" to count complements-to-100 simple animated characters try to get different shapes through a doorway the presenters lay out isosceles triangles in a pattern on the studio floor an animated film shows a tiling pattern of triangles being transformed in various ways the abacus counts in base 10 the presenters use Cuisenaire rods to investigate the same problem that Bert finally solved in the previous episode.
10.	Programme 10	28 Nov 1978
	The presenters cut out potato shapes and create complex designs by printing simple shapes an animation shows different ways of dividing a rectangle in half a pair of Cuisenaire rods are fitted into most, but not all, steps of a staircase the abacus counts up in base two film of a classroom shows children giving directions to a colleague moving round a maze Fred tells a story in which counting past four casues trouble.
11.	Programme 11	16 Jan 1979
	One presenter acts as the mirror image as another the tens table is introduced a shape and its mirror image rotate around each other and intersect in different ways there is mirror writing, reflections in water and other games with mirrors the presenters perform sums along the number line using strips cut into 3 units and 5 units there is a game of Four-in-a-Row, a version of noughts and crosses played on a pegboard.
12.	Programme 12	23 Jan 1979
	Various numbers are shown on the tens table for viewers to call out, moving to a rapid sequence of multiples of five another new game, Four-in-a-Square, is played on a pegboard where the players have to put their pegs into the four corners of a square shape an isosceles triangle and its mirror image rotate and intersect people are shown making tessellations in real life, using tiles and bricks a five-unit strip is used to perform subtractions on the number line carbon paper is used to check shapes for symmetry.
13.	Programme 13	30 Jan 1979
	More numbers can be read from the tens table, leading to the multiples of three a film shows images in a mirror the presenters discuss how to use a mirror to turn three counters into different amounts of counters two squares rotate and intersect there is a new pegboard game called Seven-in-a-Line a 6-unit strip is used on the number line to add, and take away again a light traces out a strange path Bert begins to lay coloured carpet tiles.
14.	Programme 14	6 Feb 1979
	The numbers on the tens table can be recorded: the numerals are picked out and then brought together to create a three-digit number two mirrors are used to make a rotating kaleidoscope two circles rotate and intersect a 9-unit strip is used to add and divide on the number line the story of The Phantom Tollbooth begins a rectangle is divided by a moving line which rotates and bends, but always so that the rectangle is split exactly in half Bert finds that he does not have enough of each colour of tile to finish his pattern.
15.	Programme 15	13 Feb 1979
	A 10-unit strip is used for addition and subtraction on the number line Bert is still having problem producing a suitable pattern two hexagons rotate and intersect in the second episode of The Phantom Tollbooth Milo meets a Dodecahedron who thinks himself superior because he has more faces the rows on the tens table are divided by ten so that the rows now display tens, units and tenths paper is folded and paper shapes are cut to demonstrate reflective symmetry.
16.	Programme 16	27 Feb 1979
	In The Phantom Tollbooth, The Dodecahedron takes Milo to a number mine the presenters play a game of Fine My Rule, investigating the relationship between numbers using arrows a square with sides 5 units in length rolls along the number line producing a pattern of numbers 5 apart a mime artist illustrates measurement phrases such as "tall as a house" an animation shows a rectangle being split into half again and again, creating a series of fractions Bert has created a tessellation but wants to try different patterns the presenters discuss patterns on a pegboard - is one 'the same' as another?
17.	Programme 17	6 Mar 1979
	Two people compare their pieces of knitting, one wants to measure by length and the other by number of rows, and both are convinced that they have the larger piece Bert seems to be making progress with his carpet patterns a rectangle rolls along the number line creating a pattern of numbers 6 and 4 units apart the presenters use arrows to write rules such as "treble and take off 1" in The Phantom Tollbooth the Mathemagician shows Milo some very precious numbers patterns are made on the pegboard using four pegs which are all next to each other in different ways.
18.	Programme 18	13 Mar 1979
	There is a mime about trying to cut a shelf to exactly the right length a rectangle of 1 unit by 9 units rolls along the number line Bert has almost completed a pattern but he is one tile out another mysterious spot of light moves around the darkened studio the presenters work on more arrow rules to describe the relationship between numbers square tiles of different colours are used to make patterns in The Phantom Tollbooth Milo tries the subtraction stew.
19.	Programme 19	20 Mar 1979
	Two people find that the length of time can feel quite different, depending on what you are doing Bert tries to work out all the possible rectangles that he could make from the number of tiles that he has the presenters come up with more rules, using repeated arrows an isosceles triangle is split into half then half again and so on the Mathemagician tells Milo about multiplication in The Phantom Tollbooth a 6 by 4 triangle rolls along the number line, but falls backward as well as moving forward the presenters all try cutting shapes out of folded paper to make interesting shapes.
20.	Programme 20	27 Mar 1979
	Empty boxes are used in basic algebraic statements, which are made true by putting appropriate numbers in the boxes Bert finally completes his carpet pattern, but now it is not just a pattern - it's a picture two mimes try to put four things in order by mass, one person compares the objects while another plays the balance a 9 by 1 rectangle rolls forward, and sometimes backward, down the number line in the final episode of The Phantom Tollbooth, Milo is shown some very big numbers the studio is filled with hanging mobiles with all sorts of objects balancing and swinging around.
21.	Programme 21 (Number 5)	1 May 1979
	Some box statements, including one that is rather complicated, are solved by trial and error a look at the number 5 with different images of five, five used for counting in Roman numerals, and multipyling five times five times five patterns are made on a 3-by-3 geoboard the presenters play Sprouts, where dots are drawn on a piece of paper and the players take it in turns to join two points & make a new point in the middle of their line, the lines cannot cross each other and no more than three lines can join to any one point, so the game proceeds until one player cannot draw a new line.
22.	Programme 22 (Growth)	8 May 1979
	A group of children begin to keep count of how many times they can skip, the screen forms an abacus to keep track of the number - here as far as 19 one presenter introduces the programme but grows larger and larer until eventually they burst, a second presenter takes over but grows smaller and smaller until they go pop! there is a reading from Alice in Wonderland in which Alice takes a potion marked DRINK ME and grows small enough to pass through a tiny door, but finds that she has forgotten the key on the table the presenters discuss growing up as children and show wall markings of how tall they were in different years the children have skipped over 400 times there is film of plants and animals growing the presenters halve a sandwich to share between them, but then it has to be halved again and again an animation shows the surface area of a square flowing out to outline the square multiple times to create concentric squares the children have skipped over 800 times two twigs grow from the branches of a tree successively so that there are four twigs the next year, eight the next and so on the children finally skip 1000 times.
23.	Programme 23 (Number 4)	15 May 1979
	There is a box statement which is true for every number that is put in the box (it is an identity rather than an equation) number 4 is investigated with an animation showing the corners of a square splitting into four squares successively to show the powers of four, the powers are shown on the tens table, and the 'sound' of four is heard in various languages the screen is filled up at different rates in an animation about growth a shape is made on a 3-by-3 geoboard, which is then rotated and the pattern made again, creating a pattern the story of The Dot and the Line begins.
24.	Programme 24 (Number 3)	22 May 1979
	The presenters try to find out how many triangles can be made on a 3-by-3 geoboard, but disagree about what are "different" triangles the three presenters face the problems of the oddness of three, they have "triadic accoutrements" such as a three-legged stool and a tricycle, and try to work out how they can all link arms, an animated triangle is repeatedly tripled, showing the powers of three, the presenters discuss a handshaking problem, and trisections of a triangle dance together in an extract from the film Notes on a Triangle an algebraic statement with two unknown numbers - a box and a triangle - is introduced, and solved using the lists of number complements introduced in the autumn term there is a second extract from The Dot and the Line.
25.	Programme 25 (Number 2)	5 Jun 1979
	The presenters use triangular dotty paper to split up different shapes into triangles images representing choices between left and right, yes and no, etc, introduce the number 2, a chess board is numbered so that the black squares are all even and the white squares odd, then the chessboard is cut up to leave pieces of 32 squares, 16 squares, 8 squares etc, there is a cartoon telling the story of the merchant who asked to be rewarded with a single grain of wheat on the first square of a chessboard, 2 grains on the second, 4 on the third and so on pairs of complements are changed into complements of much larger numbers there is a film showing circular motion in preparation for the next episode and the final episode of The Dot and the Line.
26.	Programme 26 (Circles)	12 Jun 1979
	The circle is introduced as the outside edge of a ring the presenters draw circles in different ways and make up various designs coins, counters, wheels and other solid forms of the circle are explored three-dimensional shapes based on the circle - cones, cylinders and spheres - are introduced, and holes are put to practical use.
27.	Programme 27 (Number 1)	19 Jun 1979
	Complements-in-20 and complements-in-30 are introduced triangular dotty paper is used to make a pattern of equal-sized triangles, and the presenters must determine how many colours are needs to fill in the triangles so that no two of the same colour are touching a triangle is moved around a grid by shearing (stretched by moving the top point from left to right while the base remains in place) there is a film about kite flying a piece of string is pulled into lots of different shapes, but the area inside it always remains the same one is the number that makes up all others, the presenters solve the problem of "what's one and one and one and one and one and one and one and one and one and one?" and then play a game where they have to make any number up to 20 by adding together not more than ten 1s (they can use two of the 1s to make 11) they play a Three-in-a-Row game, like noughts and crosses on triangular dotty paper.
28.	Programme 28 (Number 0)	26 Jun 1979
	The presenters come up with more complements, in-100 and even beyond they draw larger triangles on dotty paper an animation shows lots of different sized circles moving together the number zero is considered as nothing, what happens when you add zero to another number, and what happens when you add zero to the end of another number? a word transformation game turns the word LEAP into FROG.

Credits

Presenters	Anni Domingo Sheelagh Gilbey Fred Harris
with	Sylveste McCoy

Written by	Ray Hemmings Derick Last Leo Rogers David Sturgess Dick Tahta
Music by	Ron Geesin
Film editor	Francis Robertson
Graphics	Steve Safe
Designer	John Hickson
Director	Francis Fuchs
Producer	Paul Martin

Broadcasts

• 1978-1979: Tuesdays 11:05am, repeated Fridays 9:30am (autumn, spring & summer)
• 1979-1980: Tuesdays 11:05am, repeated Fridays 11:22am (autumn, spring & summer)
• 1980-1981: Tuesdays 11:05am, repeated Fridays 11:26am (autumn, spring & summer)

The series was broadcast over three academic years, always networked at the same time across all of the regional ITV companies, and always with its first transmission on Tuesdays at 11:05am (basically the same timeslot which its predecessor Figure It Out had occupied since 1972). Repeats were shown firstly at 9:30am on Fridays (also the same timeslot as Figure It Out) and in subsequent years later on Friday mornings.

In autumn 1979 the first five episodes of the series were not screened due to the long ITV strike that year, but the series picked up with episode six and proceeded through the rest of the year's episodes as scheduled.

Resources

Teacher's notes 1978-9

Leapfrog was accompanied by an extremely thick - 118 pages long - and comprehensive booklet of teacher's notes covering the entire year's programmes, written by the same Leapfrogs teachers group who wrote the episodes themselves.

Each episode was given a detailed outline synopsis listing each item and the mathematical point that it covered (though not always in exactly the same order that the items were broadcast), cross-referenced with several pages of detailed suggestions for follow-up work. There were black and white diagrams throughout.

The booklet also featured an essay on 'Television, Mathematics and Leapfrog' which explained the reasoning behind the introduction of the series and its position in the development of maths on schools television ("up to three years ago, the output of both the BBC and ITV in (the area of mathematics) was predominantly direct teaching or programmes that looked very like it."). Each term's episode listings were preceded by a section deatailing the on-going sequences through that year's programme.

The cover of the booklet used the picture Day and Night by M. C. Escher, with 'night' on the front cover and 'day' on the back. In 1978-9 the cover was printed in purple (pictured), in 1979-80 it was red and in 1980-81 it was pink.

Sources & References

• Hemmings, Ray et al (1978) Leapfrog Independent Television for Schools and Colleges Autumn 1978 Spring 1979 Summer 1979. Birmingham: ATV Network Ltd.
• Hemmings, Ray et al (1979) Leapfrog Independent Television for Schools and Colleges Autumn 1979 Spring 1980 Summer 1980. Birmingham: ATV Network Ltd.
• Hemmings, Ray et al (1980) Leapfrog Independent Television for Schools and Colleges Autumn 1980 Spring 1981 Summer 1981. Birmingham: ATV Network Ltd.
• IBA (1982) Independent Broadcasting Authority Annual Report and Accounts 1981-82. London: IBA p.32
• Langham, Josephine (1990) Teachers and Television: A History of the IBA's Educational Fellowship Scheme. London: John Libbey & Company ISBN 0-861-96264-8
• TV Times (London region) listings, 1978-1981, via TV Times Project database
• Womack, David (1983) Maths on Television: Doing or Viewing? The Role of Television in the gaining of Early Mathematical Concepts - with particular reference to Slower-Learning Children. London: Independent Broadcasting Authority
• and recordings of episodes 1-10

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