What are the problems with multi
More often than not children don’t like word problems. There is a sense of fear associated with trying to decode math word problems. Try in a multi-step word problem and forget it. As a child I can remember freezing up when I got to the word problems in my textbook. Even if I knew the skill procedurally I would panic. I was never properly taught how to evaluate and solve word problems. As a teacher I make sure to equip my students with the tools they need to solve word problems with confidence and ease. Show
How Often Do I Give My Students Multi-Step Word Problems?The easiest way to create a classroom of students that are used to solving word problems is to flood your students with word problems. It sounds obvious, but most textbooks and workbooks provide practice with procedural based questions. In my classroom 80% of the questions I give to my students are word problems and 20% are procedural based questions. At first your students will hate this. They will look at you with sheer panic. Don’t back down. We learn best when we practice something daily. Word problems are no different. I use a word problem to start my math block every day. They are complex and conceptual based. Most often my students are not going to successfully solve it on the first try, but it’s the grit I’m targeting. I’m building their stamina. Give Your Students the Proper ToolsAt the start of the year I teach my students strategies for solving word problems. From pulling out important information and numbers to looking for words that lead to the correct operation needed to solve the questions, I provide my students with a toolkit for the year. This toolkit comes in the form of a flipbook that has examples and tips for how to solve world problems. Give your students something to reference to ease anxiety. Spiral ReviewMulti-step word problems can help you review curriculum that has been previously taught. If you review place value at the beginning of the year and never reference back to the skill, your students will forget what you taught them. I use Step Up Math Task Cards during math rotations to keep previously covered standards fresh for my students. It’s great practice for standardized testing. Step Up Math Task Cards can be used for practice, review, and test prep. I use these task cards when introducing a new standard and I need complex word problems for practice. I will use that same set during math rotations when I’m working with my groups for remediation and enrichment. I’ll then spiral the different steps into my math rotations throughout the year for test prep. Teaching your pupils to solve 2-step word problems and multi-step word problems at KS2 is one of hardest parts of a mastery led approach in maths. There are several cognitive functions at play, as children have to wrestle with their knowledge of maths vocabulary, maths operations, and often basic comprehension skills.In this article we set out some of the sorts of maths word problems pupils can expect from the KS2 maths national curriculum and look at strategies for solving them. In total we’ve provided 30 KS2 word problems to work through, showing the variety of 2-step word problems and multi-step word problems pupils are likely to encounter. Table of Contents
What are word problemsWord problems in maths are sentences describing a real life scenario where children must apply their maths knowledge to reach a solution or unpick the maths problem. To solve maths word problems children must be familiar with the maths language associated with the mathematical symbols they are used to in order to make sense of the word problem; for example: plus, more, total = add; difference, less, minus = subtract, etc. What are two-step word problems?Two-step word problems are problems in which two separate calculations (usually different operations) are required to reach the answer. By different operations we mean addition, subtraction, multiplication or division. What are multi-step word problems?Multi-step word problems are maths problems that require multiple calculations to solve them. They will usually will involve more than one operation and often more than one strand from the curriculum. For example a multi-step word problem on area and perimeter may also involve ratio and multiplication. In KS2 SATs multi-step word problems can be awarded up to 3 marks for a correct answer, but 1 or 2 marks can be achieved by solving some of the steps in the problem correctly. Two-step word problems and multi-step word problems pupils will encounter in KS2In Key Stage 2, there are nine ‘strands’ of maths – these are then further split into ‘sub-strands’. For example, ‘number and place value’ is the first strand: a Year 3 sub-strand of this is to “find 10 or 100 more or less than a given number”; a Year 6 sub-strand of this is to “determine the value of each digit in numbers up to 10 million”. The table below shows how the ‘sub-strands’ are distributed across each strand and year group in KS2. StrandYear 3Year 4Year 5Year 6TotalNumber and place value695727Calculations7815939Fractions, decimals and percentages710121140Ratio and proportion00044Algebra00055Measurement17910844Geometry: properties of shape546722Geometry: position and direction03126Statistics22228As well as varying in content (sometimes by using a combination of strands in one problem, e.g. shape and calculations), word problems will also vary in complexity, from one-step to multi-step problems. Different word problems will provide a different level of cognitive demand as an alternative method of adapting the level of difficulty. The STA mathematics test framework (2015) sets these out. Strand1234Depth of understandingrecall of facts or application of proceduresuse facts and procedures to solve simple problemsuse facts and procedures to solve more complex problemsunderstand and use facts and procedures creatively to solve complex or unfamiliar problemsComputational complexityno numeric stepsone, or a small number of numeric stepsa larger number of numeric steps all steps are simplea larger number of numeric steps, at least one of which is more complexSpatial reasoningno spatial reasoning requiredmanipulation of the geometric information is requiredcomplex manipulation of the geometric information is requiredinterpret, infer or generate new geometric informationData interpretationno data interpretation requiredselect and retrieve informationselect and interpret informationgenerate or infer new information from dataResponse strategyselect one or more responses or construct a simple responseconstruct a small set of responsesconstruct a straightforward explanation shows evidence of a methodconstruct a complex explanation Skills required for multi-step word problemsThere is a high level of cognitive demand on children when they are faced with multi-step word problems: interpreting the question to find the arithmetic behind it and then calculating the arithmetic itself. Therefore, a secure knowledge of times tables and a confident understanding of arithmetic are essential skills for being able to successfully solve word problems. Year 3 to 6 Rapid Reasoning (Weeks 1-6) Download 480 two-step and multi-step word problems for Years 3 to Year 6 (4 a day x 6 weeks for each year group) Download Free NowArithmetic within multi-step word problemsA useful strategy to use in class is to provide children with a list of arithmetic questions you have previously ‘extracted’ from some word problems. Generally, children are much more confident with arithmetic than word problems, so they should be able to answer these with relative ease. In the next lesson, give the children the word problems – after a while, ask them which they found easier and why. Then show the children the arithmetic from the previous day and ask if they can see the similarities. They could then try to ‘extract’ the arithmetic from word problems themselves. How to teach multi-step word problemsHere are two simple strategies that can be applied to most two-step word problems and multi-step word problems before solving them.
How to solve a year 6 multi-step word problemHere’s an example. There are 29 pupils in a class. The teacher has 7 litres of apple juice. She pours 215 millilitres of apple juice for every pupil. How much apple juice is left over? 1. What do you already know?
2. How can this problem be drawn/represented pictorially?Bar modelling is always a brilliant way of representing even multi step word problems in year 6, but there are always other ways of drawing it out. For example, for this question, you could draw 29 pupils (or stick man x 29) with ‘215 ml’ above each one and then a half-empty bottle with ‘7 litres’ marked at the top. Now to put the maths to work. This is a Year 6 multi-step problem, so we need to use what we already know and what we’ve drawn to break down the steps. 3. How to answer step by step
How to solve a year 5 multi-step word problemA similar approach can be used for this one.
1. What do you already know?
2. How can this problem be drawn/represented pictorially?See this example of bar modelling for this question: Now to put the maths to work using what we already know and what we’ve drawn to break down the steps. 3. How to answer step by step
There are plenty more teacher guides and resources available from Third Space for problem solving in KS2. Find out how to develop maths reasoning in KS2, how to balance fluency, reasoning and problem solving in your maths lessons, and get ideas for developing and running maths investigations at KS2. 2-step word problems Year 3In Year 3, children will move away from solely using concrete resources when solving word problems and start using written methods. This is also the year in which two-step problems will be introduced. As some children may not be confident readers, it is important that word problems are explored in a variety of contexts: as a class, in groups, in partners, with an adult, with a list of ‘mathematical vocabulary’ accessible, etc. It is important that children’s literacy skills don’t hinder their progress or in maths. Two step word problems worksheet from All Kinds of Word ProblemsExample Year 3 word problems
2-step word problems Year 4By year 4, children should feel confident using the written method for each of the four operations. This year children will be presented with a variety of problems, including two-step problems, and be expected to work out the appropriate method required to solve each one. While children should be focusing on formal written methods, it is important that concrete resources and pictorial representations are still used to consolidate their understanding. Two step word problems from All Kinds of Word ProblemsExample Year 4 word problem
Multi-step word problems: Year 5Although one and two-step word problems are the mainstay of Year 5 reasoning and problem solving, this is also when children may start to extend their range to include multi-step problems; In Upper Key Stage 2, word problems become more complex not only in the calculations (higher numbers, decimals etc.) but also the vocabulary – a subtlety of maths language may mean it is less obvious as to which operation is required. In the first example below, the children are essentially being asked to add and divide by 7 – or find the ‘mean’ – but the word problem doesn’t use the vocabulary children usually associate with addition or division, such as total, sum, share, split, etc. To reduce the cognitive demand of questions such as these, the numbers could be altered so that children are still required to extract the calculations from the word problems but can then complete those calculations with simpler numbers. Example Year 5 multi-step word problems
Multi-step word problems Year 6In Year 6, children move on from 2-step word problems to multi-step word problems. These could include fractions, decimals and percentages. Some of the most complex problems in KS2 SATS papers are worth 3 marks – these are intended to challenge more able mathematicians. As previously mentioned, one or two marks can be achieved for correctly solving different ‘steps’ of the problem even without arriving at the correct final answer. Multi-step word problems from Rapid ReasoningExample Year 6 multi-step word problem
For more like this, please refer to this collection of 35 year 6 maths reasoning questions to support teaching in the run up to SATs or if you want to focus specifically on using the bar model as a problem solving tool, try these Year 6 word problems. 2-step and multi-step word problems by topicWhat follows are a series of 2-step word problems and multi-step worded problems based around the national curriculum objectives for each topic in maths. These show you a full range of question and problem types and the type of skills and knowledge your pupils will need to develop. We’ve also added some links to relevant word problems worksheets. Year 3 to 6 Rapid Reasoning (Weeks 1-6) Download 480 two-step and multi-step word problems for Years 3 to Year 6 (4 a day x 6 weeks for each year group) Download Free NowPlace value word problemsPlace value problems appear throughout KS2. In Year 3, they will be based on five objectives:
The progression in place value through KS2 ends in Year 6 with problems being based on three objectives:
Place value multi-step word problem: Year 6
For free multi-step word problems worksheets download these free number and place value word problems for Years 3, 4, 5 and 6 Addition and subtraction word problemsAddition and subtraction problems appear throughout KS2. In Year 3, they will be based on three objectives:
The progression in addition and subtraction through KS2 ends in Year 6 with problems being based on three objectives:
Addition and subtraction multi-step word problem: Year 6
For free multi-step and two-step word problems worksheets download these free addition and subtraction word problems for Years 3, 4, 5 and 6 Tips for solving addition multi-step word problemsChildren should be taught to recognise the vocabulary used in word problems to signify that the addition operation is required, for example, altogether, combined, total, sum etc. Be mindful that although more can be used for addition (e.g. What is 7 more than 9?), it can also be used for subtraction (e.g. How many more is 9 than 7?). Addition multi-step word problem: Year 6
Tips for solving subtraction multi-step word problemsChildren should be taught to recognise the vocabulary used in word problems to signify that the subtraction operation is required, for example, change (money), difference, fewer than, minus etc. They should also by now know their subtraction facts. Subtraction two-step word problem: Year 5
Multiplication and division word problemsMultiplication and division problems appear throughout KS2. In Year 3, they will be based on three objectives:
The progression in multiplication and division through KS2 ends in Year 6 with problems being based on six objectives:
Multiplication and division multi-step word problem: Year 6 (crossover with decimals)
Tips for solving multiplication multi-step word problemsChildren should be taught to recognise the vocabulary used in word problems to signify that the multiplication operation is required, for example, product, double, triple, groups etc. Be mindful that groups can be used in both multiplication and division problems, e.g. ‘What are 7 groups of 5?’ (multiplication) or ‘How many groups of 4 fit into 28?’ (division). Multiplication multi-step word problem: Year 6
For free multi-step and two-step word problems worksheets download free multiplication word problems for Years 3, 4, 5 and 6 Tips for solving division multi-step word problemsChildren should be taught to recognise the vocabulary used in word problems to signify that the division operation is required, for example, halve, share, groups, split etc. Division two-step word problem: Year 4
For free multi-step and two-step word problems worksheets download free division word problems for Years 3, 4, 5 and 6 Mixed operations word problemsIn the Year 3 non-statutory notes and guidance of the National Curriculum, it is recommended that pupils practise solving varied addition and subtraction questions and simple multiplication and division problems in contexts, deciding which of the four operations to use and why. These include measuring and scaling contexts, and correspondence problems in which m objects are connected to n objects. At the end of KS2, the guidance states that pupils could practise addition, subtraction, multiplication and division for larger numbers, using the formal written methods of columnar addition and subtraction, short and long multiplication, and short and long division. Mixed operations two-step word problem: Year 6 (crossover with money)
Four operations multi-step word problem: Year 5
Read more
Fraction word problemsWord problems involving fractions require a good understanding of division and multiplication. Bar models or other pictorial representations are useful strategies in helping children solve problems like these. Fraction problems appear throughout KS2. In Year 3, they will be based on seven objectives:
The progression in fractions through KS2 ends in Year 6 with problems being based on seven objectives:
Fraction multi-step word problem: Year 6
For free multi-step and two-step word problems worksheets download fractions and decimals word problems for Years 3, 4, 5 and 6 Decimals word problemsDecimal word problems are commonly used in questions involving money, although they also often appear alongside fractions and/or percentages, requiring children to calculate their equivalences. Decimal problems begin in Year 4 and will be based on six objectives:
The progression in decimals from Year 4 ends in Year 6 with problems being based on six objectives
Decimals two-step word problem: Year 6 (crossover with multiplication)
Percentage word problemsChildren need a secure understanding in fractions before attempting percentage problems; they are therefore not introduced until Upper Key Stage 2. Percentage word problems begin in Year 5 and will be based on two objectives:
The progression in percentage continues into Year 6 with problems being based on two objectives:
Percentage multi-step word problem: Year 6
For free multi-step and two-step word problems worksheets download decimals and percentages word problems for Years 3, 4, 5 and 6 Measurement word problemsMany measurement word problems require children to convert between metric measures, thus children should be confident in multiplying and dividing by powers of 10. More complex measurement word problems (such as those involving imperial measures) may require children to have an understanding of ratio and proportion. Word problems involving measures begin in Year 3 and will be based on six objectives:
The progression continues into Year 6 with problems being based on three objectives:
Measurement multi-step word problem: Year 6 (crossover with ratio)
Money word problemsProblems involving money link with decimals (money notation) and measures (converting between £ and p). Where possible, especially until their understanding is secure, children should be handling real money to help them solve problems. Word problems involving money begin in Year 3 and will be based on one objective: add and subtract amounts of money to give change, using both £ and p in practical contexts. The non-statutory guidance in the curriculum recommends that pupils continue to become fluent in recognising the value of coins, by adding and subtracting amounts, including mixed units, and giving change using manageable amounts. The decimal recording of money is introduced formally in year 4, where word problems will be based on one objective: solve simple measure and money problems involving fractions and decimals to two decimal places. Money problems continue throughout KS2 but are not specifically mentioned in the National Curriculum beyond Year 4. Two-step money word problem: Year 6 (crossover with mixed operations)These are the different prices of tickets at a cinema.
Area word problemsMathematical questions related to area require a secure understanding of arrays, times tables, multiplication, division and factors. Concrete resources such as Numicon and multilink can be used to support children to solve these problems. Word problems involving area begin in Year 4 and will be based on one objective: find the area of rectilinear shapes by counting squares. The progression continues into Year 6 with problems being based on three objectives:
Area multi-step word problem: Year 6
Perimeter word problemsAs well as being an important life skill, it is important for children to be able to measure accurately with a ruler for some aspects of this mathematical strand. As above, Numicon and multilink are extremely useful resources in supporting children in their calculation of perimeter word problems. These problems begin in Year 3 and will be based on one objective: measure the perimeter of simple 2-D shapes. The progression continues into Year 6 with problems being based on one objective: recognise that shapes with the same areas can have different perimeters and vice versa. Perimeter word problem: Year 6 (crossover with decimals and multiplication)
Ratio word problemsIn my experience, ratio is most successful when taught with concrete resources such as multilink, Cuisenaire rods or beads. Once children are taught how to represent ratio word problems using equipment (and eventually transferring to a pictorial representation, such as a bar model), the process is a lot easier. Children won’t encounter ratio word problems until Year 6, where they will be based on three objectives:
Ratio word problem: Year 6 (crossover with measurement)
Order of operations word problemsChildren won’t encounter word problems about the order of operations until Year 6, where they will be based on one objective: use knowledge of the order of operations to carry out calculations involving the four operations. The non-statutory guidance in the National Curriculum also recommends that children explore the order of operations using brackets (otherwise known as BODMAS or BIDMAS); for example, 2 + 1 x 3 = 5 and (2 + 1) x 3 = 9. Bodmas word problem: Year 6
Volume word problemsChildren won’t encounter volume-related word problems until Year 6, where they will be based on two objectives:
Volume word problem: Year 6This large cuboid has been made by stacking shipping containers on a boat. Each individual shipping container has a length of 6m, a width of 4m and a height of 3m. What is the volume of the large cuboid? Answer: 864m3 Algebra word problemsAgain algebra word problems only really come up in Year 6; the objectives they will be based on are:
Algebra word problem: Year 6This question is from the 2018 KS2 SATs paper. It is worth 2 marks as there are 2 parts to the answer. Amina is making designs with two different shapes. She gives each shape a value. Calculate the value of each shape. Answer: 36 (hexagon) and 25. More support with KS2 word problemsFor more multi-step and 2-step word problems register for free on the Third Space Learning Maths Hub which includes lots more printable word problems worksheets including as part of the free resources on offer a complete set of place value word problems with answer sheets for Year 3 to Year 6: All Kinds of Word Problems on Number and Place Value If you have any pupils who are struggling to master word problems they may need a more intensive personalised intervention. Third Space Learning’s tuition follows a rigorous step by step process to teaching problem solving with excellent success – pupils make on average double their expected progress with us. What are the common problems in multi threaded programming?Multithreaded and multicontexted applications present the following disadvantages:. Difficulty of writing code. Multithreaded and multicontexted applications are not easy to write. ... . Difficulty of debugging. ... . Difficulty of managing concurrency. ... . Difficulty of testing. ... . Difficulty of porting existing code.. What are multiA multi-step-word problem is like a puzzle with lots of pieces. Multi-step word problems are math problems that have more than one operation. An operation is addition, subtraction, multiplication, or division. Multi-step word problems can have any combination of these operations.
What is multiA multi-step equation is an equation that takes two or more steps to solve. These problems can have a mix of addition, subtraction, multiplication, or division. We also might have to combine like terms or use the distributive property to properly solve our equations. So get your mathematical toolbox out!
What is an example of a 2 step word problem?A two-step problem is a word problem that requires two operations to solve it, for example: I buy a magazine costing 83p and a pencil costing 45p. I pay with a voucher that gives me 20p off the things I am buying. How much do I spend?
|