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Reasoned Rounding

Reasoned Rounding printable sheet

This is a rounding game for two players. 

You will need a  recording sheet  shared between the two players. One sheet is enough for three games. The first player rolls a 0-9 dice twice and chooses which two-digit number they would like to make from the numbers rolled. They then round this number to the nearest 10, find the matching circle on the recording sheet and write their two digit number in one of the spaces in that circle. The second player rolls the dice twice to take their turn in a similar way. A circle is complete when it has two numbers in it and this scores a point for the person who wrote the second number in. (Even if the first number was written in by the other player.) The game is over when all the circles are full and then the points are counted up to find the winner.

We received some solutions from children who wanted to share their ideas about this game with us. Sky from Cubitt Town Junior School in the UK explained their strategy:

When I rolled the dice, I looked at the sheet to see what spaces were available. I looked to see if I could block my partner or complete my own circles. When we played a round where we could choose the order of the digits, I switched them around to help me. If I was blocked with one way, I could switch the digits and round the other way.

Georgina from Wavell Junior in the UK thought that going second gives a better chance of winning:

If you want to win the game you would need to think carefully about the choices you have. If your opponent had got half the circle of 70 and you rolled 3 and 7 you could make 73 and you would get the point. It is best not to roll first because it is less likely for you to get a point. If you want to get a point you should not start a circle. It also is a bit of luck for the numbers you roll.

Rosie from King's College Madrid in Spain agreed with Georgina, and also spotted some circles that are more difficult to fill than the others:

In Maths class we decided that the 0 and 100 circles were the hardest to fill as only 5 numbers rounded to each circle whereas 10 numbers round to the other circles. We tried to fill the 0 and 100 circles as soon as we could. We also found that out of 14 pairs the player who went second won 12/14 times. We decided that because each circle needs two numbers it was better to go second.

The children from Central CofE Junior School in the UK noticed lots of things about this game:

We really enjoyed playing Reasoned Rounding and noticed lots of things to help us win the game and develop our reasoning.

• The first and last circles are the hardest to win as there are fewer chances of rolling a number that rounds to it. E.g. to win 0 you have to roll 00, 01, 02, 03 or 04 and for 100 you would need 95, 96, 97, 98 or 99 so there are only 5 chances but for the other circles there are 10 chances - from the 5 before to the 4 after. So, if you rolled a 9 and 6 it would be better to make 96 to round to 100.
• Also, if you go second you have more chance of winning as your partner will already have filled in one number of the circle so you can get the other one.
• One pair got down to the last circle which was 0. They knew that if they rolled a number over 5 with their first throw then there was no point rolling again as they couldn't win the circle.
• As you get further into the game it is harder to find a place to put your number as the circles are full.
• To vary the game, you could roll 3 times to create a number with 2 decimal places and round to the nearest tenth.

These are all great ideas! I like your idea for varying the game - we've made some similar extensions to this game on the  Teachers' Resources page for this activity.

Why do this problem?

The game offers a competitive context which provides pupils with lots of practice in rounding numbers and helps develop their reasoning by encouraging them to talk about their strategies for winning points whilst playing. Possible approach

Play as a class first by projecting the recording sheet onto the board and asking pupils to roll dice, suggest what numbers could be made and explain to the class where they would want to put them and why. Key questions What two-digit numbers can you make from the digits you rolled? Where might be a good place to put your number? What numbers are you hoping might come up on your next turn? Can you explain why you chose that circle? Possible extension Some other versions of the same game are available here: Reasoned Rounding to the nearest hundred recording sheet This time the players roll the dice three times each per turn and can be encouraged to record the different 3-digit numbers possible before making strategic decisions as to where they could best place their chosen number. Reasoned Rounding to the nearest whole number recording sheet Players roll the dice twice and then place one number on each side of a decimal point. They round their chosen number to the nearest whole number and then place it in the appropriate circle as before. Reasoned Rounding to the nearest tenth recording sheet Players still roll the dice twice, but then decide in which order to place them after a decimal point.  Having created a number which has two decimal places, they must then round it to the nearest tenth and place it in the appropriate space on the recording sheet. What other variations can pupils come up with for themselves?   What if they were to use different dice? What recording sheets would be needed now? Possible support Ask pupils to play in groups of four, one pair against another, in order to support their discussion of options whilst carrying out the rounding.  

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Year 4 Round to the Nearest 10 Reasoning and Problem Solving

Give children the opportunity to use and apply their rounding skills with this Year 4 Round to the Nearest 10 Reasoning and Problem Solving worksheet. It includes a range of engaging questions such as identifying which child's statement is correct and which place value counters are hidden by a splat. As always, we've got the answers covered too to save you valuable marking time!

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National Curriculum Objective

Round any number to the nearest 10, 100 or 1,000

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Application of Rounding in Problem Solving

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Solving problems involving rounding

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Lesson details

Key learning points.

• In this lesson, we will use knowledge of rounding to the nearest 1000, 10 000 and 100 000 to solve problems involving rounding.

This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.

Starter quiz

5 questions, lesson appears in, unit maths / reasoning with large whole numbers.

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Rounding Decimals Worksheet Challenges

Welcome to our Rounding Decimals Worksheet collection of Rounding Challenges. Here you will find a wide range of free printable math Worksheets, which will help your child learn to apply their rounding knowledge to solve a variety of rounding challenges involving decimals.

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Rounding Decimals Worksheets

Here you will find a range of selection of printable rounding challenges to give your child practice and consolidation with their rounding work.

These sheets are carefully graded so that the easier sheets come first.

Each challenge consists of 4 clues and 8 possible answers, of which only one is correct.

Children have to look at the clues and use them to work out the correct answer.

These activities can be used individually with children working through the challenges on their own, but they are also great for partner work, and children discussing and sharing their ideas, and developing their mathematical language.

The activities are also a great way of extending more able mathematicians.

Each sheets comes with a separate printable answer sheet.

Using these sheets will help your child to:

• apply their rounding knowledge to solve problems;
• solve mathematical problems;
• develop children's vocabulary and understanding of the properties of numbers.

Rounding Decimals Challenges to the nearest whole

• Decimal Numbers Rounding Challenge 1
• Challenge 1 Answers
• PDF version
• Decimal Numbers Rounding Challenge 2
• Challenge 2 Answers

Rounding Decimals Challenge to the nearest whole / tenth

• Decimal Numbers Rounding Challenge 3
• Challenge 3 Answers
• Decimal Numbers Rounding Challenge 4
• Challenge 4 Answers

Rounding Decimals Challenges up to 2 decimal places

• Rounding Decimals Challenge 5
• Challenge 5 Answers
• Rounding Decimals Challenge 6
• Challenge 6 Answers

Looking for something easier?

The rounding challenges in this section involve rounding numbers to the nearest 10, 100 or 1000.

They are at a more basic level than those on this page, and do not involve decimals.

• Rounding Numbers Worksheet Challenges

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

How to Round whole numbers

• learn to round decimals to the nearest whole, tenth or 2 decimal places.

Each of the webpages below comes with rounding help as well as practice worksheets.

• Rounding Decimals to the nearest whole
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Decimal Place Value Worksheets

Here you will find a range of Free Printable Decimal Place Value Worksheets.

The following worksheets involve using and understanding decimal notation - tenths and hundredths.

• Understand decimals;
• Use place value notation with tenths and hundredths;

The free place value worksheets in this section support elementary math benchmarks.

• Decimal Place Value Worksheets to 2dp
• 5th Grade Place Value to 3dp

Online Rounding Practice Zone

In our Rounding Practice zone, you can practice rounding a range of numbers. You can round numbers to the nearest 10, 100 or even 1000. Want to round numbers to the nearest decimal place, you can do that too!

Select the numbers you want to practice with, and print out your results when you have finished.

You can also use the practice zone for benchmarking your performance, or using it with a group of children to gauge progress.

• Rounding Practice Zone

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Word Problems Grade 3 Place Value and Rounding

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11 grade 3 place value and rounding questions to develop reasoning and problem solving skills.

• 10 place value and rounding questions with an additional challenge question.
• Answers included with reference to the associated standard.
• Questions include skip counting, finding 1,000 more and less, making numbers using given digits and rounding numbers.

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Rounding Decimals: Reasoning and Problem Solving

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Rounding Word Problems

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

1 October 2023

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These word problems will help your pupils with mastery of rounding through problem solving and reasoning - suitable for Year 6 and above.

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