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Number Pyramids

In this meeting, we explored Henri Piccioto’s number pyramid puzzles through notice/wonder, generating questions for problem-solving and additional puzzles for students.

number pyramid problem solving

At the beginning of the meeting, we shared some favorite sources of puzzles we like to use with students, include Which One Doesn’t Belong , Sometimes, Always, Never , and Open Middle .

Then I introduced Number Pyramids. Thank you to Henri Piccioto and his amazing web site of math resources . Here is the sequence we used:

number pyramid problem solving

Try these pyramids on your own.

number pyramid problem solving

Some shared language

2-row pyramid, 3-row pyramid, 4-row pyramid, …

seeds : the numbers that are given

middle number/cell : a number or cell that does not have an outside edge

wings: We decided on this term to refer to the bottom leftmost and bottom rightmost numbers

What do you notice?

  • Adding two even numbers yields an even sum
  • Adding an odd and an even number yields an odd sum
  • The pyramids on the bottom – the numbers given are all on the outside diagonal
  • In 4-row pyramids, the sums of each row increase by the same constant number found in the middle cell of 2nd row, or middle two cells of bottom row.
  • The sum of the top of a 3-row pyramid is double the center bottom number, plus the wings (bottom corner numbers).
  • The sum of the top of a 4-row is triple the middle number, plus the wings.
  • Two matching numbers lead to a “mirror pattern” in the row below: 7, 7 leads to 3, 4, 3 below.

Mark noticed that the sum of each row a 3-row pyramid and a 4-row pyramid increase by a constant value that can be found in the middle of the bottom row of a 3-row pyramid and in the middle cell of the 4-row pyramid.

Maggie noticed that in a 3-row pyramid, the top number is 2 times the bottom middle number, plus the wings . In a 4-row pyramid, the top number is 3 times the middle number, plus the wings.

number pyramid problem solving

What do you wonder?

  • Would a 5-row pyramid have Maggie’s pattern? Conjecture: 4 times all the sums of the middle bottom numbers, plus the wings.
  • Is this only a whole number puzzle? Could the boxes have decimals or fractions? Could they have negative numbers?
  • What’s the fewest seeds needed to solve a puzzle? Where do the seeds need to be in the pyramid?
  • Given the top number, can we fill in any-sized pyramid?
  • Could we fill in a blank pyramid? Could that be a puzzle?
  • Do we need numbers at all?
  • At what point does it become too difficult to solve? 2 seeds on a 5-row pyramid, for example. Would we still be able to solve it?
  • How do you choose the seeds and the positions of the numbers? Do only 2-digit numbers work? Is it possible with 3-digit and 4-digit numbers?
  • Is there an application for this pattern? Building a building, road, etc?
  • Is there a certain number of seeds where a finite number of solutions is possible? Fewer seeds where multiple solutions are possible?
  • How could we represent this algebraically? How could we make the unfolding of Mark’s and Maggie’s patterns explicit?
  • What would happen if we changed the pyramid rule? Subtraction, multiplication, …

Small Groups

We then spent about 15 minutes working individually to consider the questions we generated, then worked in groups.

Nadia and Amy experimented with making number pyramid puzzles with fractions.

number pyramid problem solving

Rebecca, Older, and Mark examined the pattern of the constant growth in the sum of the pyramid rows and found that the pattern changed in a 5-row pyramid. In the pyramids below, there is a constant difference between rows 2 and 3, and rows 3 and 4, but the difference changes between rows 4 and 5.

number pyramid problem solving

Maggie, Sarah, and Spencer used algebra to analyze a 6-row pyramid.

number pyramid problem solving

They found patterns in the coefficients of the variables for the numbers used in the base row: A, B, C, D, E, F. They noticed that the coefficients of the variables within each of the cells are the same as a row in Pascal’s Triangle. The coefficients of the variables in the top cell is also the same as a row in Pascal’s Triangle.

  • The coefficients for the total of row 1 are 1, 1, 1, 1, 1, 1.
  • The coefficients for the total of row 2 are 1, 2, 2, 2, 2, 1.
  • The coefficients for the total of row 3 are 1, 3, 4, 4, 3, 1.
  • The coefficients for the total of row 4 are 1, 4, 7, 7, 4, 1.
  • The coefficients for the total of row 5 are 1, 5, 10, 10, 5, 1.

Additional puzzles/questions to consider

  • Knowing the three corner numbers in a 3-row pyramid, is it possible to predict the number that will go in the middle of the bottom row without any trial and error?
  • Knowing the three corner numbers in a 4-row pyramid, is it possible to predict the number that will go in the middle cell without any trial and error?
  • How many seeds are necessary to create one solution? Does the position change how many seeds are necessary?
  • Make a pyramid puzzle that cannot be solved. Make a pyramid puzzle that can be solved in more than one way.
  • What would be a useful sequence of puzzles for a group of students?

If you create more number pyramids, please share them so that we can add them to our worksheet for students.

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number pyramid problem solving

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Number pyramid puzzle game

Complete the addition pyramid puzzle. Solve math number pyramid puzzle game online. Play missing number pyramid puzzle for kids. Learn how to solve number pyramids. Download math pyramid puzzle worksheet, number pyramids worksheet, addition pyramids worksheet and 4-layer number pyramid online. Play math number pyramid game. Learn how to play math pyramid game. number pyramid generator. Download printable math pyramid worksheet and pyramid addition worksheets. Play number pyramid game.

number pyramid problem solving

Fill in missing numbers in the number pyramid puzzle game. Click the blue button to choose the maximum value on the top: 20, 30, 50 or 100:

number pyramid problem solving

Math number pyramid puzzle game online

number pyramid problem solving

Math number pyramids are pyramids of numbers. In a number pyramid puzzle game, numbers next to each other are added together to make the number above it.

You can choose the maximum value on the top of the addition pyramid: 20, 30, 50 or 100. Math pyramid puzzle game is a great way how kids can learn addition.

How to play addition pyramid game

Addition pyramid worksheets

Addition pyramids worksheets help you to make math lessons more interesting. Kids have to complete the missing number pyramid puzzle.

Download our free printable addition pyramids worksheets in PDF below. Each number pyramids worksheet consists of two pages: the first page is the worksheet, the other page contains the answer key. All these number pyramid puzzles are generated automatically: every time a new addition pyramid worksheet.

You can find even more free 1st grade math worksheets here .

number pyramid problem solving

How do you solve an addition pyramid math puzzle?

In the addition pyramid math puzzle kids must add together two numbers. They can use the knowledge they have gained from playing the number bonds game .

Students solve the math pyramid game by adding adjacent numbers and writing the sum above them, working this way up to the top of the 4-layer number pyramid puzzle.

The bottom row is filled with random numbers. Each number in the upper rows is the sum of the two numbers below it.

Press "Check it" to find out if your answer is OK. The correct boxes will be green, wrong boxes will be red. Press the button "New game" and you can play a new number pyramid puzzle game. You can also watch this tutorial on YouTube .

Why to play math pyramid puzzle game?

Number pyramid game is a nice way how to learn addition. To play this game kids need to have basic knowledge of addition up to 20 and addition up to 30 .

Math pyramid puzzle game is suitable for training 1st Grade Math . Do you want to practice addition and subtraction at the same time? Then play this math crossword puzzle game .

You might also like these number pyramid games:

  • Subtraction pyramids
  • Multiplication pyramids

Math number pyramid puzzle game online. Addition pyramid game. missing number pyramid puzzle.

Pyramid number puzzle

In math pyramid puzzle game every brick contains the sum of the two bricks below. Fill in the missing numbers in the empty bricks.

This pyramid number puzzle can be played on any device, you need only the internet connection.

Math Puzzles Addition Games 1st Grade Math Games 2nd Grade Math Games

Author: Šárka Novotná

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number pyramid problem solving

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© Some rights reserved https://www.mathed.page/early-math/pyramids Henri Picciotto's Math Education Page

Number Pyramids

pyramid

Henri Picciotto

This is an activity for upper elementary or middle school students. First, students solve puzzles, and then they make up puzzles. This video explains the basic idea, with specific page references to the worksheet:

Download the worksheet , which includes some teacher notes in the back.

Your students will also need some blank pyramids on which they can experiment.

Possible follow-up: I scripted a condensed version of this unit for a TED-Ed animated riddle . I recommend only showing this to your students after doing the activities I shared above, because the video jumps quickly to the final question, thus not allowing for a full exploration of the ideas. On the other hand, after they have done and discussed the worksheets, students probably would enjoy the animation, and appreciate the explanations that follow the pause.

This unit was inspired by Brad Fulton’s Pyramid Math (of which I only saw two pages.) Many thanks to James Propp and James Tanton for valuable feedback.

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Number Pyramids

Subject: Mathematics

Age range: 7-11

Resource type: Lesson (complete)

Elastic Maths Resources

Last updated

15 September 2019

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docx, 230.08 KB

Differentiated number pyramids worksheet containing positive whole numbers with answers.

Red - Completing pyramids by adding. Amber - Completing pyramids by adding and subtracting. Green - Problem solving with pyramids.

Like this resource? Try these bundles of Number Pyramids worksheets…

Number Pyramids Bundle A Number Pyramids Bundle B Number Pyramids Bundle C

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Get this resource as part of a bundle and save up to 56%

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

Maths Number Pyramids Bundle A

Number pyramids are a challenging and engaging way to learn lots of different maths topics. Values in lower layers of the pyramid determine the values above them with the goal to completely fill pyramid. Each worksheet is differentiated (Red, Amber and Green) with the last section tailored towards problem solving and enhancing a student's mathematical resilience. This bundle contains number pyramids worksheets on... 1. Adding Integers [try for free](https://www.tes.com/teaching-resource/number-pyramids-12157123) 2. Adding Negative Numbers 3. Adding Fractions 4. Multiplying Fractions 5. Collecting Terms 6. Multiplying Terms 7. Algebraic Fractions

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Number pyramid problem (algebra 1)

Write an equation that can be used to find d , the difference between the last number and the first number, for any row r . (Show work please)

Row 2; 8 10

Row 3; 15 17 19

Row 4; 24 26 28 30

Row 5; 35 37 39 41 43

Row 6; 48 50 52 54 56 58

1 Expert Answer

number pyramid problem solving

Hadi B. answered • 04/02/19

BS in Mathematics with 5+ years of tutoring experience

the difference in the last and first number in row 2 is 2

so, 2 times 1

the difference in the last and first number in row 3 is 4

so, 2 times 2

the difference in the last and first number in row 4 is 6

so, 2 times 3

the difference in the last and first number in row n is 2 times n-1

so, d = 2(n-1) = 2n-2

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Put the numbers 1 to 5 in the bottom row of this pyramid. They can be arranged in any order. The numbers in the other bricks are found by adding the two bricks immediately below together. What arrangement of the numbers in the bottom row gives the largest total in the top brick of the pyramid?

What arrangement gives the smallest total in the top brick of the pyramid?

A pyramid puzzle worksheet is available here

A Mathematics Lesson Starter Of The Day

Teacher: Scroll down the page to find the link to the interactive, self-checking pupil version of Pyramid Puzzle.

Starter of The Day Transum Mathematics Topics

Topics: Starter | Algebra | Arithmetic | Functions | Number | Problem Solving

  • Claire Erving, Clapham
  • Loved this starter - worked for a wide range of ages and abilities. I also extended it by getting the pupils to multiply - though you do get an answer in millions!
  • Sue Johnson,
  • Excellent preparation for Yr 7 equation work See Badger Starters and Constructing Linear Equations pack
  • class 5 6 a, St Catherines
  • A really fun way to start the day!
  • Simon Sandys, Northwood College
  • My students showed me that the logical way to get the highest score is to put 5 in the middle so that you are maximising the highest number and 1 and 2 on the sides so that you are minimising their effects. The opposite, of course, to find the lowest number.
  • Teacher Paul, Dublin Ireland
  • My Year 5 class loved this starter..Worked great together in small groups..
  • Neve - Year 6, Charnwood Primary Lichfield
  • A good starter as it got my brain working!
  • Poppy Larn, Dorking
  • This is a great website!
  • Mr Draper, Harrogate
  • This puzzle was challenging, fun and got everyone in my year 5 class thinking. One pupil described it as 'mind-boggling'!
  • Neve, Hothfield Junior School
  • We did this at school and it was really fun. I was able to get the smallest and the largest and it is really fun to experiment with.
  • Yazan Alamer, Dubai International Academy
  • I loved that starter challenge. It was so fun and helped me with my maths skills.
  • Maths Brainy Badgers, United Kingdom
  • We found this fun. Charlie was very logical and managed to find the biggest number.

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Number Pyramids

HUGE COLLECTION OF NUMBER PYRAMIDS WORKSHEETS IN PDF FORMAT TO PRINT

Improve your basic math skills and practice your mental math with this huge collection of number pyramids. Which contains 15 addition pyramids worksheets of 3 and 4 floor levels.

Find the missing numbers of each pyramid, in order to get completed these math puzzles. You will have to alternate addition and subtraction operations. In this way, it would be easy for you to understand the relationship between them as inverse operations. It’s very important to establish addition and subtraction as inverse operations in order to later be able to solve equations.

Get a tailored math challenge to you or to your students. Since, this math puzzles have different variants of difficulty. Also you can practice basic math operations, mental math, arithmetic thinking and algebraic thinking, all these on a differentiated and transversal way.

Firstly, you can find the easiest number pyramids, which are meant to strengthen basic addition and subtraction operations. In this way you can practice mental math and basic math skills.

After that, you will have the most complex pyramids, which can be solved by linear equations or systems of linear equations. Although, we think it’s better to use ingenuity and numerical analysis to determine the missing values.

You can also find more pyramids in our application Pyramid Sums .

Practice problems of the pyramid

Number of problems found: 248.

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  • all math problems 18398
  • solid geometry 2255
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  • area of a shape 97
  • algebra 5435
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  • basic functions 5777
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COMMENTS

  1. Number Pyramids

    Student Solutions Teachers' Resources Number Pyramids printable sheet In a number pyramid, the numbers on the lower layers determine the numbers above them. Start by choosing three single-digit numbers and enter them in the bottom row of the interactive number pyramid.

  2. PDF p. 1 Number Pyramids

    1. Fill out the empty cells in the examples. If you did this correctly, the top number in the last pyramid should be 32. Pyramid Puzzles The given numbers are called seeds. You are given three seeds in each pyramid: 2. Fill out the empty cells in the pyramids above. (You don't have to do them in order.) 3.

  3. What are and how to solve number walls?

    Number walls, also called number pyramids or calculation walls, are solved with a specific method. In each brick the sum of the two bricks below is shown. To calculate the content of each...

  4. Number Pyramids

    In this meeting, we explored Henri Piccioto's number pyramid puzzles through notice/wonder, generating questions for problem-solving and additional puzzles for students. Facilitator (s): Eric Appleton Date of Meeting: June 18, 2020 Problem: · url · url

  5. Math Number Pyramid Puzzle Game + Worksheets

    WORKSHEETS Number pyramid puzzle game Fill in missing numbers in the number pyramid puzzle game. Click the blue button to choose the maximum value on the top: 20, 30, 50 or 100: Please, share it: Math number pyramid puzzle game online Math number pyramids are pyramids of numbers.

  6. More Number Pyramids

    Age 11 to 14 Challenge Level Secondary curriculum Problem Getting Started Student Solutions Teachers' Resources More Number Pyramids printable sheet This problem follows on from Number Pyramids. In the number pyramid below, the number in the bottom left hand corner determines all the other numbers.

  7. More Number Pyramids

    Maxim and Leslie also found ways to find the bottom number from the top number. This is Maxim's method: $(n-12)\div8$ I worked this out by doing the inverse of the first problem. This is Leslie's method. The way I found was to first subtract the top number by four, and then to divide the result by eight and then subtract one.

  8. Number Pyramids

    Student Solutions Teachers' Resources Why do this problem? This problem introduces the idea of number pyramids as a context to explore number relationships that can be generalised and justified using algebra.

  9. How to Solve a Number Pyramid

    0:00 / 4:14 How to Solve a Number Pyramid Mathematics 113 subscribers 28K views 3 years ago In this video I will tell you how to solve a number pyramid. ...more ...more Addition/Subtraction...

  10. Using number pyramids to practise non calculator addition

    Howard Astley-Jones, an Assistant Director at the NCETM, explains how to use number pyramids to add consecutive numbers. He explores the patterns that emerge...

  11. More Number Pyramids Extension

    More Number Pyramids Extension. Age 11 to 14. Interactive environment. This follows on from More Number Pyramids . Change the bottom left number and explore how it affects the top number. You can select different step sizes for the numbers on the bottom layer.

  12. Number Pyramids

    This is an activity for upper elementary or middle school students. First, students solve puzzles, and then they make up puzzles. This video explains the basic idea, with specific page references to the worksheet: Download the worksheet, which includes some teacher notes in the back. Your students will also need some blank pyramids on which ...

  13. Number Pyramids

    1. Adding Integers [try for free] (https://www.tes.com/teaching-resource/number-pyramids-12157123) 2. Adding Negative Numbers 3. Adding Fractions 4. Multiplying Fractions 5. Collecting Terms 6. Multiplying Terms 7. Algebraic Fractions £4.00 Report this resource to let us know if it violates our terms and conditions.

  14. Number Pyramids

    This video shows you the three stages in solving Number Pyramid problems

  15. Number pyramid problem (algebra 1)

    Lex A. asked • 04/02/19 Number pyramid problem (algebra 1) Write an equation that can be used to find d, the difference between the last number and the first number, for any row r. (Show work please) Row 2; 8 10 Row 3; 15 17 19 Row 4; 24 26 28 30 Row 5; 35 37 39 41 43 Row 6; 48 50 52 54 56 58 Follow • 2 Add comment Report 1 Expert Answer

  16. Math Pyramid Puzzle Worksheet

    6 reviews Maths Mastery - Fluency, Reasoning and Problem Solving Activities and Games Why is this Maths Pyramid Worksheet useful? This maths worksheet is ideal for helping students practice their math problem-solving skills by finding out the missing numbers in the pyramid using addition. Show more Related Searches

  17. Pyramid Puzzle

    of the pyramid? A pyramid puzzle worksheet is available here A Mathematics Lesson Starter Of The Day Teacher: Scroll down the page to find the link to the interactive, self-checking pupil version of Pyramid Puzzle. Starter of The Day Transum Mathematics Topics Topics: Starter | Algebra | Arithmetic | Functions | Number | Problem Solving

  18. Number Pyramids

    Download Share This HUGE COLLECTION OF NUMBER PYRAMIDS WORKSHEETS IN PDF FORMAT TO PRINT Improve your basic math skills and practice your mental math with this huge collection of number pyramids. Which contains 15 addition pyramids worksheets of 3 and 4 floor levels.

  19. KS2 Maths Number Pyramid Puzzle Game

    These Number Pyramid Worksheets are great for helping KS1 & KS2 children practice their addition and subtraction skills in a challenging and engaging puzzle game. Show more Related Searches multiplication pyramids maths puzzles year 5 pyramid puzzles ks2 maths number pyramids maths games Ratings & Reviews Curriculum Links Make a Request

  20. The Chinese Number Pyramid Puzzle

    The Chinese Number Pyramid Puzzle Puzzles are excellent tools for promoting logical reasoning, observational skills, and criti-cal thinking abilities among students. The Chinese Number Pyramid is one such puzzle that requires students to observe data, analyze them critically, and obtain a logical solution.

  21. Practice problems of the pyramid

    The cast The cast in the body of a regular quadrilateral pyramid with a base edge 60 cm long and 5 cm high is made of a material with a density of 7.8 g/cm cubic. Calculate its weight. Pyramid Z8-I-6 Each brick of the pyramid contains one number.