MENTAL STRATEGIES & W RITTEN S TRATEGIES IN MATHS Presented by Dot Shea

A CKNOWLEDGEMENT The majority of the information about Mental Strategies I am presenting today has been taken from the following text: Number Talks Helping children build mental math and computation strategies. By Sherry Parrish Produced by Math Solutions

W HY TEACH M ENTAL C OMPUTATION 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.

T HE 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.

B ENEFITS 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.

W RITTEN S TRATEGIES 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

M ENTAL V W RITTEN 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

A DDITION S TRATEGIES 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

S UBTRACTION 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 Hundred board- -9, -29

M ULTIPLICATION S TRATEGIES 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

D IVISION Repeated Subtraction or sharing/dealing out Partial quotients Multiplying up Proportional Reasoning Classroom clip- Year divided by 8

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