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Mental Mathematics

Aims. To consider the purpose of the starter in the daily maths lessonTo consider possible content of the starterTo look at some starter activities . Background and context . Concern that children's mental calculation skills and recall of facts were generally weak. Framework referred to the first

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Mental Mathematics

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    1. Mental Mathematics

    2. Aims To consider the purpose of the starter in the daily maths lesson To consider possible content of the starter To look at some starter activities NB mental skills need to be taught in the main part of the lesson!NB mental skills need to be taught in the main part of the lesson!

    3. Background and context Concern that children’s mental calculation skills and recall of facts were generally weak. Framework referred to the first part of the lesson as: • Oral work and mental calculation (about 5 to 10 minutes) (Whole-class work to rehearse, sharpen and develop mental and oral skills) Focus was on strengthening children’s oral and mental skills through regular daily practice. 1999 Framework lists a number of activities that might form part of this oral work and mental work. Oral and mental ‘starter’ and was often judged by Ofsted to be the strongest part of mathematics lessons. Successful starters were short, focused activities that prepared the children for the main teaching activity by getting them to think mathematically. These ‘starters’ were objective-led activities that supported children’s learning and moved it on. OFSTED now often say that the starter is the worst part of the lesson. Discuss.OFSTED now often say that the starter is the worst part of the lesson. Discuss.

    4. Current situation Range of purposes and related activities has increased. Focus on oral and mental calculation has widened and become a vehicle for teaching a range of mathematics. Too often, the ‘starter’ has become an activity extended beyond the recommended 5 to 10 minutes. In these situations, there can be more teacher talk than there is oral and mental work Some evidence that the focus on oral and mental calculation has been lost and needs to be reinvigorated. The ‘starter’ to a lesson remains an effective way of engaging children at the start of a lesson through a brisk, well-focused activity that helps to secure children’s knowledge and sharpens their skills. Some evidence that mental work is only done in the starter Some evidence that teachers see mental mathematics as giving children a test

    5. Starter Activities may continue to be rehearsal activities. Rehearsal and practice are designed to strengthen knowledge and skills. Important that children have sufficient opportunity to consolidate all the mathematics teaching they have received. Mental work fulfils many other purposes. See handout on Y6 Common Y6 mental test paper themesSee handout on Y6 Common Y6 mental test paper themes

    6. The six Rs of oral and mental work Rehearse Recall Refresh Refine Read Reason Handout 6 Rs in the mental starterHandout 6 Rs in the mental starter

    7. Rehearse Practise and consolidate existing skills. (usually mental calculation skills, including using and applying) Vocabulary and language of number Properties of shapes or describing and reasoning. Interpret words such as more, less, sum, altogether, difference, subtract; find missing numbers or missing angles on a straight line (demonstrate ITP “Calculating Angles”); say the number of days in four weeks or the number of 5p coins that make up 35p; describe part-revealed shapes, hidden solids; (do a hide and reveal activity) describe patterns or relationships; explain decisions or why something meets criteria. Interpret words such as more, less, sum, altogether, difference, subtract; find missing numbers or missing angles on a straight line (demonstrate ITP “Calculating Angles”); say the number of days in four weeks or the number of 5p coins that make up 35p; describe part-revealed shapes, hidden solids; (do a hide and reveal activity) describe patterns or relationships; explain decisions or why something meets criteria.

    8. Recall To secure knowledge of number facts, (developing speed and accuracy) Recall quickly names and properties of shapes Recall quickly units of measure or types of charts or graphs to represent data. Count on and back in steps of constant size; recite the 6-times table and derive associated division facts; (demonstrate “Number Dials” ITP) name a shape with five sides or a solid with five flat faces; (handout polygons) list properties of cuboids; state units of time and their relationships. Count on and back in steps of constant size; recite the 6-times table and derive associated division facts; (demonstrate “Number Dials” ITP) name a shape with five sides or a solid with five flat faces; (handout polygons) list properties of cuboids; state units of time and their relationships.

    9. Refresh To draw on and revisit previous learning To assess, review and strengthen children’s previously acquired knowledge and skills Return to aspects of mathematics with which the children have had difficulty Draw out key points from learning. Refresh multiplication facts or properties of shapes and associated vocabulary; find factor pairs for given multiples; return to earlier work (e.g. identifying fractional parts of given shapes) (this could include curricular targets) locate shapes in a grid as preparation for lesson on coordinates; refer to general cases and identify new cases. Refresh multiplication facts or properties of shapes and associated vocabulary; find factor pairs for given multiples; return to earlier work (e.g. identifying fractional parts of given shapes) (this could include curricular targets) locate shapes in a grid as preparation for lesson on coordinates; refer to general cases and identify new cases.

    10. Refine To sharpen methods and procedures Explain strategies and solutions Extend ideas; develop and deepen the children’s knowledge Reinforce their understanding of key concepts Build on earlier learning so that strategies and techniques become more efficient and precise Find differences between two two-digit numbers, extend to three-digit numbers to develop skill; find 10% of quantities, then 5% and 20% by halving and doubling; use audible and quiet counting techniques to extend skills; give coordinates of shapes in different orientations to hone concept; review informal calculation strategies. Curricular targets! Find differences between two two-digit numbers, extend to three-digit numbers to develop skill; find 10% of quantities, then 5% and 20% by halving and doubling; use audible and quiet counting techniques to extend skills; give coordinates of shapes in different orientations to hone concept; review informal calculation strategies. Curricular targets!

    11. Read To use mathematical vocabulary To interpret images, diagrams and symbols correctly To read number sentences and provide equivalents To describe and explain diagrams and features involving scales, tables or graphs To identify shapes from a list of their properties To read and interpret word problems and puzzles To create their own problems and lines of enquiry. Tell a story using an interactive line graph, alter the chart for children to retell the story; (use “Line Graph ITP”) start with a number sentence (e.g. 2 + 11 = 13) children generate and read equivalent statements for 13; read values on scales with different intervals; (use “Measuring Scales” or “”Measuring Cylinder” ITPs) read information about a shape and eliminate possible shapes; (polygon handout) set number sentences in given contexts; (32 ÷4 write a problem to go with this calculation) read others' results and offer new questions and ideas for enquiry. Tell a story using an interactive line graph, alter the chart for children to retell the story; (use “Line Graph ITP”) start with a number sentence (e.g. 2 + 11 = 13) children generate and read equivalent statements for 13; read values on scales with different intervals; (use “Measuring Scales” or “”Measuring Cylinder” ITPs) read information about a shape and eliminate possible shapes; (polygon handout) set number sentences in given contexts; (32 ÷4 write a problem to go with this calculation) read others' results and offer new questions and ideas for enquiry.

    12. Reason To use and apply acquired knowledge, skills and understanding To make informed choices and decisions To predict and hypothesise To use deductive reasoning to eliminate or conclude To provide examples that satisfy a condition always, sometimes or never and say why. Sort shapes into groups and give reasons for selection; discuss why alternative methods of calculation work and when to use them; decide what calculation to do in a problem and explain the choice; deduce a solid from a 2-D picture; use fractions to express proportions; draw conclusions from given statements to solve puzzles. Sort shapes into groups and give reasons for selection; discuss why alternative methods of calculation work and when to use them; decide what calculation to do in a problem and explain the choice; deduce a solid from a 2-D picture; use fractions to express proportions; draw conclusions from given statements to solve puzzles.

    14. Activities for Mental Work? Show smart board file Show smart board file

    15. Target boards How could this be used at the level at which you are teaching? E.g. finds pairs that sum to 100; double them all; add 20 to them all; Target boards How could this be used at the level at which you are teaching? E.g. finds pairs that sum to 100; double them all; add 20 to them all;

    16. Demonstrate Excel spreadsheet “Find the Multiple”Demonstrate Excel spreadsheet “Find the Multiple”

    17. Useful Strategies for developing mental skills Ensure children have understood a question by: -repeating the question more slowly -rephrasing the question -presenting the question visually -asking the children to put the question into their own words -giving an example of a possible answer -give them thinking time Help all children to answer by asking them to: -say an answer in unison -show an answer with their fingers -point to a number on a grid, target board or line -asking questions with a range of possible answers -waiting before expecting an answer -getting the children to tell their partner the answer -giving children digit cards to hold up -writing answers on personal whiteboards -taking an answer but asking the children to discuss whether it’s correct

    18. Key messages Cover all areas of maths Think of the 6Rs Involve all children 2 or 3 sessions in a week should be to do with your target area in maths Counting and rapid recall should occur every day

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