It’s taken me a while to get back to this, but here we are again, at last! It’s time to move on from KS1 English (see Archaeology & the National Curriculum Part 1, Part 2 and Part 3) and move on to mathematics (I can hear the whoops of joy from here!).

So, we begin with Ma2, Using and applying number.

The first section is all about problem-solving, and the curriculum states that children should be taught to…

*a. approach problems involving number, and data presented in a variety of forms, in order to identify what they need to do.*
*b. develop flexible approaches to problem solving and look for ways to overcome difficulties*
*c. make decisions about which operations and problem-solving strategies to use*
*d. organise and check their work.*

Archaeology very naturally presents opportunities through which each of these objectives can be taught. For example, simple counting and sorting activities could be arranged, using objects. Archaeologists always want to know how many artefacts they have found, or how big something is. After excavating artefacts from a trench as part of a mini-dig, children can make decisions about which strategies to apply to find out the answers to such questions as: How many artefacts did you find? How many pieces of pottery did you find with decoration? How many are left? And so on. Pictures, pictographs, simple graphs and charts can also be used, as well as actual artefacts. Given a certain amount of freedom, children may decide it is easier to cut out pictures or move pieces of pottery about and put them into piles for sorting and counting. They can then be asked to check their own and others work. During a site visit, children can be asked to find out how big something is – a wall, a bank or other structure – and can be encouraged to think about how they find out. In the first place, children can use the number of strides it takes to walk, or the number of children lined up, and then move on to using standard measures. In fact, this could be a good activity for explaining why we use standard measures.

Whilst partaking in these activities children can be encouraged to…

*e. use the correct language, symbols and vocabulary associated with number and data,*
and
*f. communicate in spoken, pictorial and written form, at first using informal language and recording, then mathematical language and symbols, *such as more, less or fewer, add, plus, take way.

They can create charts using pictographs, and progress to writing number sentences for the calculations they have been doing as part of the problem-solving activities. This could be done as part of creating an ‘archaeological report’ or a guide to an historical or archaeological site.

Creating such a report or guide also allows the opportunity for children to *g. present results in an organised way. *In addition, the questions posed as part of the problem solving could be used as statements, such as “there are more decorated pieces of pottery than plain pieces of pottery” in order to address the learning objective *h. understand a general statement and investigate whether particular cases match it.* Different trenches could have different numbers of decorated and plain ware, and the children can find out which of the trenches match this statement. Through talking to children about what they have been doing they can be asked to *i. explain their methods and reasoning when solving problems involving number and data.*

In terms of counting (*2 Numbers and the number system*), depending on which stage children are at, the numbers of objects can be adjusted, or part of a site to be measured can be carefully chosen so that children can learn to *a. count reliably up to 20 objects at first and recognise that if the objects are rearranged the number stays the same; be familiar with the numbers 11 to 20; gradually extend counting to 100 and beyond.*

Historical and archaeological contexts can be used in order to teach children how to…

* b. create and describe number patterns; explore and record patterns related to addition and subtraction, and then patterns of multiples of 2, 5 and 10 explaining the patterns and using them to make predictions; recognise sequences, including odd and even numbers to 30 then beyond; recognise the relationship between halving and doubling.*

This can be done by simply using pictures of figures and objects from the past. For example, a laminated plan of Roman baths showing each of the different rooms (e.g. tepidarium, caldarium, frigidarium) could be used with moveable pictures of Romans. At first, 2, then 5, then 10 Romans could be put in each room, and children asked to say how many are there all together. This could be adapted for any period – Victorian school children in classrooms, Ancient Greeks competing in the Olympic Games, houses burnt in the Great Fire of London, and so on. Of course, this could also be done via taking part in real or mini-excavations, extending the exercises described above regarding problem solving and using actual objects from the past.

Following on from 2a above, children can be taught how to…

*c. read and write numbers to 20 at first and then to 100 or beyond; understand and use the vocabulary of comparing and ordering these numbers; recognise that the position of a digit gives its value and know what each digit represents, including zero as a place-holder; order a set of one and two-digit numbers and position them on a number line and hundred-square; round any two-digit number to the nearest 10. *

For example, a basic timeline can be used where events are given a number rather than a date at this stage, which children can then put in the correct order. Children can round numbers to the nearest 10 using large numbers of pottery sherds – again this could be done in order to include mathematical data in an archaeological report.

All of the above can address *3. Number operations and the relationships between them. *Whilst children are addressing the problems as suggested above, and are engaging with counting and arranging artefacts or pictures, they will begin to…

*a. understand addition and use related vocabulary; recognise that addition can be done in any order; understand subtraction as both ‘take away’ and ‘difference’ and use the related vocabulary; recognise that subtraction is the inverse of addition; give the subtraction corresponding to an addition and vice versa; use the symbol ‘=’ to represent equality; solve simple missing number problems [for example, 6 = 2 + ? ],*
and
*b. understand multiplication as repeated addition; understand that halving is the inverse of doubling and find one half and one quarter of shapes and small numbers of objects; begin to understand division as grouping (repeated subtraction); use vocabulary associated with multiplication and division.*

Using objects, such as pottery sherds or other artefacts, will also allow children to see these relationships quite clearly, appealing to a number of learning styles and a range of abilities.

Again, the types of activities already suggested, can be the context in which children can be taught mental maths and…

*c. develop rapid recall of number facts: know addition and subtraction facts to 10 and use these to derive facts with totals to 20, know multiplication facts for the x2 and x10 multiplication tables and derive corresponding division facts, know doubles of numbers to 10 and halves of even numbers to 20*
* d. develop a range of mental methods for finding, from known facts, those that they cannot recall, including adding 10 to any single-digit number, then adding and subtracting a multiple of 10 to or from a two-digit number; develop a variety of methods for adding and subtracting, including making use of the facts that addition can be done in any order and that subtraction is the inverse of addition*
* e. carry out simple calculations of the form 40 + 30 = ?, 40 + ? = 100, 56 – ? = 10; record calculations in a number sentence, using the symbols +, -, x , ÷ and = correctly [for example, 7 + 2 = 9].*

In addition, the above also provides the context in which children can be taught how to *4. Solve numerical problems, *and allow children the chance to…

*a. choose sensible calculation methods to solve whole-number problems (including problems involving money or measures), drawing on their understanding of the operations*
and
*b. check that their answers are reasonable and explain their methods or reasoning.*

Again, activities already outlined, in this case compiling data for an archaeological report or similar, gives the context for children to be taught to…

*5. a. solve a relevant problem by using simple lists, tables and charts to sort, classify and organise information,*
and
*b. discuss what they have done and explain their results.*

Of course, many things inter link, so there is often repetition, but I did say I wanted to be thorough! If any of you out there has addressed any of these learning objects using archaeology, heritage or history as a context, and would like to share what you have done, I would love to hear from you.

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