Calculations with whole numbers, simple ratio and direct proportion

Transcription

1 Externally assessed by OCR Unit Title: Level: 1 Credit value: 5 Guided learning hours: 50 Unit reference number: Calculations with whole numbers, simple ratio and direct proportion T/504/5990 Unit purpose and aim On completion of this unit the learner will be able to add and subtract whole numbers up to 100,000, without using a calculator, multiply and divide whole numbers with up to three digits and round whole numbers to the power of ten. They will have gained an understanding of square numbers, simple ratio and proportion and be able to solve multi-step problems expressed in word and in simple algebraic form. The learner will be able to apply this knowledge in everyday situations, such as interpreting numerical information published in the media, scaling quantities found in recipes and ordering quantities of goods. Learning Outcomes Assessment Criteria Additional Information The Learner will: 1 Be able to recognise the value of digits in whole numbers up to ten million The Learner can: 1.1 State the value of each digit in a seven-digit whole number 1.2 Order whole numbers in numbers up to sevendigits in length Read, write, order and compare numbers, including large numbers N1/L1.1 Read, write, order and compare numbers in words and figures, including large numbers Order rational numbers Understand and use whole 2 Be able to add and subtract whole numbers of any size, without using a calculator 2.1 Add two numbers with answers in the range zero to 100, Subtract two numbers with answers in the range zero to 100,000 N1/L1.3 Add, subtract, multiply and divide using efficient written and mental methods OCR

2 Understand and use whole 3 Be able to multiply whole numbers with up to and including threedigits by whole numbers from 1 to 99, 100 and Be able to divide whole numbers with up to and including three digits by whole numbers from 1 to 99 and Multiply whole numbers in the range of 1 to 999: single-digit numbers two-digit numbers, including multiples of Divide two-digit in the range 1 to 999 by: single-digit numbers two-digit numbers including multiples of N1/L1.3 Add, subtract, multiply and divide using efficient written and mental methods N1/L1.4: Multiply and divide whole numbers by 10, 100 and 1000 N1/L1.5: Recall multiplication facts up to 10 x 10 and make connections with division facts Understand and use whole Answers must result in whole numbers. Derive division facts from: Known multiplication facts up to 10 10; Given multiplication pairs with products up to three digits N1/L1.3: Add, subtract, multiply and divide using efficient written and mental methods N1/L1.4: Multiply and divide whole numbers by 10, 100 and 1000 N1/L1.5: Recall multiplication facts up to 10 x 10 and make connections with division facts 2 OCR 2012

3 Understand and use whole. 5 Be able to recognise factors, multiples and squares of whole numbers 6 Be able to use simple ratio and direct proportion 5.1 Use factors and partitioning in multiplication involving non-calculator methods 5.2 Identify: square numbers up to 100 multiples of 10, 50, 100, Simplify given ratios into a 1:n form 6.2 Calculate quantities which are in a given ratio (Form 1: n and n = 2, 3 or 4) 6.3 Calculate quantities using direct proportion and simple multipliers (2, 3 and 4) N1/L1.6 Recognise numerical relationships, e.g. identify multiples and square numbers Use the concepts and vocabulary of factor, multiple, common factor, highest common factor, least common multiple, prime number and prime factor decomposition. Use the terms square, positive and negative square root, cube and cube root Understand and use whole. N1/L1.7: Work out simple ratio and direct proportion Use ratio notation, including reduction to its simplest form and its various links to fraction notation Understand and use direct and indirect proportion Divide a quantity in a given ratio Solve simple problems involving ratio where one number is a multiple of another OCR

4 7 Be able to round numbers to a given degree of accuracy 7.1 Round numbers to the nearest power of Estimate answers to calculations by rounding the numbers used 7.3 Interpret remainders, as appropriate to the situation N1/L1.8: Approximate by rounding N1/L1.9: Use estimation to find appropriate solutions to problems Approximate to specified or appropriate degrees of accuracy including a given power of ten, number of decimal places and significant figures Understand and use whole 8 Be able to solve one and two-step problems expressed in word and algebraic form resulting in whole number answers 8.1 Translate problems from word form to symbolic form 8.2 Apply arithmetic operations to: one-step problems two-step problems expressed in algebraic form Answers must result in whole numbers Know how to form word expressions from simple expressions in symbols, such as translating a multi-step problem written in words to symbolic form and matching word problems to problems written in symbols N1/L1.10: Solve problems with and without a calculator involving positive numbers N1/L1.11: Solve problems involving algebra Set up and solve simple equations including simultaneous equations in two unknowns. Use simple formulae expressed in words for one-or two-step operations Assessment Externally assessed by OCR set and marked tests, requiring short-answer responses. Available as paper-based and on-screen assessment. No calculator can be used for this unit. 4 OCR 2012

5 *Mapping and Signposting Information This unit covers areas of the Adult Numeracy Core Curriculum (ANCC). For ease of reference we have indicated which parts of the unit map to which elements of the ANCC. Achievement of this unit will also support learners who wish to progress to other programmes of learning and the Signposting information indicates areas within a Functional Skills (mathematics) or GSCE (mathematics) programme of learning that a learner will be able to more confidently progress towards after completion. This unit will not support progression towards any parts of the GCSE or Functional Skills criteria that are in italics. OCR