Mathematical goals. Starting points. Materials required. Time needed


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1 Level A1 of challege: C A1 Mathematical goals Startig poits Materials required Time eeded Iterpretig algebraic expressios To help learers to: traslate betwee words, symbols, tables, ad area represetatios of algebraic expressios; recogise the order of operatios; recogise equivalet expressios; uderstad the distributive laws of multiplicatio ad divisio over additio (expasio of brackets). This uit develops the ideas preseted i N5 Uderstadig the laws of arithmetic. Learers will eed to recall how to fid the area of simple compoud shapes made from rectagles ad simple idices, ad to uderstad the differece betwee 3 ad 3. For each learer you will eed: miiwhiteboard. For each small group of learers you will eed: Card set A Algebraic expressios; Card set B Explaatios i words; Card set C Tables of umbers; Card set D Areas of shapes; glue stick; felt tip pes; large sheet of paper for makig a poster. From 1 to hours. If your sessios are ormally shorter tha this, you ca split this sessio ito two. Level of challege: C A1 Iterpretig algebraic expressios A1 1
2 Level of challege: C A1 Iterpretig algebraic expressios Suggested approach Begiig the sessio Hold a short questio ad aswer sessio, usig miiwhiteboards, to revise how the order of operatios is represeted algebraically. Show me a algebraic expressio that meas: Multiply by 3, the add 4. Add 4 to, the multiply your aswer by 3. Add to, the divide your aswer by 4. Multiply by, the multiply your aswer by 4. Multiply by, the square your aswer. Workig i groups (1) Arrage learers i pairs or threes. Give each group Card set A Algebraic expressios ad Card set B Explaatios i words. Ask learers to take turs at matchig cards ad explaiig their reasos for each matchig. Poit out that some cards are missig. Learers will eed to make these extra cards themselves. The activity is desiged to help learers iterpret the symbols ad realise that the symbolism defies the order of operatios. Some learers may otice that some expressios are equivalet, e.g. ( + 3) ad +. Do ot commet o this at this stage. Now give learers Card set C Tables of umbers ad ask them to match these to Card sets A ad B. Some tables have umbers missig. Learers will eed to work these out. Learers will soo otice that there are fewer tables tha algebraic expressios. This is because some tables match more tha oe expressio. Allow learers time to discover this for themselves. This activity is desiged to ecourage learers to substitute ito expressios ad thus, agai, to iterpret their meaig. At this stage, they will begi to otice that several expressios are equivalet, but they may ot realise why. For learers who fiish quickly, ask them to fid out if the pairs of expressios always give the same aswer, eve whe fractios or decimals are substituted. Push them further to explai why these pairs match for all umbers. Ecourage those who struggle to substitute umbers for letters i the algebraic expressios. A1
3 Reviewig ad extedig learig (1) Ask learers to suggest reasos why differet expressios always appear to give the same aswer. (You do t eed to provide aswers yourself at this stage). Ca you geerate additioal examples of your ow? Voluteers may like to offer suggestios o the board. Leave ope the questio of why expressios are equivalet. The ext part of the sessio will take these ideas further, so they do ot eed to be resolved at this poit. (If you ru this over two sessios, this would be a good poit to break off.) Workig i groups () Begi this part of the sessio by cosiderig just the Algebraic expressios cards (Set A). Ask learers to try to remember which expressios wet together/were equivalet. If they have forgotte, they should try substitutig some umbers of their ow for. This will ecourage them to iterpret the expressios without the help of the Explaatios i words cards (Set B). Now had out Card set D Areas of shapes. Ask learers to match these with the cards i Set A Algebraic expressios. Whe learers reach agreemet, they should paste their cards oto a large sheet of paper, to make a poster. They should write o the poster why the areas show that differet algebraic expressios are equivalet. These posters may the be displayed for the fial whole group discussio. Reviewig ad extedig learig () Hold a whole group discussio to review what has bee leared durig this sessio. Ask pairs of learers to preset their posters. Use miiwhiteboards ad questioig to begi to geeralise the learig. Draw me a area that shows this expressio: 3(x + 4). Write me a differet expressio that gives the same area. Draw me a area that shows this expressio: (4y). Write me a differet expressio that gives the same area. Draw me a area that shows this expressio: (z + 5). Write me a differet expressio that gives the same area. Level of challege: C A1 Iterpretig algebraic expressios A1 3
4 Level of challege: C A1 Iterpretig algebraic expressios What learers might do ext Further ideas Draw me a area that shows this expressio: w +. Write me a differet expressio that gives the same area. What rules have you foud for rearragig expressios? Ask learers if they ca draw diagrams that might show a set of expressios cotaiig subtractios, such as the followig: (x 3) (x + 3)(x 3) x 9 (x 3) x x + 9 Learers might cotribute their ow questios as a homework activity ad evaluate the work of other learers as a followup. This activity uses multiple represetatios to deepe uderstadig of algebra. This type of activity may be used i ay topic where a rage of represetatios is used. Examples i this pack iclude: SS SS7 S5 S Represetig 3D shapes; Trasformig shapes; Iterpretig bar charts, pie charts, box ad whisker plots; Iterpretig frequecy graphs, cumulative frequecy graphs, box ad whisker plots. A1 4
5 A1 Card set A Algebraic expressios E1 E E E4 3 + A1 Iterpretig algebraic expressios E5 ( + 3) E + E7 E8 (3) ( + ) E E E11 E1 + + E13 E14 A1 5
6 A1 Card set B Explaatios i words W1 W3 Multiply by two, the add six. Add six to, the multiply by two. W W4 Multiply by three, the square the aswer. Add six to, the divide by two. A1 Iterpretig algebraic expressios W5 Add three to, the multiply by two. W Add six to, the square the aswer. W7 Multiply by two, the add twelve. W8 Divide by two, the add six. W9 Square, the add six. W10 Square, the multiply by ie. W11 W1 W13 W14 A1
7 A1 Card set C Tables of umbers T As T As A1 Iterpretig algebraic expressios T3 T As As T5 T As As T7 T As 4 5 As A1 7
8 A1 Card set D Areas of shapes A1 A 3 A1 Iterpretig algebraic expressios A3 A4 A5 A A7 A8 1 A1 8
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