year 2 problem solving powerpoint

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Problem-solving maths investigations for year 2.

Hamilton provide an extensive suite of problem-solving maths investigations for Year 2 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 2 .

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 2:

• Individually, they are incorporated into every unit in our Year 2 flexible maths blocks .
• Collectively, they appear on our resources page where you can explore all our in-depth problem solving investigations for Year 2 .

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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I See Problem-Solving - Y2

The eBook I See Problem-Solving - Y2 gives coherent sequences of mathematical problem-solving tasks to build understanding and deepen learning. The initial tasks in each 'task family', with visual representations, allow children to build confidence and practice key skills. Then the challenges are opened up and extended! The ultimate resource for building children as problem-solvers.

Download I See Problem-Solving - Y2, Task Build-Up (PowerPoint)

Download I See Problem-Solving - Y2, Task Build-Up (PDF)

The purchase price is £30  (which includes VAT) for the PDF digital download. I See Problem-Solving - Y2 Sample provides 3 free sample task families for you to try out.

For each 'task family', the Task Build-Up examples introduce children to the format of the activities and help to build the key skills step-by-step. Children are able to practice these skills using the introductory tasks in each task family. Visual representations are used and misconceptions are addressed. Then, the tasks become progressively more open and extended. This will ensure that all children are both supported and challenged. It will give all children the excitement of engaging in rich problem-solving!

The 28 Task Families of I See Problem-Solving - Y2 , written by Gareth Metcalfe, cover all areas of the English mathematics curriculum. This corresponds to US Grade 1. To purchase, click on the link below. If you need any assistance with ordering, please email [email protected].

Online Training: Inspiring Mathematical Thinking Using I See Problem-Solving - Y2

You can access the recording of this 60-minute online training session by emailing [email protected] stating the name of your school and the number of people who will view the recording. The cost is £15+VAT per person. This video gives an overview of the session:

Resources you can trust

A reference PowerPoint for the 2 times table designed to be used with Year 2. The 2 times table is demonstrated visually in a variety of ways, including as counters on a grid and as number lines. The resource also includes word problems where children must use facts from the 2 multiplication table to find the answer.

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Watch CBS News

How two high school students solved a 2,000-year-old math puzzle

By Bill Whitaker , Aliza Chasan , Sara Kuzmarov, Mariah Campbell

May 5, 2024 / 7:00 PM EDT / CBS News

A high school math teacher at St. Mary's Academy in New Orleans, Michelle Blouin Williams, was looking for ingenuity when she and her colleagues set a school-wide math contest with a challenging bonus question. That bonus question asked students to create a new proof for the Pythagorean Theorem, a fundamental principle of geometry, using trigonometry. The teachers weren't necessarily expecting anyone to solve it, as proofs of the Pythagorean Theorem using trigonometry were believed to be impossible for nearly 2,000 years.

But then, in December 2022, Calcea Johnson and Ne'Kiya Jackson, seniors at St. Mary's Academy, stepped up to the challenge. The $500 prize money was a motivating factor.

After months of work, they submitted their innovative proofs to their teachers. With the contest behind them, their teachers encouraged the students to present at a mathematics conference, and then to seek to publish their work. And even today, they're not done. Now in college, they've been working on further proofs of the Pythagorean Theorem and believe they have found five more proofs. Amazingly, despite their impressive achievements, they insist they're not math geniuses.

"I think that's a stretch," Calcea said.

The St. Mary's math contest

When the pair started working on the math contest they were familiar with the Pythagorean Theorem's equation: A² + B² = C², which explains that by knowing the length of two sides of a right triangle, it's possible to figure out the length of the third side.

When Calcea and Ne'Kiya set out to create a new Pythagorean Theorem proof, they didn't know that for thousands of years, one using trigonometry was thought to be impossible.  In 2009, mathematician Jason Zimba submitted one, and now Calcea and Ne'Kiya are adding to the canon.

Calcea and Ne'Kiya had studied geometry and some trigonometry when they started working on their proofs, but said they didn't feel math was easy. As the contest went on, they spent almost all their free time developing their ideas.

"The garbage can was full of papers, which she would, you know, work out the problems and if that didn't work, she would ball it up, throw it in the trash," Cal Johnson, Calcea's dad, said.

Neliska Jackson, Ne'Kiya's mother, says lightheartedly, that most of the time, her daughter's work was beyond her. 

To document Calcea and Ne'Kiya's work, math teachers at St. Mary's submitted their proofs to an American Mathematical Society conference in Atlanta in March 2023.

"Well, our teacher approached us and was like, 'Hey, you might be able to actually present this,'" Ne'Kiya said. "I was like, 'Are you joking?' But she wasn't. So we went. I got up there. We presented and it went well, and it blew up."

Why Calcea' and Ne'kiya's work "blew up"

The reaction was insane and unexpected, Calcea said. News of their accomplishment spread around the world. The pair got a write-up in South Korea and a shoutout from former first lady Michelle Obama. They got a commendation from the governor and keys to the city of New Orleans. 

Calcea and Ne'Kiya said they think there's several reasons why people found their work so impressive. 

"Probably because we're African American, one," Ne'Kiya said. "And we're also women. So I think-- oh, and our age. Of course our ages probably played a big part."

Ne'Kiya said she'd like their accomplishment to be celebrated for what it is: "a great mathematical achievement."

In spite of the community's celebration of the students' work, St. Mary's Academy president and interim principal Pamela Rogers said that with recognition came racist calls and comments. 

"[People said] 'they could not have done it. African Americans don't have the brains to do it.' Of course, we sheltered our girls from that," Rogers said. "But we absolutely did not expect it to come in the volume that it came."

Rogers said too often society has a vision of who can be successful.

"To some people, it is not always an African American female," Rogers said. "And to us, it's always an African American female."

Success at St. Marys 

St. Mary's, a private Catholic elementary and high school, was started for young Black women just after the Civil War. Ne'Kiya and Calcea follow a long line of barrier-breaking graduates. Leah Chase , the late queen of Creole cuisine, was an alum. So was Michelle Woodfork, the first African American female New Orleans police chief, and Dana Douglas, a judge for the Fifth Circuit Court of Appeals. 

Math teacher Michelle Blouin Williams, who initiated the math contest, said Calcea and Ne'Kiya are typical St. Mary's students. She said if they're "unicorns," then every student who's matriculated through the school is a "beautiful, Black unicorn."

Students hear that message from the moment they walk in the door, Rogers said. 

"We believe all students can succeed, all students can learn," the principal said. "It does not matter the environment that you live in."

About half the students at St. Mary's get scholarships, subsidized by fundraising to defray the $8,000 a year tuition. There's no test to get in, but expectations are high and rules are strict: cellphones are not allowed and modest skirts and hair in its natural color are required. 

Students said they appreciate the rules and rigor.

"Especially the standards that they set for us," junior Rayah Siddiq said. "They're very high. And I don't think that's ever going to change." 

What's next for Ne'Kiya and Calcea

Last year when Ne'Kiya and Calcea graduated, all their classmates were accepted into college and received scholarship offers. The school has had a 100% graduation rate and a 100% college acceptance rate for 17 years, according to Rogers.

Ne'Kiya got a full ride in the pharmacy department at Xavier University in New Orleans. Calcea, the class valedictorian, is studying environmental engineering at Louisiana State University. Neither one is pursuing a career in math, though Calcea said she may minor in math.

"People might expect too much out of me if I become a mathematician," Ne'Kiya said wryly. 

Bill Whitaker is an award-winning journalist and 60 Minutes correspondent who has covered major news stories, domestically and across the globe, for more than four decades with CBS News.

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New Orleans teens solve 2,000-year-old math problem

Posted: May 11, 2024 | Last updated: May 11, 2024

Some ingenuity

Teacher Michelle Blouin Williams initiated a math competition with a bonus question tasking students to develop a new proof for the Pythagorean theorem using trigonometry, without anticipating that anyone would successfully tackle the challenge.  

She said, “I was just looking for some ingenuity.”   

Williams' expectations

Calcea Johnson and Ne’Kiya Jackson exceeded Williams' expectations by successfully solving the challenge in 2023.   

St. Mary's Academy

These two teenagers, who were seniors at St. Mary's Academy in New Orleans, a renowned Catholic school for girls with impressive college acceptance and graduation rates, were featured on CBS News' "60 Minutes" to discuss their accomplishment.   

$500 reward

Initially enticed by the math competition's $500 reward, their determination to complete the task intensified as they delved into the complex bonus question.   

Over a period of two months, these high school seniors dedicated themselves to completing their proof.  

Pages and pages

During an interview with "60 Minutes," CeCe Johnson, the mother of Calcea, said “It was pages and pages and pages of, like, over 20 or 30 pages for this one problem.”  

The garbage can

Her father, Cal Johnson, added, “Yeah, the garbage can was full of papers, which she would, you know, work out the problems and — if that didn’t work she would ball it up, throw it in the trash.”  

Upon completion

Upon completion, the teachers at St. Mary's Academy acknowledged the significance of Calcea and Ne'Kiya's achievement and submitted their proof to the American Mathematical Society for recognition at a conference in March 2023, where the students presented their findings.  

The Pythagorean theorem

The Pythagorean theorem, at its core, states that knowing the lengths of two sides of a right triangle allows you to determine the length of the third side using the formula a² + b² = c².   

While commonly attributed to the Greek mathematician Pythagoras, historical evidence suggests its existence in Babylon and Iron Age India. This theorem finds practical applications in construction, architecture, navigation, and surveying.  

A mathematical proof

A mathematical proof is a logical argument that demonstrates the truth of a mathematical theorem. American mathematician Daniel Kane likens proofs to essays, but rooted in mathematical concepts.  

Using trigonometry

As per the "60 Minutes" segment, “there had been more than 300 documented proofs of the Pythagorean Theorem using algebra and geometry, but for 2,000 years a proof using trigonometry was thought to be impossible.”  

Mathematician Elisha Loomis

Back in 1927, mathematician Elisha Loomis made a statement in his book "The Pythagorean Proposition." Loomis contended that a trigonometric proof of the theorem was impossible as it would create a circular argument.  

Stuart Anderson

Stuart Anderson, a retired mathematics professor from Texas A&M University-Commerce, mentioned to Scientific American, “A lot of the basic trig ‘identities’ are nothing more than Pythagoras’ theorem.”  

Trigonometric functions

Loomis contended that attempting to use trigonometric functions to prove the Pythagorean theorem would result in a circular reasoning loop, as the functions themselves are built upon the theorem. This, according to Loomis, would constitute a fundamental mathematical mistake.  

The law of sines

As reported by Scientific American, the teenagers challenged this notion during their presentation in 2023 and stated that “a trigonometric identity called the law of sines didn’t depend on the Pythagorean theorem and that they could use it to prove the theorem.”  

Final peer review

Calcea and Ne'Kiya are now part of a select few who have achieved a similar milestone, such as mathematician Jason Zimba, who developed a new proof in 2009. They submitted their proof for the final peer review earlier this year and are actively working on crafting additional proofs.  

In recognition

In recognition of their accomplishment, the teenagers were honored with the keys to the city of New Orleans and received commendations from the governor of Louisiana, along with other public acknowledgments.  

Widespread recognition

Despite the widespread recognition of their accomplishment which “blew up,” as Ne'Kiya expressed it, the two students maintain their humility and even chuckled at being labeled as geniuses.  

Surprised and skeptical

Upon the revelation of their achievement, there were individuals who appeared surprised and skeptical, dismissing the news as untrue, as mentioned by St. Mary's president Pamela Rogers during the interview.  

African Americans

“They were saying, ‘Oh, they could not have done it. African Americans don’t have the brains to do it.’ ... People — have a vision of who can be successful. And — to some people, it is not always an African American female. And to us, it’s always an African American female.”  

The significant reaction

When questioned by interviewer Bill Whitaker about their thoughts on the significant reaction, Ne’Kiya said, “Probably because we’re African American, one. And we’re also women. So I think — oh, and our age. Of course our ages probably played a big part.”  

Great mathematical achievement

“I’d like to actually be celebrated for what it is. Like, it’s a great mathematical achievement,” she continued.  

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Addition and Subtraction - Year 2

Subject: Mathematics

Age range: 5-7

Resource type: Other

Last updated

4 February 2024

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This resource contains a PowerPoint lesson to support the delivery of the Year 2 Addition and Subtraction - Autumn Term - Block 2 White Rose (WRM) ‘small steps’ programme. This PowerPoint is for Week 1.

The resource contains a fully editable and interactive 85-slide PowerPoint lesson that contains tasks and activities (pictorial and abstract) linked to the White Rose small steps with an emphasis on the mastery approach to learning advocated by the White Rose scheme and includes reasoning and problem-solving tasks.

The PowerPoint focuses on the following objectives and small steps:

Year 2 Maths’ National Curriculum Objectives

Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100. Add and subtract numbers using concrete objects, pictorial representations, and mentally, including: a two-digit number and ones; a two-digit number and tens; two two-digit numbers; adding three one-digit numbers. Solve problems with addition and subtraction: using concrete objects and pictorial representations, including those involving numbers, quantities and measures; applying their increasing knowledge of mental and written methods. Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems.

White Rose Small Steps

Fact families Addition and subtraction bonds to 20 Check calculation Compare number sentence Related facts

If you buy this resource and are pleased with your purchase, I would be extremely grateful if you could leave a review. As a token of appreciation, you can have a free resource of your choice up to the same value as your purchased resource. Just email [email protected] with your user name, the resource you have reviewed and the resource you would like for free.

You may also be interested in an accompanying 21-page workbook and progress check which can be used alongside the PowerPoint.

Year 2 Week 1 Addition and Subtraction: Autumn Term Block 2 Workbook 1

More Maths Resources

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A bundle is a package of resources grouped together to teach a particular topic, or a series of lessons, in one place.

Addition and Subtraction: Year 2

This bundle contains four fully editable 75+ slide PowerPoint presentation lessons to support the delivery of the Year 2, Block 2 Place Value - Autumn Term White Rose (WRM) ‘small steps’ programme for weeks 1 to 4. The PowerPoints explain how to add and subtract using different methods - including using concrete objects, a number line for counting on and back, part-whole models, partitioning and the column methods with and without exchange. It also includes a variety of tasks and activities (concrete, pictorial and abstract) linked to the White Rose small steps and embraces the mastery approach to learning advocated by the White Rose scheme. These resources can be used flexibly as whole lessons, starters, plenaries, to introduce topics, to consolidate and to revise. The PowerPoints focus on the following objectives and small steps: **Year 2 Maths’ National Curriculum Objectives** Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100. Add and subtract numbers using concrete objects, pictorial representations, and mentally, including: a two-digit number and ones; a two-digit number and tens; two two-digit numbers; adding three one-digit numbers. Show that the addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot. Solve problems with addition and subtraction: using concrete objects and pictorial representations, including those involving numbers, quantities and measures; applying their increasing knowledge of mental and written methods. Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems. **White Rose Small Steps** Fact families – Addition and subtraction bonds to 20 Check calculations Compare number sentences Related facts Bonds to 100 (tens) Add and subtract 1s 10 more and 10 less Add and subtract 10s Add a 2-digit and 1-digit number – crossing ten Subtract a 1-digit number from a 2-digit number – crossing ten Add two 2-digit numbers – not crossing ten – add ones and add tens Add two 2-digit numbers – crossing ten – add ones and add tens Subtract a 2-digit number from a 2-digit number – not crossing ten Subtract a 2-digit number from a 2-digit number – crossing ten – subtract ones and tens Bonds to 100 (tens and ones) Add three 1-digit numbers Click on the individual links for further details. *If you buy this resource and are pleased with your purchase, I would be extremely grateful if you could leave a review. As a token of appreciation, you can have a free resource of your choice up to the same value as your purchased resource. Just email [email protected] with your user name, the resource you have reviewed and the resource you would like for free.* **[More Maths Resources](https://www.tes.com/resources/search/?authorId=884045&q=%20&shop=Krazikas&subjects=GB%7C0%7CMathematics%7C&sortBy=newest)** Thinking of publishing your own resources? Check out this step-by-step guide: **[How to Become a Successful TES Author: Step-by-Step Guide]( https://www.tes.com/teaching-resource/-how-to-become-a-successful-tes-author-step-by-step-guide-by-a-top-selling-tes-author-11508391)**

This resource contains a PowerPoint lesson and a 21 page workbook to support the delivery of the Year 2 Addition and Subtraction - Autumn Term - Block 2 White Rose (WRM) 'small steps' programme. This PowerPoint is for Week 1. The fully editable and interactive 85-slide PowerPoint lesson contains tasks and activities (pictorial and abstract) linked to the White Rose small steps with an emphasis on the mastery approach to learning advocated by the White Rose scheme and includes reasoning and problem-solving tasks. The PowerPoint focuses on the following objectives and small steps: **Year 2 Maths' National Curriculum Objectives** Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100. Add and subtract numbers using concrete objects, pictorial representations, and mentally, including: a two-digit number and ones; a two-digit number and tens; two two-digit numbers; adding three one-digit numbers. Solve problems with addition and subtraction: using concrete objects and pictorial representations, including those involving numbers, quantities and measures; applying their increasing knowledge of mental and written methods. Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems. **White Rose Small Steps** Fact families Addition and subtraction bonds to 20 Check calculation Compare number sentence Related facts The workbook contains 21 worksheets / activities (concrete, pictorial and abstract) linked to the White Rose small steps. The workbooks are available in both PDF and word format to enable editing and personalisation of the workbook. *If you buy this resource and are pleased with your purchase, I would be extremely grateful if you could leave a review. As a token of appreciation, you can have a free resource of your choice up to the same value as your purchased resource. Just email [email protected] with your user name, the resource you have reviewed and the resource you would like for free.* **[More Maths Resources](https://www.tes.com/resources/search/?authorId=884045&q=%20&shop=Krazikas&subjects=GB%7C0%7CMathematics%7C&sortBy=newest)** Thinking of publishing your own resources? Check out this step-by-step guide: **[How to Become a Successful TES Author: Step-by-Step Guide]( https://www.tes.com/teaching-resource/-how-to-become-a-successful-tes-author-step-by-step-guide-by-a-top-selling-tes-author-11508391)**

This bundle contains four workbooks (with answers), four accompanying PowerPoint lessons and progress checks to support the delivery of the Year 2, Block 2 Place Value - Autumn Term White Rose (WRM) ‘small steps’ programme for weeks 1 to 4. There are a total of 84 worksheets / activities (concrete, pictorial and abstract) linked to the White Rose small steps with an emphasis on the mastery approach to learning advocated by the White Rose scheme and includes reasoning and problem-solving tasks. The resources focus on the following objectives and small steps: **Year 2 Maths’ National Curriculum Objectives** Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100. Add and subtract numbers using concrete objects, pictorial representations, and mentally, including: a two-digit number and ones; a two-digit number and tens; two two-digit numbers; adding three one-digit numbers. Show that the addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot. Solve problems with addition and subtraction: using concrete objects and pictorial representations, including those involving numbers, quantities and measures; applying their increasing knowledge of mental and written methods. Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems. **White Rose Small Steps** Fact families – Addition and subtraction bonds to 20 Check calculations Compare number sentences Related facts Bonds to 100 (tens) Add and subtract 1s 10 more and 10 less Add and subtract 10s Add a 2-digit and 1-digit number – crossing ten Subtract a 1-digit number from a 2-digit number – crossing ten Add two 2-digit numbers – not crossing ten – add ones and add tens Add two 2-digit numbers – crossing ten – add ones and add tens Subtract a 2-digit number from a 2-digit number – not crossing ten Subtract a 2-digit number from a 2-digit number – crossing ten – subtract ones and tens Bonds to 100 (tens and ones) Add three 1-digit numbers Click on the individual links for further details. *If you buy this resource and are pleased with your purchase, I would be extremely grateful if you could leave a review. As a token of appreciation, you can have a free resource of your choice up to the same value as your purchased resource. Just email [email protected] with your user name, the resource you have reviewed and the resource you would like for free.* **[More Maths Resources](https://www.tes.com/resources/search/?authorId=884045&q=%20&shop=Krazikas&subjects=GB%7C0%7CMathematics%7C&sortBy=newest)** Thinking of publishing your own resources? Check out this step-by-step guide: **[How to Become a Successful TES Author: Step-by-Step Guide]( https://www.tes.com/teaching-resource/-how-to-become-a-successful-tes-author-step-by-step-guide-by-a-top-selling-tes-author-11508391)**

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