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Welcome to the Maths@Home blog

By Admin, on 2 February 2021

The Maths@Home Blog

These blogs are written by academics at UCL Institute of Education who developed the Maths@Home activities. These blogs provide further information about mathematical abilities in children aged 2 to 6 years old, based on recent research evidence from mathematical development as well as best evidence-based practice to support children’s mathematical abilities.

The Maths@Home app is freely available to all users. However, in order to keep the app freely available we need to raise a minimum amount of funding each year to ensure the app is compatible with any software updates. So please donate if you can:

DONATE HERE

Shapes

By Admin, on 13 February 2023

Although in the UK, the early years learning goals no longer include shapes, space and measures, as part of the maths curriculum (click here to read more), children will be exposed to a wide range of opportunities to learn about shapes and Development Matters (the non-statutory curriculum guidance for the early years foundation stage) still expects children to talk about and explore 2D and 3D shapes (for example, circles, rectangles, triangles and cuboids) using informal and mathematical language: ‘sides’, ‘corners’; ‘straight’, ‘flat’, ‘round’ .

At younger ages children are only expected to recognize these and see the difference, from year 1 onwards children are expected to name them and name some features of these shapes (see Table below).

So what are different types of shapes?

• 2d shapes are completely flat and only have 2 dimensions such as width and height (but not depth).
• 3d shapes have 3 dimensions and have width, height and depth.

Below is a list of common 2D shapes with their features and 3D equivalent. Those that are commonly used are highlighted in bold.

 2D shape Features 3D equivalent circle Round shape with no corners made from one curved line and each point on the curved line is the same distance to the center of the shape. sphere square A four equal sides. four straight sides and four 90 degree angles. Cube rectangle two pairs of equal sides. four straight sides and four 90 degree angles. Cuboid trapezium One pair of parallel lines trapezoidal prism Parallelogram Two pairs of parallel lines parallelepiped Rhombus Two pairs of parallel lines with all sides equal in length and opposite corners are equal rhombohedron triangle three sides and three corners Pyramid or prism (tetrahedron) pentagon A shape with five sides and five equal angles Dodecahedron oval A closed shape made by a curved line but not all points are a similar distance to the centre. Looks like a stretched circle. Ovoid hexagon six sides that are equal in length and six angles that are equal in size hexagonal prism N/A cone N/A cylinder

Want to know more about Development matters and EYFS?

https://www.gov.uk/government/publications/early-years-foundation-stage-framework–2

Maths and Narratives

By Admin, on 11 February 2023

By Jo Van Herwegen

At first glance, it may look as if mathematics and narratives do not have much in common. Mathematics concerns itself with theory and facts whilst narratives can include fiction, fabricated characters and fantasy worlds. Recently however, there has been an increased interest within the academic world in the overlap between mathematics and narratives. This interest covers the mathematics of narratives, using mathematical ideas to study narrative techniques, the stories of mathematics teachers, and the importance of narratives in teaching mathematics.

Stories are powerful tools for learning for a number of reasons. People enjoy stories and stories can help to motivate learners when learning. Stories create more vivid, powerful and memorable images in a listener’s mind which helps both learning and recall. In addition, stories embed concepts within a context; this can make abstract concepts more accessible and helps show how concepts can be applied in real life. So according to recent research, narratives can be a powerful tool to teach mathematics.

Narratives as an anchor for mathematical development

Learning is not just some abstract thing that happens in the brain; rather, learning happens in the context in which a concept is used. Narratives can represent mathematical concepts through their prose, illustrations, logical development and context. An example of how narratives can be used to teach young children comes from a study by Kinnear and Clarke[1]. Earlier studies which examined probabilistic reasoning (calculating the likelihood that something will happen) in 6- and 7-year-old children had found that although children were able to use data to draw inferences,  when they explained their answers, they would use subjective examples from their own experiences and show little understanding of how they achieved their answer. Kinnear and Clarke used a story picture book including the character Litterbug who was first very wasteful but then learned about recycling and started to collect litter everywhere in the town. In their study, 5-year-olds were presented with the book Litterbug and a table with information about the rubbish that Litterbug had collected on Monday, Tuesday and Wednesday per type of items (e.g. 5 cans, two apple cores, three papers, etc). Children were then asked to predict how much of each litter category Litterbug would collect on Thursday. In contrast to previous studies which showed just data tables, children who were presented with the Litterbug story drew exclusively from contextualised knowledge of the picture story book to explain their predicted values when asked. This shows that children have the capacity and ability to draw meaningfully from data and use context knowledge to explain data observations if the connection to the data context source is indeed meaningful.

Since narratives are an integral part of our everyday activities, and our counting system is a cultural notation that has evolved as a result of these every day activities, it is not surprising at all to see that narratives are a powerful tool in helping children to develop mathematical abilities. There are a number of ways in which narratives can help mathematical abilities. First of all, narratives can teach children new concepts and promote mathematical reasoning. Secondly, they contextualise mathematical ideas as well as engage the child. Finally, they allow for rich discussions and wider exploration.

For example, a recent study by Carrazza and Levine[2] at the University of Chicago compared typical maths books that simply include sets of objects and books with the same objects and sets incorporated into stories (rich narratives) for numbers 1 to 10. They asked two groups of parents, one for the classic number books and one for the rich number stories, to use the books each day with their three-year olds. The researchers examined how well children could count and understand cardinality before they started using the books as well as after 4 days of using the books. Even though parents in both groups reported the same number of book reading sessions during the four days, children in the rich narrative condition performed better on the cardinality and counting task than those who used the simple pictures of the same sets of objects. This shows that embedding knowledge into rich narratives aids children in learning mathematics faster.

Storybooks as a way to develop mathematical vocabulary

Not only can the context help to embed knowledge and understanding, storybooks are also extremely useful in teaching children mathematical vocabulary. The development of mathematical vocabulary is important for young children as its use is necessary for them to reason and to understand maths. For example, when children learn that the words “more” and “less” can be used to describe number, they have a way to verbally explain the differences between a basket with ten apples and a basket with 5 apples. The use of storybooks that highlight mathematics vocabulary and explain numbers and how they relate to each other might help children “mathematize” or understand everyday situations in mathematical terms.

We can see then that while the richness of narratives allows young children to learn concepts faster and foster a deeper understanding of mathematical vocabulary, there is evidence that even just reading books, whether they have a mathematical content or not, influences children’s mathematical abilities.

Reading from left to right helps to understand the number line

People have been argued to have an internal number line that goes from left to right in most western countries and it is thought that the direction of this number line is influenced by the reading direction in those countries. A recent study showed that when reading The Very Hungry Caterpillar, a children’s book in which the caterpillar comes out of an egg, looks for food, and eats one apple, two pears, three plums, four strawberries, and five oranges, children who read the book with the pictures presented from right to left and page turning from left to right (so opposite of usual books) changed their counting direction from right to left when counting a row of coins. Therefore, the orientation of the pages and pictures in shared book reading activities can activate and change the child’s spatial representation of numbers along a number line (see Göbel and colleagues, 2018)[3].

It has been shown that children who have a firm mental number line are more able to manipulate numbers and as a result have better mathematical abilities. Number lines and narratives share the fact that both have a structure or sequence to them. Therefore, using words such as ‘before’, ‘after’, ‘in front’,’ ‘next’, ‘forward’ and ‘backward’ in stories will help understanding of sequences and of number lines. In addition, books are like number lines in that a book goes from page 1 to the final page just like a number line goes from the start to the finish. As pages are flipped, pages with smaller numbers are placed on the left and pages with larger numbers remain on the right. Therefore, as children get more familiar with books they get a stronger understanding of the relationship between space and numbers.

A study by Daniela O’Neill and colleagues (2004)[4] examined the narratives of 3-year-old children who were asked to tell a story from a wordless picture book. The researchers analysed various aspects of the children’s narratives, including how many conjunctions children used, i.e. sentences that include words such as ‘and’, ‘but’, ‘or’, ‘because’, ‘after’, along with the event content of the stories, i.e. how many different parts the story contained (which shows the richness of the content of the story). The number of conjunctions and events used when children were three years old correlated to their mathematical performance at that age, as well as predicted their mathematical performance two years later. This suggests that there is a relationship between exposure to books, narratives, and number line development and improved number line abilities allow for improved mathematical abilities.

In reality, all books and stories contain some kind of mathematical content, as mathematics is truly embedded within our culture (telling the time, reading the number of a bus/train to catch, postcodes, telephone numbers, cooking etc.). Therefore, it is less about the kind of story or book but rather how they can be used to highlight mathematical concepts.

Teaching mathematical concepts

The best way to teach children mathematical concepts is to first read the story while pointing out pictures and highlighting mathematical concepts and vocabulary words such as ‘same’, ‘different’, ‘bigger’, ‘smaller’, ‘half’, ‘whole’, ‘next’, ‘after’, ‘before’. We often assume that children will implicitly absorb the information we tell or teach them. Although this is true to some extent, it is better to talk to children about the vocabulary words and define them within the context of the story. For example, when reading the story ‘Two of Everything’, a child might not be familiar with the word ‘double’ and thus it may be necessary to explain this explicitly. In order to check that your child has understood the mathematical concept in the story, you could ask your child some other examples of this mathematical concept from the book or even from outside of the book. For example, when reading Goldilocks you can ask, “There were three bowls in the book. Were there any other groups of three in the book?”.

Conclusion

In conclusion, mathematical learning starts at home from birth onwards. Through narratives and shared book reading, children develop an improved mathematical understanding which can influence mathematical abilities later on in life. There are a number of ways in which narratives can help children. First of all narratives can teach children new concepts such as counting, number words, and cardinality. Secondly, books and narratives provide a structure and sequence that may influence children’s mathematical number line visualisation and understanding of how numbers relate to each other. Thirdly, narratives and books facilitate children’s development of a rich mathematical vocabulary. And finally, books and narratives help to engage children and to provide a rich context in which mathematical concepts and ideas can be applied, which allows for deeper mathematics knowledge.

References

[1] Kinnear, V. and Clark, J. (2014) ‘Probabilistic reasoning and prediction with young children.’ In J. Anderson, M. Cavanagh, and A. Prescott (eds) Curriculum in focus: Research guided practice Proceedings of the 37th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 335–342). Sydney: MERGA.

[2] Carrazza, C. and Levine, S.C. (2019) ‘How numbers are presented in counting books matters for children’s learning: A parent-delivered intervention’. Conference talk: Society for Research in Child Development. Baltimore, USA.

[3] Göbel, S.M., McCrink, K., Fischer, M.H., and Shaki, S. (2018) ‘Observation of directional storybook reading influences young children’s counting direction.’  Journal of Experimental Child Psychology 166, 49-66.

[4] O’Neill, D.K., Pearce, M.J., and Pick, J.L. (2004) ‘Preschool children’s narratives and performance on the Peabody individualised achievement test-revised: Evidence of a relation between early narrative and later mathematical ability’ First Language 24, 2, 149-183.

Transcoding and math

By Admin, on 30 January 2023

By Prof Chris Donlan

Why is the game of Bingo so popular? Perhaps because there’s a simple pleasure in matching a spoken number, e.g. “sixty six”, to its Arabic numeral form ‘66’. Spoken numbers and Arabic numerals are complementary codes. Each pair of items is a unique match. Translating from one to the other is called ‘transcoding’, and it’s a feature of everyday life. If someone asks you the time, you might look your phone and, without thinking, transcode 09:10 to “nine ten” or “ten past nine”. Transcoding becomes effortless, for most of us. But it has to be learned, and that learning starts early in childhood.

A recent US study found that 70% of a sample of pre-schoolers were able to choose reliably between numerals ‘36’ and ‘306’ when hearing the spoken number “thirty-six”.

Recent longitudinal studies have confirmed the essential role of early transcoding skills in the development of later arithmetic competence. In order to use the number system effectively, there is a need to understand place value, the principle whereby the position of a digit registers its value. Not only is ‘306’ greater than ‘36’, but also ‘21’ is greater than ‘12’, and ‘321’ is greater than ‘123’, etcetera. A recent Canadian study found that most children were able to apply the place-value system by the age of 6. Importantly, those who were able to read multi-digit numerals aloud (i.e. to transcode them) were most likely to apply the place value rule.

The linkage between spoken numbers and Arabic numerals is seen clearly in children’s early efforts to write multidigit numbers to dictation. For “five hundred and sixty-two” they may write ‘500602’. Here the regularities of the spoken English forms are evident in the child’s production. At this stage of learning each element of the spoken form is fully expressed. The ordering of the spoken form corresponds to the left-right structure of multi-digits and provides a scaffold for learning about place value.  However, the English number system, while transparent for transcoding hundreds (“five hundred” represents ‘5 x 100’), and semi-transparent for decades (“sixty” represents ‘6 x 10’),  presents major challenges in teen numbers where spoken forms reverse the order of their Arabic equivalents, e.g. “fourteen” for ‘14’, and sound confusingly similar to the decade forms, e.g. “forty”.

Spoken number systems vary widely between languages. Portuguese, for example, assimilates the sounds of the hundreds. The spoken form of ‘500’ is expressed as “quinhentos” instead of “cinco cem”, with consequent challenges for the learner. Many Asian languages, in contrast provide a fully transparent correspondence between spoken and Arabic forms. Some researchers view this systematicity as a significant advantage in mathematical development.

Children across the world acquire transcoding skills, many learning through informal exposure (like through the Maths@Home games). However, some individuals struggle, especially if they have learning difficulties and if the number systems to which they are exposed are not transparent. These learners may require structured exposure, building on regularities to provide a firm basis for the development of number knowledge.

Gilmore, C., Goebel S.M., Inglis M. (2018). An introduction to mathematical cognition. Abingdon: Routledge. Chapter 3, Symbolic Number, pp. 29-49.

Yuan, L., Prather, R., Mix, K.S., Smith, L.B. (2019). Preschoolers and multi-digit numbers: A path to mathematics through the symbols themselves. Cognition, 189, 89-104.

https://doi.org/10.1016/j.cognition.2019.03.013

Habermann, S., Donlan, C., Göbel, S.M.,Hulme, C. (2020) The critical role of Arabic numeral knowledge as a longitudinal predictor of arithmetic development. Journal of Experimental Child Psychology, 193, 104794. https://doi.org/10.1016/j.jecp.2019.104794

Cheung, P., Ansari, D. (2021). Cracking the Code of Place Value: The Relationship Between Place and Value Takes Years to Master. Developmental Psychology, 57, 227-240. https://doi.org/10.1037/dev0001145

By Admin, on 16 December 2022

Have you ever wondered where money comes from? Or how long we can use a paper note for?

Although you may think your child is too young for these facts, a touch of trivia can spark rich conversations and lead to further interest in knowledge about money.

Here are some facts you can discuss with your child.

• Currency is the type of money a country uses. For example, the U.S. uses the dollar, while Great Britain uses the pound.
• If you travel to another country you need to use their currency. For example, in Europe they use Euros and not pounds
• Romans used salt as a currency at one time.
• Money is made in special factories called mints.
• The first coins were minted (made) around 2,500 years ago.
• Paper money was first used in China over 1,000 years ago.
• 1p is the lowest value in coins in the UK.
• It costs more than 2.4 pennies to make 1 penny!
• Paper money isn’t made from paper but from a combination of cotton and linnen.
•  To prevent people from just making fake money the ink on paper money is very special and can even change colour (as well as being traceable and being magnetic).

Want to find out more? Here are some helpful websites:

Number Formation

By Admin, on 16 December 2022

By Tugce Cetiner

Number writing is a significant handwriting skill because it is positively related to academic performance (Dinehart & Manfra, 2013). There are different systems for number writing including the Roman numeral system and the Hindu-Arabic or Arabic system that is commonly used in the UK.

As the brain loves automaticity as that frees up thinking space to do other things (such as working out number problems whilst writing them down), it is important to always use the same formation when writing a number. For example, to write the number 7, it is necessary to start from the top and go down. This allows the creation of motor memory in the brain. Motor memory allows us to perform a specific motor task (e.g., handwriting) with minimum cognitive resources (Magill & Anderson, 2010).

photo copyright by Dr Jo Van Herwegen

When learning to write down numbers, the first thing children need is motor planning. Motor planning is the process of creating a plan to complete motor tasks before starting the task (Magill & Anderson, 2010). Motor planning includes all components of the task like “Where should I start?”, or “Which way should I draw the line?”. Due to their motor memory, children can remember all these components with minimum cognitive resources once learned how to write a number, allowing number writing to become automated. Thus, cognitive resources can instead be used for mathematical operations as well as to think about which number to write rather than how to write the number.

Automation of number writing can be achieved through increasing the repetition of practice trials. Using the correct starting point during these trials is important as it is allowed to create the correct motor memory. Moreover, using different activities such as different rhythm / song, and different sensory inputs  (e.g., writing in the air, writing with different pens or painting) also help to children to create better motor memory.

Tugce Cetiner is currently a PhD student at IOE, UCL’s Faculty of Education and Society, in the department of Psychology and Human Development. Her PhD focuses on the motor skills of autistic children. She developed a motor-based early intervention program to support the handwriting (including number formation) of young autistic children aged 4-5 years. This program can be implemented in the homes of parents of young autistic children.

References

Dinehart, L. & Manfa, L. (2013). Associations between low-income children’s fine motor skills in preschool and academic performance in second grade. Early Education & Development, 24(2), 138-161.

Tucha, O., Tucha, L., & Lange, K. W. (2008). Graphonomics, automaticity and handwriting assessment. Literacy, 42(3), 145-155.

Dinehart, L. H. (2015). Handwriting in early childhood education: Current research and future implications. Journal of Early Childhood Literacy15(1), 97-118.

Feder, K. P., & Majnemer, A. (2007). Handwriting development, competency, and intervention. Developmental Medicine & Child Neurology49(4), 312-317.

Magill, R., & Anderson, D. (2010). Motor learning and control. New York: McGraw-Hill Publishing.

Lage, G. M., Ugrinowitsch, H., Apolinário-Souza, T., Vieira, M. M., Albuquerque, M. R., & Benda, R. N. (2015). Repetition and variation in motor practice: a review of neural correlates. Neuroscience & Biobehavioral Reviews, 57, 132-141.

Different types of numbers

By Admin, on 16 December 2022

Did you know there are many different types of numbers?

Your child will be learning about these as they go through the curriculum, so the list below will hopefully help you as a parent to support your child’s number knowledge journey.

• Natural Numbers.

Any numbers that are used for counting or ordering. These include cardinal numbers used for counting and ordinal numbers used for ordering items (e.g., third in a row).

• Whole Numbers

The numbers that include natural numbers and zero but are not a fraction or decimal.

• Integers

A counting number, zero, or the negative of a counting number but cannot be a fraction or decimal. (E.g., -3, -2, -1, 0, 1, 2, 3).

• Rational Numbers

Numbers that can be expressed as a fraction. (E.g., 1, 4/4, 1.0).

• Irrational Numbers.

Numbers that cannot be expressed as a fraction. (E.g., Π, √2).

• Real numbers

Any number that we can think of, except complex numbers, is a real number. It includes rational and irrational numbers.

• Complex numbers.

A complex number is the sum of a real number and an imaginary number. https://www.cuemath.com/numbers/complex-numbers/

Then you also have

• Positive numbers: real numbers that are greater than zero
• Negative numbers: real numbers that are smaller than zero.
• Odd numbers: Number that cannot be divided into two parts equally
• Even numbers: numbers that can be divided by 2.
• Prime numbers: numbers that only have two factors: 1 and itself. These numbers can only be divided by themselves and by 1. (e.g., 5, 7, 11, 13, …)

Mathematical Vocabulary

By Admin, on 16 December 2022

Mathematics has its own vocabulary that children have to learn. For example, they need to learn the number names such as zero, one, two ,three in English. In addition, children need to learn what different symbols mean as well as learn about specific concepts (like pi or hexagon). This is also referred to as number talk.

In addition to this, children need to learn wider concepts and words that are important for the mathematical development as they allow children to comprehend and participate in mathematical activities, which is often referred to as mathematical or math language. Mathematical language is important when learning about number, shape, size, capacity, spatial relationships, time, money and many other aspects of maths.

Below is a table with words that are important for children’s maths language.

 Area Example Numbers One, three, five, seven, ten, eleven, fifteen… Cardinality Four more left, two plates for us, how many, one in the fridge… Ordinality First, second, third, fourth… next, last one,… Magnitude + magnitude comparison Some, more, a lot of, any, many, a bit of, a little bit, same, less, every, enough, as many as big as, smaller than, larger than, greater Math Operations/Arithmetic Minus, add, in addition, moreover, in sum… Fractions Half, whole, complete, one quarter, two quarters, piece, one half, unequal, Spatial Relationship (including Distance/ Location) In, out, on, under, above, middle, up, down, front, below, back, far, near… Size (including height, weight, length) Big, small, long, short, heavy, light, thin, thick Shapes Square, circle, triangle, rectangle, oval, star Round, dot, spot, line, circle, rectangle, square, hexagon, pentagon, oval, triangle, diamond, sphere, cylinder, cuboids, pyramid. Money How many, how much, cost, price, pounds, pence, dollar, pennies, Volume/ Capacity Full, empty, half, a little, more, the same… Classifier Sheet, piece, cup, bag, slice, glass Time and age One year old, four years old… Two o’clock, twelve o’clock, seven thirty, two thirty… Others

The development of mathematical vocabulary is important for young children as its use is necessary for them to reason and to understand maths. For example, when children learn that the words “more” and “less” can be used to describe number, they have a way to verbally explain the differences between a basket with ten apples and a basket with 5 apples. Studies have shown that there is a positive correlation between preschool-aged children’s number skills and their math vocabulary over and above their general vocabulary (Purpura & Reid, 2016).

Try and highlight mathematical concepts in your everyday environment (the Maths@home activities can help you with this) as studies have shown that parents’ use of number talk is significantly associated with children’s early math skills (Elliott et al. (2017) and the more mathematical language children hear at school and at home, the more likely it is that they have higher mathematical skills.

Also reading story books with your child can help develop their mathematical language as well as their mathematics vocabulary. Especially books that explain numbers and how they relate to each other might help children “mathematize” or understand everyday situations in mathematical terms. If you want to know more about how narratives can help develop your child’s mathematical language, read our blog on maths and narratives here.

References:

Elliott, L., Braham, E. J., & Libertus, M. E. (2017). Understanding Sources of Individual Variability in Parent’s Number Talk with Young Children. Journal of Experimental Child Psychology, 1-15.

Purpura, D. J., & Reid, E. E. (2016). Mathematics and Language: Individual and Group Differences in Mathematical Language Skills in Young Children. Early Childhood Research Quarterly, 259-268.

Purpura, D. J., Napoli, A. R., & King, Y. (2019). Development of mathematical language in preschool and its role in learning numeracy skills. In D. C. Geary, D. B. Berch, & K. M. Koepke (Eds.), Cognitive foundations for improving mathematical learning (pp. 175–193). Elsevier Academic Press. https://doi.org/10.1016/B978-0-12-815952-1.00007-4

Turan, E. & De Smedt, B. (2022) – Mathematical language and mathematical abilities

in preschool: A systematic literature review. Educational Research Review 36, 100457

.

Maths and measurements

By Admin, on 17 May 2021

At the end of the Second World War, a number of different systems of measurement were in use throughout the world. In 1960, the 11th General Conference on Weights and Measures synthesised the results of a 12-year study and created a new system that was named the International System of Units, abbreviated SI from the French name, Le Système International d’Unités. The SI is the only system of measurement with an official status in nearly every country in the world, with some countries still using different measurement systems, such as the Imperial measurement system used in the UK.

Table 1 shows the units of measurements and some derived units for length, mass, and volume in the two systems:

 International System of Units (SI) Imperial System Length Metre, centimetre, millimetre, kilometre inch, feet, yard, mile Mass Kilogram, gram, ton pound, ounce, stone Volume Litre, millilitre pint, gallon

Table 1. Units of measurements in different measurement systems.

Your child might be too young to learn all of these yet. However, your child will hear these measures being used all of the time in their daily lives. Showing your child how these are used in your everyday life and how they relate to each other (how many centimetres in a meter, how many millimetres in a foot) will help your child develop a full understanding of how and when we use these words. Moreover, you might want to create, with your child, visual resources to support their understanding of measurements in different systems and their relationships (Figure 1 and 2).

Figure 2

Figure 1 and Figure 2. Visual resources to support your child’s understanding of measurements.

Capacity, volume and more mathematical concepts

By Admin, on 17 May 2021

Mathematics is a term that is often used as if it is one thing. However, the Greek origin of the word actually refers to ‘learning or knowledge’ and includes a number of things, including quantity (numbers), algebra (structure), space (geometry) and analysis (change). As such there are a number of concepts that children need to learn.

When it comes to measurement there are two concepts that are often confused: volume and capacity. They are both properties of three-dimensional objects. Three dimensional objects can be a cube, a cone, a cylinder etc.

Volume is the space that a three-dimensional object occupies or contains. For example, the volume of a cube that is 3 cm by 3 cm by 3 cm is 27 cm3 (3 x 3 x 3 or 33). As you can see in the drawing below it is the space that it occupies.

Capacity, on the other hand, is the property of a container and describes how much a container can hold. So, when we refer to a measuring jug or a glass/ beaker or mug and how much liquid it can hold, we should refer to the capacity of it.

Number line knowledge

By Admin, on 17 May 2021

Have you ever thought about how children represent numbers in their head when they learn to count?

The dominant theory is that numbers are stored along a mental number line, with small numbers associated with the left-hand-side of space and large numbers associated with the right (for languages where one reads from left to right). Just like a tape measure.

When children are young and they learn numbers, the tape measure in their head is not yet very accurate and their idea of how numbers relate to each other might be incorrect. For example, whilst the distance (2) between number 1 and number 3 is the same as between numbers 7 and 9, when asked to place numbers on a blank number line, young children might place 1 and 3 more far away than 7 and 9 (Figure 1).

 A. 1     2     3     4 5 6 7 8 9 10 B. 1     2     3     4     5     6     7     8     9     10

Figure 1. Line A shows the representation of a compressed number line, typical of young children.

Line B shows the representation of a developed number line.

The more children learn how numbers relate to each other, the more their number line will develop. It has been shown that children who have a firm mental number line are better at manipulating numbers (add and subtract numbers but also multiplicate and divide) and, as a result, they have better mathematical abilities.