maths problem solving for year 1

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Unit 1: Place value

Unit 2: addition and subtraction, unit 3: measurement, data, and geometry.

Reasoning/Problem Solving Maths Worksheets for Year 1 (age 5-6)

Reasoning about number, sorting and counting.

To build on the work done in Early Years children need to sort groups in various ways before counting the objects within the groups.

Counting a variety of things.

Sorting and counting activities.

Sorting and counting activities (3)

How many flowers, balls etc can you see in the picture?

How many boats, trains, bikes and buses can you see in the picture?

Looking for similarities in groups of sorted objects.

Explaining the criteria for sorting into groups - there may be more than one possible answer.

Guess how many objects and then count to see how accurate you are!

Sorting a variety of fruit into groups.

Sorting a variety of objects into groups.

Explaining answers: counting forwards and backwards.

Making number sentences and using number cards

Children will be asked to find different ways of making numbers using addition and subtraction. Number cards are an excellent resource in the classroom for this type of activity.

Use number cards to find different ways of making 3.

How many ways can you make 4 using the cards shown?

How many ways can you make 5 using the numbers and signs?

Use number cards to find different ways of making 6.

How many ways can you make 8 using the numbers on the cards?

How many ways can you add 2 numbers to make 7?

Use cards to make numbers.

Use cards to make numbers, including zero.

Reasoning about money

Using coins is a great way to explore different ways of making amounts. The later pages on shopping require logical thinking and children should be able to explain verbally or on paper how they reached their answers.

How many ways can you pay 8p?

What coins could you use to buy the ragdoll?

What shapes can you buy for 10p? Costs according to the number of sides the shape has.

Solving 2-step problems with money up to 10p.

2-step money problems.

More shopping: 2-step problems with whole pounds.

Simple reasoning with small amounts of money.

Reasoning skills with small amounts of money.

Reasoning about addition and subtraction

Plenty of opportunity to select numbers and add and subtract to reach totals. Finding all the possible combinations can be an important part of these activities.

A first look at word problems needing addition or subtraction to solve.

More problem solving where addition or subtraction is needed.

Sharks know that there's more than one way to catch a fish. And there's usually lots of ways to make a total by adding two numbers.

'How many ways?' investigation using 7, 8 and 9.

How many different answers can you get?

Three darts to score on the board. Good adding up revision.

A little age problem.

Make subtraction sentences using the numbers around the hexagon.

Put the numbers 1, 2, 3, 4 and 5 onto the grid so that both lines add up to the same total. How many ways?

Can you put the numbers in the circles so that each side of the triangle adds up to 9?

Pick three numbers from those shown and add them. How many different additions can you find?

Completing missing symbols in number sentences.

Completing number sentences using more and less than.

Completing simple number patterns.

More reasoning activities

More activities to challenge children’s reasoning and logical thinking. Plenty of, 'How many ways ....' activities.

Find how many cubes can be held in one hand and record data collected in a table.

How many different ways can the ice lolly be coloured, using just two colours?

How many different ways can you put the cubes in the boxes?

How many rectangles can be made?

How many ways can the 9 tiles be put together to make a square?

How many ways can I join 4 triangles to make other shapes?

Make four 2-digit numbers from just two 1-digit numbers.

Put the numbers into the grid so that there is always a difference of more than one.

Find and describe routes to the bus stop.

How many numbers can you make with 6 beads on the abacus?

How many different routes are there from head to tail? Great logical thinking challenge.

Fun counting challenge which encourages logical thinking.

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• Measurement and data
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• Place value
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Problem-solving maths investigations for year 1.

Hamilton provide an extensive suite of problem-solving maths investigations for Year 1 to facilitate mathematical confidence, investigative inquiry and the development of maths meta skills in 'low floor – high ceiling' activities for all.

Explore all our in-depth problem solving investigations for Year 1 .

Use problem-solving investigations within every unit to encourage children to develop and exercise their ability to reason mathematically and think creatively.

Investigations provide challenges that offer opportunities for the development of the key mathematical skills while deepening conceptual understanding. They are designed to be accessible in different ways to all children. An added bonus is the substantial amount of extra calculation practice they often incorporate! The problems are designed to help children identify patterns, to explore lines of thinking and to reason and communicate about properties of numbers, shapes and measures.

Hamilton provide a mix of our own specially commissioned investigations, that include guidance for teachers together with a child-friendly sheet to guide your pupils through the investigation, as well as links to investigations on other highly regarded websites.

I am very grateful for Hamilton Trust resources, particularly the maths investigations. Julia, teacher in Wiltshire

You can find Hamilton's investigations for Year 1:

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Do read our extensive range of advice for more information about the investigations and for tips on how to use them effectively.

Hamilton’s problem-solving investigations are 'low floor, high ceiling' activities that give all children opportunities to develop mastery and mathematical meta-skills. Explore a set for a whole year group.

Hamilton’s Problem-solving Investigations provide school-wide solutions to the challenges of building investigative skills from Early Years to Year 6.

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Game - Karate Cats Maths

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Game - Bud's Number Garden

Help your child practise recognising numbers, counting, sequencing and much more with this educational game!

Counting and ordering

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Addition and Subtraction Word Problems- Year 1- DIFFERENTIATED

Subject: Mathematics

Age range: 5-7

Resource type: Worksheet/Activity

Last updated

22 February 2018

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Addition and Subtraction KS1

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

Pairs of Numbers

Age 5 to 7 challenge level.

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

Butterfly Flowers

Can you find two butterflies to go on each flower so that the numbers on each pair of butterflies adds to the number on their flower?

Equivalent Pairs

Can you match pairs of cards which show the same amount?

Number Lines

A resource to try once children are familiar with number lines, and they have begun to use them for addition. It could be a good way to talk about subtraction. Leah and Tom each have a number line. Can you work out where their counters will land?

Two Spinners

What two-digit numbers can you make with these two dice? What can't you make?

The Add and Take-away Path

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

What Could It Be?

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Find all the numbers that can be made by adding the dots on two dice.

Unit Differences

This challenge is about finding the difference between numbers which have the same tens digit.

Cuisenaire Counting

Here are some rods that are different colours. How could I make a yellow rod using white and red rods?

What's in a Name?

What do you notice about these squares of numbers? What is the same? What is different?

Sort Them Out (1)

Can you each work out the number on your card? What do you notice? How could you sort the cards?

Number Balance

Can you hang weights in the right place to make the the number balance balanced?

What Was in the Box?

This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

Arranging Additions and Sorting Subtractions

Order these four calculations from easiest to hardest. How did you decide?

Domino Sorting

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

One Big Triangle

Make one big triangle so the numbers that touch on the small triangles add to 10.

Subtraction Slip

Can you spot the mistake in this video? How would you work out the answer to this calculation?

Eggs in Baskets

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. How many eggs are in each basket?

Birthday Cakes

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?

Find the Difference

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Noah saw 12 legs walk by into the Ark. How many creatures did he see?

Heads and Feet

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

Jumping Squares

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

Ladybirds in the Garden

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

Secret Number

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

The Brown Family

Use the information about Sally and her brother to find out how many children there are in the Brown family.

The Tall Tower

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

Number Round Up

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

Age 5 to 11 Challenge Level

What could the half time scores have been in these Olympic hockey matches?

Strike it Out

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Dicey Addition

Who said that adding couldn't be fun?

This is an adding game for two players. Can you be the first to reach the target?

Doing and Undoing

An investigation looking at doing and undoing mathematical operations focusing on doubling, halving, adding and subtracting.

Sitting Round the Party Tables

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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Toyota recalls 1.85 million RAV4s, citing fire risk

Toyota is recalling more than 1.85 million RAV4 vehicles due to a loose battery problem that could increase the risk of fire when the car makes “forceful turns,” the company said in a news release Wednesday.

The recall will affect 2013-2018 model year RAV4s, Toyota said. Some of those vehicles, which are compact SUVs, may have replacement batteries that “have smaller top dimensions.” Toyota said that this small-top shape could make the batteries move “when the vehicle is driven with forceful turns” and “cause the positive battery terminal” to contact a clamp and short-circuit, raising the risk of fire.

The automaker is preparing a fix. “When the remedy is available, Toyota dealers will replace the battery hold-down clamp, battery tray, and positive terminal cover” at no cost, it added. The company will notify affected customers by late December.

52M air-bag inflaters could be recalled by U.S. auto regulators: What to know

The move comes after the National Highway Traffic Safety Administration said in 2021 that it had received 11 complaints alleging fires on the left side of the RAV4 engine, which were not caused by car crashes. The majority of the events occurred “during driving conditions, with four taking place with the ignition off,” the agency said in a report .

In December 2020, one RAV4 owner reported leaving the vehicle in a parking lot with the ignition turned off, according to NHTSA. The driver returned after a few minutes to find the car on fire. “The fire appeared to originate in front of vehicle,” NHTSA wrote in a summary of the incident. Firefighters were called in, but the vehicle was a total loss.

In August 2020, an owner of a 2017 RAV4 hybrid said the vehicle was going at 50 miles per hour when warning messages began appearing on the dash screen and white smoke began emerging from under the hood. “Moments later flames were coming from the engine compartment,” according to an NHTSA report. The vehicle was destroyed during the incident. A Toyota spokesman said Thursday that the recall does not include hybrids, meaning this particular incident was not relevant to the recall.

The “overall number of vehicle fire allegations with the battery as the area of origin is larger than its peer population,” NHTSA wrote .

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October 31, 2023

This article has been reviewed according to Science X's editorial process and policies . Editors have highlighted the following attributes while ensuring the content's credibility:

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The math problem that took nearly a century to solve

by University of California - San Diego

What was Ramsey's problem, anyway?

A good problem fights back.

Journal information: arXiv

Provided by University of California - San Diego

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‘This isn’t right’: Victorian maths exam errors prompt apology to year 12 students

Education minister says two errors appeared in VCE maths exam despite ‘thorough vetting process’

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Thousands of year 12 students have received an apology from Victoria’s education minister after “unacceptable” errors were discovered in questions in a VCE maths exam.

Students completed the second paper of the general maths exam on Monday afternoon, with some noticing a typo in one question and a misplaced number in another.

On Tuesday, the education minister, Ben Carroll, conceded two errors appeared in the final exam despite a “thorough vetting process”.

He said he had spoken to the chief executive of the Victorian Curriculum and Assessment Authority (VCAA), Stephen Gniel, and an investigation would be conducted by into how the mistakes occurred.

“First and foremost, we know how stressful doing any exam is for our year 12s, and the Victorian Curriculum and Assessment Authority and myself as the minister unreservedly apologise to the students and their families for what occurred,” Carroll said.

“It is unacceptable, given the checking and the vetting process, that there were two errors.”

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Carroll, who is also the state’s deputy premier, said no students would be unfairly affected by the mistakes, which were largely in the formatting of the exam.

He said the first error, which was picked up before the exam, was an extra “of” in a preamble to part D of question 14. Due to the paper’s formatting, the preamble appeared to be part of an earlier question but was in fact the introduction to a new question.

Students were told to cross out the extra “of” to avoid confusion.

The second error was another typo in part D of question nine, related to a matrix, which incorrectly included two 1s in a column. The mistake was discovered after the exam ended.

“One error was picked up before the mathematics exam was undertaken but it was deemed too late to do the reprinting of that exam,” Carroll said.

“Then there was a second error that occurred in a matrix that’s part of the exam. Students were instructed on the day to very clearly amend their sheet on the day of the examination but the second error wasn’t picked up.

“I want to reassure students and their families that they will not be impacted by this error. It will have no bearing on their marks.”

The mistakes came less than a year after Monash University’s Prof Burkard Polster and Dr Marty Ross wrote a critique of the VCE exams. They said they had identified “major mathematical errors” in past exams, including five in the 2022 specialist and mathematical methods papers.

“Every specialist mathematics and mathematical methods exam that we have seen is marred by at least minor mathematical problems, and most exams contains at least one major error,” they wrote.

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An online maths educator, known as MaffsGuru , wrote on social media that Monday’s exam was “different from other years” and “much harder” than the previous general maths paper completed by students on Friday.

“I think question 13 was written by the devil himself,” he wrote. “Other parts were just time-consuming. It was different from other years. Not helped by the mistake in the matrix question!”

MaffsGuru said the second error was a “much bigger mistake” than the inclusion of an extra “of”.

“This isn’t right!” he posted.

Students across Victoria were left reeling after completing the exam, taking to social media to complain about its difficulty.

Carroll said the errors on the general maths paper were believed to be an isolated incident, with no other exams containing mistakes.

He said the government would “strengthen the integrity of the process and get to the bottom of how this occurred, given it did go through a thorough vetting process”.

Exams will continue in Victoria until 15 November.

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General Aviation News

Because flying is cool

Mental Math for Pilots updated

By General Aviation News Staff · October 31, 2023 · Leave a Comment

Aviation Supplies & Academics (ASA) has released the third edition of “ Mental Math for Pilots ” by Ronald D. McElroy.

The book helps sharpen pilot math skills for a job interview and in the cockpit with tips for figuring math problems without paper or a calculator, according to ASA officials.

The book shares the “tricks of the trade” for the areas where pilots have traditionally needed to sharpen their mental math skills, such as fuel planning, temperature conversions, reciprocal headings, turn radius, crosswind components, time-speed-distance problems, calculating true airspeed, the 60-to-1 rule, and many others, company officials said.

The softcover book is available now for $24.95 while the eBook is $19.95.

For more information: ASA2Fly.com

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Math Problems for Children 1st Grade

Welcome to the Math Salamanders Math Problems for Children 1st Grade. Here you will find our range of First Grade Math Word Problem Worksheets which will help your child apply and practice their Math skills to solve a range of problems.

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Math Problems for Children

Here you will find a range of problem solving worksheets.

The sheets involve using a range of math skills and knowledge to solve problems.

Each problem sheet is based around an interesting theme and comes complete with an answer sheet. The sheets are graded so that the easier sheets come first.

Using these sheets will help your child to:

• apply their addition and subtraction skills;
• apply their knowledge of place value;
• solve a range of problems.

1st Grade Math Word Problems

• At the Seaside 1

At the seaside 1 involves counting, as well as adding and subtracting small numbers. There are pictures to help children count on and back.

• PDF version
• Salamander Towers

Salamander Towers involves counting, working out small differences and comparing. There are pictures to support.

• Captain's Party

Captain's party involves adding and subtracting with small numbers without any pictures to support.

• The Bead Necklace

The Bead Necklace involves patterns and sequences, as well as counting, adding and reasoning.

• Salamander Fishing

This problem worksheet involves adding and subtracting numbers up to 20, and also ordering 2 digit numbers.

• Salamander Bowling

Salamander Bowling involves adding and subtracting numbers to 20, as well as ordering 2 digit numbers.

• At the Seaside 2

At the Seaside sheet 2 involves working out differences, adding and subtracting with numbers to 20.

Looking for some harder word problems?

If you are looking for some more challenging word problems, then try our 2nd Grade math word problems.

The problems are at a more challenging level and involve larger numbers.

• 2nd Grade Math Word Problems

More Recommended Math Worksheets

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

More 1st Grade Math Word Problems

Here you will find a range of math word problems aimed at first grade level. Each problem sheet is based on an interesting theme such as parties or the seaside.

Using these first grade math worksheets will help your child to:

• Add and subtract with numbers to 12;
• order numbers to 100;
• solve a range of math problems.
• 1st grade Addition Word Problems
• 1st Grade Subtraction Word Problems
• 1st Grade Addition and Subtraction Problems

Longer Math Problems

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First Grade Place Value and Counting Worksheets

Here you will find a range of 1st Grade Place Value Worksheets.

These first grade math worksheets will help your child learn their place value, reading, writing and ordering numbers up to 100.

There are also some money worksheets involving counting in dimes and pennies to support place value learning.

• learn to count in tens and ones;
• learn to order numbers to 100;
• learn to count in dimes and pennies;
• learn to read and write numbers to 100.

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First Grade Math Games

Here you will find a range of free printable First Grade Math games. All children like to play Math games, and you will find a good range of 1st Grade Math Games here for your child to play and enjoy.

The following games involve different First Grade Math activities which you and your child can enjoy together.

All the free Math sheets in this section are informed by the Elementary Math Benchmarks for First Grade.

• 1st Grade Math Games

First Grade Math Puzzles

Here you will find a range of printable first grade math puzzles for your child to enjoy.

The puzzles will help your child practice and apply their addition and subtraction facts as well as developing their thinking and reasoning skills in a fun and engaging way.

Using these puzzles will help your child to:

• learn their addition facts to 12+12;
• develop thinking and reasoning skills;
• develop perseverance.
• Math Puzzles 1st Grade

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