#How do you do division problems full#

You might like to discuss the efficiency of multiplication versus repeated addition.

Be aware that some students may elect to add rather than multiply. Accept all the strategies that are elicited at this stage, recording them to reflect upon later in the unit (perhaps in a modelling book). The strategy can be written as 5 x 38 = 5 x 30 + 5 x 8 or in working form:ДЄs different strategies arise ask the students to explain why they chose to solve the problem in that way.

#How do you do division problems full#

In full the strategy might be written as 5 x 38 = 10 x 19 Solve instead 10 x 19 using doubling and halving (by doubling 5 and halving 38). In full the strategy might be written as 5 x 38 = 5 x 40 вЂ“ 5 x 2. ДЈ8 is rounded to 40 so the problem becomes 5 x 40 = 200, then 10 (5 x 2) is subtracted from the product to get 5 x 38 = 190. Note that the convention is to record the multiplier first so equations should be written as 5 x 38 =. Then ask them to share their solutions with their learning partner. Give the students an appropriate amount of thinking time.

How many kilometres has she travelled by the end of the five days?ДЄsk students to work out the answer in their head if they can and record their strategy on paper. Vanessa bikes 38 kilometres each day for five days. This will enable you to evaluate which strategies need to be focused on in greater depth as well as identifying students in your group as 'expert' in particular strategies. The purpose of this session is to explore the range of strategies that your students already use to solve multiplication and division problems. For example, fundraising for an event, preparing a class feast, and teams in waka ama may provide useful story shells. Other situations of relevance to your students might be used to capitalise on contextual knowledge and motivate ДЃkonga. The contexts for this unit include cycling, working at a fruit shop, transporting people to netball, rowing crews, and delivering pamphlets. Varying the size and complexity of numbers in the problems to cater for a range of proficiencies.Encouraging students to work in collaborative teams to develop explanation and justification strategies.Developing supportive algorithms that allow students to take progressive steps towards an answer, e.g., The ladder method of division.Using place value-based materials alongside symbols to develop both understanding and fluency with calculation methods.The learning opportunities in thisВ unitВ can be differentiatedВ by providingВ or removingВ support to students and by varying the task requirements.В Ways to differentiate include: In division both the dividend and divisor must be adjusted by the same factor. Division with factorisation can be viewed as a form of proportional reasoning. Proportional adjustment is useful when there is a вЂcommon factorвЂ™ connection between the factors in multiplication, or dividend and divisor in division, that can be used to simplify the problem such as doubling and halving or quadrupling and quartering.For example, 6 x 43 is best solved as 6 x 40 + 6 x 3. Standard place value partitioning is always a trustworthy strategy that is particularly appropriate where one or both factors are not easily rounded up.For example, 6 x 2 must be subtracted from 300 to get the product of 6 x 48. When applying tidy numbers in multiplication and division it is important to keep track of what has been changed in a problem in order to compensate (rounding and compensating).For example, 6 x 48 might be solved using 6 x 50 = 300. Tidy number strategies (rounding and compensating) are useful when number(s) in an equation are close to an easier number to work from.Useful strategies for division include proportional adjustment (with factorisation), rounding and compensating, and partitioning or вЂchunkingвЂ™.Useful strategies for multiplication include place value partitioning, rounding and compensating, proportional adjustment and factorisation.Teachers should elicit strategy discussion about problems in order to encourage students to justify their decisions about strategy selection in terms of the usefulness and efficiency of the strategy for the given problem situation.

Features of problems, particularly the numbers involved, privilege the efficiency of particular strategies.Understanding whole number place value underpins all strategies in this unit.

Students at this stage partition and recombine numbers to simplify calculations and draw on their knowledge of multiplication facts and related division facts with factors up to ten. This unit of work is useful for students working at or towards Level Four Stage 7-Advanced Multiplicative of the Number Framework). The New Zealand Curriculum requires students to understand and use a range of mental, written and digital calculation strategies to multiply and divide multi-digit whole numbers.