MENTAL STRATEGIES &

WRITTEN STRATEGIESIN

MATHS

Presented by

Dot Shea

ACKNOWLEDGEMENT

The majority of the information about Mental Strategies I am presenting today has been taken from the following text:

Number TalksHelping children build mental math and

computation strategies.By

Sherry ParrishProduced by Math Solutions

WHY TEACH MENTAL COMPUTATION Our Classrooms are filled with students and adults who think

of mathematics as rules and procedures to memorise without understanding the numerical relationships that provide the foundation of these rules.

While our current understanding and approaches to Maths may have been sufficient during earlier time periods, today’s information age requires students and adults to develop a deeper understanding of Maths.

Our students must have the ability to reason about quantitative information, process number sense and check for the reasonableness of solutions and answers.

We need people who are able to discern whether numbers make sense and are applicable to specific situations and who are capable of communicating solutions to problems.

Today’s mathematics curriculum and instruction focuses on preparing students to be mathematically proficient and compute accurately, efficiently and flexibly.

THE ROLE OF MENTAL MATHS

Mental computations is a key component to enable students to build on number relationships to solve problems instead of relying on memorized procedures.

When students approach problems without paper and pencil they are encouraged to rely on what they know and understand about the numbers and how they are interrelated.

Mental computation causes them to be efficient with the numbers to avoid holding numerous quantities in their head.

BENEFITS OF SHARING AND DISCUSSING COMPUTATION

STRATEGIES.

Students have the opportunity to: 1. Clarify their own thinking 2. Consider and test other strategies to see if they are

mathematically logical 3. Investigate and apply mathematical relationships 4. Build a reporte of efficient strategies. 5. Make decisions about choosing efficient strategies

for specific problems Note: For classroom conversations to occur when

discussing mental computation strategies the teachers role needs to shift from being the sole authority in imparting information and confirming correct answers to assuming the interrelated roles of facilitator, questioner, listener and learner.

WRITTEN STRATEGIES Some students have difficulty processing information

mentally and need to use written strategies to work out a problem

Some more complex or larger operations require students to use a written strategy rather than a mental strategy.

Students need to be shown how we process written strategies differently than mental strategies. ( starting with the ones versus starting with the largest part of the number.

Written strategies need to be taught kinaesthetically and visually using hands on materials to explain the concept – not just learnt by rote, eg addition with regrouping.

Students need to be shown a variety of written strategies so they can choose the one that suits their way of thinking, eg Multiplication- standard algorithm, split system, lattice method

MENTAL V WRITTEN

So students can distinguish between using a mental strategy – then writing down your thinking and an actual written strategy it is best to write a

Mental Strategy- horizontally Written strategy - vertically

ADDITION STRATEGIES

Counting all /Counting on Doubles/ near Doubles Making Ten Making Landmark or Friendly Numbers Breaking each Number into its Place Value Compensation Adding up in chunks

Classroom clip-Year 2- Ten frames 8+6 Hundred boards

SUBTRACTION STRATEGIES

Adding Up Removal or Counting back Place Value and Negative Numbers Adjusting one number to create an easier

problem Keeping a constant difference

Classroom clip- year 3 70-34 Hundred board- -9, -29

MULTIPLICATION STRATEGIES

Repeated addition or skip counting Making landmark or friendly numbers Partial product Double and halving Breaking factors into smaller factors

Classroom clip year 5 16x35

DIVISION

Repeated Subtraction or sharing/dealing out Partial quotients Multiplying up Proportional Reasoning

Classroom clip- Year 5 496 divided by 8

MONEY

Whole dollars Dollar more Rounding up/rounding down Less change in my pocket