Practice really helps, both in terms of the types of SATs reasoning questions that can come up, and in the skills needed to answer them. While there is one arithmetic paper, there are two reasoning papers; and the variety, breadth and level of challenge in the reasoning paper continues to impress us. Most Year 6 pupils find maths reasoning questions the hardest part of these maths papers. We teach thousands of pupils every week in the run up to SATs, and teaching them maths reasoning skills at KS2 is a big part of what we do.
We even recently took the decision to restructure our SATs lessons to introduce reasoning questions earlier in the learning journey as the level of challenge just at the end of the lesson was too high. Whatever level pupils go on to perform at in maths, maths reasoning questions and numerical reasoning tests such as those used by grammar and private schools are likely to be a part of the practice they require.
For more word problems like this, check out our collection of 2-step and multi-step word problems for you as well as tips on how to use the bar model to answer Year 6 word problems. The simplest type of reasoning question pupils are likely to encounter in the reasoning papers, single step Maths Reasoning Questions With Solutions 01 problems are exactly that: pupils are asked to interpret a written question and carry out a single mathematical step to solve it.
From here the simple mathematical step is subtraction i. The most crucial skill for primary school pupils in this question is a solid understanding of money as relating to place value. If this understanding is present, the mathematical step itself is quite easy. Pupils need to understand that one hour is equal to 60 minutes. A simple enough calculation doubling if pupils are aware that the diameter is twice the radius. A more complex version of the single step worded problem, multi-step problems require pupils to interpret a written problem, but solving it then requires the use of two or three maths skills,.
This question encompasses three different maths skills: multiplying and dividing mixed numbers, addition and subtraction. Pupils can choose to work out the multiplication or division first, but must complete both before moving on. Multi-step problems are particularly valuable to include in practice tests because they require children to apply their knowledge of maths language and their reasoning skills several times across the course of a single question, usually in slightly different contexts.
There are two steps to this problem, but both are multiplications. This sum is then multiplied by 4 � the number of days � to get to the solution. Another two step problem. Given the number of steps involved it can be easy for pupils to make arithmetic mistakes, and the mark scheme accounts for this by allowing for one mistake � but no more. A two-step problem again: multiplying 3. As with the previous problem, the mark scheme again allows for at most one arithmetic error, assuming the method is correct.
Download 6 weeks of Rapid Reasoning slides for your Year 6 pupils and help them get a head start on preparing for the SATs reasoning papers. As their name suggests, these questions ask pupils to solve a problem that includes one or more units of measurement. This is a two step problem; pupils must first be able to read and convert kilograms to grams and therefore know the relationship between the two units , then divide by 65 to work out the number of washes possible.
Questions involving measures tend to be few in number in the KS2 exam papers, but they often provide an excellent way to couch key maths skills such as the four operations. A relatively simple division problem, relying on pupils having knowledge that g is one fifth of a kilogram. Another three step problem � multiplying by 4 to get the total mass of the four melons, multiplying by 3 to get the total mass of the remaining three melons, and then subtracting from to obtain the mass of the fourth melon.
Interesting to note that in this problem unlike the previous example , the units for the answer are specified � an answer given in metres will be marked as wrong, since cm is specified in the answer box. This is why we encourage pupils to keep an eye on whether units are provided in the answer box. As with the melon question there are three steps involved to solve this problem: working out the mass of the four cars 4 x 80 , working out the mass of the remaining three cars 3 x 50 and subtracting from to get the mass of the fourth car.
Problems involving drawing require pupils to construct an accurate drawing by following a set of instructions, or through reflection, translation, or scaling. This type of question is quite rare, but there are some notable exceptions, such as the infamous Question 21 in Paper 2 of the Reasoning SATs:.
Answer: Any pair of lines that make a square of 4 units, a rectangle of 6 units, and a square of 25 units. This question is considerably more complex than it appears, and incorporates aspects of multiplication as well as spatial awareness. One potential solution is to work out the area of the card 35 , then work out the possible square numbers that will fit in understanding that square numbers produce a square when drawn out as on a grid , and which then leave a single rectangle behind.
Answer : Any quadrilateral made by joining the dots that has 3 acute angles e. Answer : a new triangle drawn with points at 2,1 , 5,1 and 2,4. Translation can be tricky for pupils. Therefore Olivia is wrong. More than most problems, this type requires pupils to actively demonstrate their reasoning skills as well as their mathematical ones.
The Maths Reasoning Questions With Solutions 80 mark scheme notes that vague answers or any answers with a mathematical error are unacceptable. Any explanation that provides a counter-example is acceptable e. Answer : Any answer that refers to the fact that there is a 5 in the hundreds place, AND a 9 in the thousands place, so that the number has to be rounded up as far as the ten-thousands place.
Another relatively simple kind of reasoning question, sequence problems involve pupils completing mathematical sequences. Answer: 35 , 42, 49, 56 , 63, Number sequence questions, particularly those that involve linear sequences or as in this case times tables, come up relatively frequently in the SATs maths tests.
Both answers must be correct to receive the mark. This question can be a little tricky; pupils need to work out that the marks on the line represent increments of 4, and count backwards and forwards in 4s to obtain the missing numbers. A slightly more complex variation of the sequence question, ordering problems require pupils to put a set of numbers, fractions or measures in the correct order.
This question throws a stick in the wheels by including an improper fraction, but this is hardly unusual. A good knowledge of the fundamentals of fractions is essential here: pupils must understand what a larger denominator means, and the significance of a fraction with a numerator greater than its denominator.
As with the example above, pupils should be encouraged to convert the fractions to make it easier to order them. They may not all be applicable to every single question type, but will apply to at least two, usually more. Necessary cookies are absolutely essential for the website to function properly.
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It is mandatory to procure user consent prior to running these cookies on your website. One to one interventions that transform maths attainment. Find out more. National Tutoring Programme Subsidised online maths tuition now available for schools in England Learn more.
Group Created with Sketch. Explore all resources. Anantha Anilkumar. The answers are all taken from the answer sheets we provide for each test paper. For more word problems like this, check out our collection of 2-step and multi-step word problems for you as well as tips on how to use the bar model to answer Year 6 word problems Maths Reasoning Question Type 1: Single step worded problems The simplest type of reasoning question pupils are likely to encounter in the reasoning papers, single step problems are exactly that: pupils are asked to interpret a written question and carry out a single mathematical step to solve it.
Reasoning Question 3 Answer : 48 cm 3 Pupils must calculate length Maths Reasoning Questions With Solutions World by breadth by height, using the figures provided by the question. Reasoning Question 4 Answer : cm A simple enough calculation doubling if pupils are aware that the diameter is twice the radius. Reasoning Question 3 Answer : 2, km Another two step problem. Reasoning Question 5 Answer : Download Free Now!
Anantha Anilkumar Content Editor. As a member of the content team at Third Space Learning, Anantha helps to ensure that teachers everywhere can enjoy the blogs and resources created by the team. Before coming to TSL, Anantha worked as a teacher and a marketing analyst.
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