Prenumber What is it It is early concepts

Prenumber • What is it? It is early concepts and beginning processes (skills) including: 1. 2. 3. 4. 5. 6. determining attributes, matching by attributes, sorting by attributes, comparing attributes, ordering attributes and patterning. • Why are these crucially important? They provide the prerequisite knowledge to commence the study of number. 1 EDMA 202/262 Prof Romina Jamieson-Proctor

1. Determining Attributes Teach children to: • Become observant using all five senses. • Recognise and name attributes such as colour, shape, size, mass or weight, texture, sound, taste, type of material, function. • Notice and recognise likeness and differences between objects based on their attributes e. g. , same. . . different. . . 2 EDMA 202/262 Prof Romina Jamieson-Proctor

• Use words related to all 5 senses not just sight. “Feels like…sounds like…tastes like…smells like…” … consider a “feely box” • Geometry (shapes) has critical attributes that must be discussed and focused on e. g. , a �has 3 sides and 3 angles; size and colour don’t matter when we are deciding if a shape is a �or not (consider equilateral vs scalene vs isosceles triangles) • Thus, there are might have attributes and there are must have attributes. A quadrilateral must have 4 sides. It might have 4 equal sides and 4 ninety degree angles. In which case it is also a square. 3 EDMA 202/262 Prof Romina Jamieson-Proctor

• Objects have same and different attributes e. g. , same colour / different shape; same thickness / different shape; same colour / same shape / different size … see the attribute blocks short demonstration video on LEO. • Look for sameness and difference in: 1. 2. 3. 4. 5. real objects Cross-curricular skills pictures words (cat / mat) sounds (p / g / d / b) and numerals (9 / 6 / MCIV / MCV) EDMA 202/262 Prof Romina Jamieson-Proctor 4

2. Matching by attributes • When matching, use only 2 objects • Match for sameness or likeness • Find objects that are the same in some way • Describe the sameness • Find objects that are completely the same (identical)…pairs of socks, dessert spoon vs soup spoon, grocery items, identical twins, symbols (signs, letters, numerals) 5 EDMA 202/262 Prof Romina Jamieson-Proctor

Find the button or key that is the same as these shapes • Match: * object to object * object to outline (button/keys to outlines) * picture to picture (pictures of children) * picture to outline • Involve all 5 senses – a variety of activities • Use puzzles & games (matching cards, I Spy, Duplo) 6 EDMA 202/262 Prof Romina Jamieson-Proctor

3. Sorting by attributes • Involves 3 or more objects • Sort or group according to a defined attribute e. g. , all � s, all red objects, all (red triangles) • Sort by 1 attribute, then 2 attributes, then 3 attributes etc. Play the 1 difference sorting game with Attribute Blocks. • Use a sorting grid to structure a 2 attribute sort: 7 EDMA 202/262 Prof Romina Jamieson-Proctor

Sorting grid example – colour and shape attributes: Red Blue Colours � Shapes 8 EDMA 202/262 Prof Romina Jamieson-Proctor

The 3 Ds of sorting: 1 Decide the attribute to sort on e. g. , colour, shape, size, texture, thickness, sound etc. ; 2 Do the sort … make the smaller groups from the large group; 3 Describe the sort… “I have sorted all the _______ into groups by their ____. These are _____ and these are ______. ” 9 EDMA 202/262 Prof Romina Jamieson-Proctor

4. Comparing • Compare 2 objects at a time More than 4 but less than 8 • Look for more or less of a mathematically significant attribute …long/longer… few/more. . . heavy/heavier…light/heavy… What about red and more red? ? ? Is colour mathematically significant? • “I am taller than my brother” “I am shorter than my mother” An object can be 2 different things at once. 10 EDMA 202/262 Prof Romina Jamieson-Proctor

Less than 6, more than 3 11 EDMA 202/262 Prof Romina Jamieson-Proctor

5. Ordering by attributes • Order more than 2 objects at a time • Based on an increase or decrease of an attribute • Order 3 things first before ordering more than 3 • Create opportunities to order familiar objects e. g. , Post Office corner (envelopes and cylinders ordered according to size), Shop corner (cans/packets ordered according to volume, weight, height, diameter) 12 EDMA 202/262 Prof Romina Jamieson-Proctor

• Order familiar events e. g. , days of the week, months of the year, birthdays of the class, lessons in the school day or happenings in a regular day (rise, dress, breakfast, leave for school…) • Order of tasks/events such as putting on shoes and taking shoes off again helps to understand algebraic equations! 2 x + 3 = 13 “What comes first/next/last? What do we have to undo first to solve for x? ” 13 EDMA 202/262 Prof Romina Jamieson-Proctor

6. Patterning • Patterning weaves prenumber mathematics concepts together (it requires matching, sorting, comparing, ordering skills) • It relies on the repetition of some recognisable feature e. g. , 1, 2, 3 or 1, 2, 1, 2 • We can create visual, auditory and movement patterns • Practise copying a pattern, extending a pattern, creating a pattern, filling in the missing elements of a pattern 14 EDMA 202/262 Prof Romina Jamieson-Proctor

• Look for patterns • Build patterns (use familiar objects, substituted materials e. g. , blocks, sticks, counters) • Copy a pattern (beads on fishing line) • Create own pattern (others copy it) • Extend a pattern (keep the pattern going) • Insert the missing element into a pattern • Translate a pattern (change mode of pattern from blocks to claps to colours etc) becomes clap hop jump 15 EDMA 202/262 Prof Romina Jamieson-Proctor

Repeating core elements of a pattern • Ask: “What is repeating? ” (What is the core element? ) • Ask: “What comes next? ” (Repeat the core element) 123 123______ cat cat dog dog __ __ 16 EDMA 202/262 Prof Romina Jamieson-Proctor

Growing the core element to create larger elements x y y y __ __ __ 17 EDMA 202/262 Prof Romina Jamieson-Proctor

Establishing the relationship between elements • Use the function machine – for older chn: 10 8 in ? ? ? out 40 20 What happened in each case? What rule could we use to describe the relationship between the in and out numbers? How does the rule change when we go from out to in? 18 EDMA 202/262 Prof Romina Jamieson-Proctor

Function machine with real world objects not symbols in ? ? ? out What happens when the button goes into the function machine? How many buttons would come out if we put 2 buttons in? What does the machine do if we go from out to in? 19 EDMA 202/262 Prof Romina Jamieson-Proctor

Why is patterning very important? • Chn. use their senses to learn by exploring • Requires chn. to organise and remember mathematics ideas and relationships • Facilitates creativity • It’s fun! • It encourages risk taking which is a necessary ingredient of problem solving • Is an essential prerequisite to later mathematics e. g. , algebra is the mathematical statement of a pattern. 20 EDMA 202/262 Prof Romina Jamieson-Proctor