number line to 100 reasoning and problem solving

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The Number Line to 100 – Reasoning and Problem Solving

The Number Line to 100 - Reasoning and Problem Solving

This worksheet includes a range of reasoning and problem solving questions for pupils to practise the main skill of using a number line to 100.

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The Number Line to 100 reasoning and problem solving worksheet Answer sheet

National Curriculum Objectives: (1N1a) Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number (1N4) Identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least

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Number Lines―A Lesson in the Planning Stage

I typically write blogs after teaching a lesson to share what I did and what I learned. This blog is different. I’m deep into planning a lesson for fourth graders about place value and number lines. It’s a lesson that I’ve never tried before with students but that I’ve been thinking about for a while.

The inspiration for the lesson is a Tweet from when Twitter was still Twitter. Mark Chubb posted it in 2016, evidence that I’ve truly been thinking about this lesson for a long while. When I first saw the Tweet, I struggled to think about where 1 billion would go. It wasn’t obvious to me.

Using the Tweet in a PD Session Shortly after seeing the Tweet, I used it as an opener in a PD session for K–5 teachers at John Muir Elementary School in San Francisco. I just searched my files and found the planning notes I had sent to Sara Liebert, who had organized the session. They’re dated December 8, 2016. Here’s what I wrote:

I won’t start with the problem Mark posed in his Tweet, but instead by having them locate points on various other numbers lines. I’ll start first, probably, with a line from 0 to 10, ask them to estimate where 7 would go, then move my finger slowly across the line from zero until they call Stop. I’ve used this technique in the classroom and kids always respond positively to the guessing part. This introduction will model for teachers how they could use simple number line problems like these with their students.  

After estimating where 7 would go, I’ll erase the 10, replace it with 100, and ask them to estimate where 10 would go, using the same finger routine. (Or maybe I’ll ask them to estimate a few numbers―50, 40, 65. I’m not sure.)

Next, I’ll replace the 100 with 1000 and ask them to estimate where 100, or some other numbers, would go. And then maybe I’ll change 1000 to 1 million and ask where 1000 would go. Finally, I’ll present the problem that Mark posted. I suspect that even though I’ve scaffolded the problem, it will still be a challenge.  

I created this outline of what I planned to do in the PD session.

Where I Am Now So now I’m planning (finally) how to use this idea with Aimee Levin’s fourth graders at Edna Maguire School in Mill Valley. In various lessons over the years, I’ve used the routine of moving my finger across a number line and asking students to tell me when to stop. (I describe this routine in a blog I wrote in 2016, “ Fractions on a Number Line .”) Now I’m thinking about using it to learn about how students would think about whole number problems.

Some of My Questions

• What problems should I use to scaffold the experience?
• Will the students be engaged in the lesson?
• What will Aimee and I learn about the students’ understanding of place value?
• Which would be difficult for them, even beyond their mathematical reach right now?
• What individual work should I ask them to do so that we would gain insights into their understanding and reasoning?

My Plan I strive when planning lessons to be sure to begin with an experience that will be accessible to all students and then feel my way into more challenges. I always have a plan, but I’m prepared to make adjustments as I receive feedback from the students. Here’s an outline of my current plan:

• Start with locating 7 on a number line with 0 and 10 located, introducing the routine of moving my finger across and asking them to tell me when to stop.
• Move to another number line with 0 and 100 located, and ask them to locate a few numbers. I’m thinking about 50, 10, 38, and 83. (I used 38 and 83 as numbers with the digits reversed, which I’m doing to plan for a follow-up independent partner activity.)
• Next introduce another number line with 0 and 1000 located, and first have them locate the numbers I used for the 0–100 number line, but each multiplied by 10―500, 100, 380, and 830.
• Stay with this number line and ask them to locate the numbers we used with the 0–100 number line―50, 10, 38, and 83.
• Give them an individual assignment with several number lines on which they should locate numbers and an additional option if they’d like to try a challenge.

I’m Not Planning Alone I appreciate Aimee’s willingness to let me “borrow” her class to try out an idea that I’m interested in. I met Aimee’s class once before when I taught a division lesson that I blogged about, “ Mulling about Teaching Division .” I planned the division lesson with Jenna Laib , and she and I talked recently about this number line lesson that I’m going to try. We agreed that starting with problems that were accessible to all was a good idea and our conversation resulted in my plan above. I also talked with Stephanie Sheffield, with whom I’ve collaborated on various projects, and she wondered about how the fourth graders might think about the distance the numbers 38 and 83 were away from the ends of the number line, that is if 38 was about the same, farther, or closer to zero than 83 was from 100.  I may also go to Muir in San Francisco and try the lesson with fourth or fifth graders there. I’ve been going to Muir since I met Sara Liebert in 2015 when she was a classroom teacher. Sara then became the school math coach, is now the principal, and we’re still collaborating.

I’ll post again after the teach the lesson to describe what occurred and offer my reflection.

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Previous Post Teaching a Number Line Lesson

Next post mulling about teaching division.

A billion is one thousandth of a trillion, so to define a billion on a number line that collates in a Trillion you would need to divide into thousands.

Yes, important for kids to learn but hard to grasp.

In your step 3, you multiply EACH number by 10 and so keep the ratios the same. Multiplying by 10 is the same as adding a zero to the end of each number. You could expand that part to add another zero, and another — seeing that the ratio [placement on the line] remains the same. Then, logically, if you took some larger numbers and REMOVED A ZERO from the end of each, that ratio would remain the same. So … If you remove all the zeroes from a billion and the same # of zeroes from a trillion, you will have the ratio of 1-to-1000. That might be a useful way to help students understand how you know to divide the line into a thousand parts.

Thanks for your response and your suggestion. I believe that it’s best to approach topics like this from multiple perspectives, and yours can be part of the mix. Comprehending these large quantities is difficult. Marilyn (a beginning birder)

© 2024 MARILYN BURNS MATH.

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Number Lines in Disguise

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Number Lines in Disguise printable sheet - main problem Number Lines in Disguise printable sheet - blank number lines

Often if a mathematician is stuck they might try an example with smaller numbers. Click below to reveal another example. 

You may be interested in the other problems in our Resilience and Perseverance Feature .

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Suppose you had to begin the never ending task of writing out the natural numbers: 1, 2, 3, 4, 5.... and so on. What would be the 1000th digit you would write down.

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Number Line up to 100 Printables

Welcome to our Number Line up to 100 printables page. We have a wide selection of printable number lines from 0 to 100 for you to choose from.

We have both filled and blank number lines, as well as coloured and plain number lines.

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Printable Number Line up to 100

Looking for a printable number line from 0 to 100?

There are a wide selection of number lines to meet your needs.

Please let us know if you want a number line that we have not created yet, and we will add it to our list!

All the number lines below are from 0 to 100.

Number lines include:

• Number values from 0 to 100 in ones with both coloured and black and white formats
• Number lines from 0 to 100 with divisions marked in tens.
• landscape and portrait versions of most sheets

Each number line comes in 3 different versions:

• a color version
• a b/w version
• an empty number line version

About Number Lines

Number lines are a great way to understand numbers and see them visually on a line.

They can be very useful in teaching counting as well as adding and subtracting.

Finding numbers on a number line, especially when the divisions are unmarked is a great way to develop counting on and back.

Try this quick and easy number line activity for 2 kids...

Find the Number on the Number Line Game

• You will need a number line sheet (version 1a - landscape or portrait), a pencil and a piece of scrap paper.
• One person is the Finder and one child is the Picker.
• The Picker chooses a number between 1 and 100 and writes it on the scrap paper and keeps it hidden.
• The Finder has to choose a number on the number line and make a mark.
• The Picker says whether his number is bigger than the marked number, smaller or whether the number is the same.
• If the number is bigger or smaller, the Finder has to choose another number on the number line and make a mark.
• If the number is the same, then the Finder has found the number and the game stops.
• The Finder's score is the number of marks made, so if they have made 5 marks on the number line, the score is 5.
• The players then swap and the Finder becomes the Picker and the Picker becomes the Finder.
• The new Finder wins the game by finding the number in fewer goes (with a lower score).

Standard Number Line up to 100 (Portrait version)

• Number Line up to 100 version 1a
• PDF version
• Number Line up to 100 version 1b
• Number Line up to 100 version 1c

My Number Line 0 to 100 (Portrait version)

• My Number Line 0 to 100 version 2a
• My Number Line 0 to 100 version 2b
• My Number Line 0 to 100 version 2c

LANDSCAPE VERSIONS

Number lines up to 100 (landscape version).

• Number Line 0 to 100 Landscape version 1a
• Number Line 0 to 100 Landscape version 1b
• Number Line 0 to 100 Landscape version 1c

My Number Line 0 to 100 (Landscape version)

• My Number Line 0 to 100 Landscape version 2a
• My Number Line 0 to 100 Landscape version 2b
• My Number Line 0 to 100 Landscape version 2c

Number Line up to 100 in TENS

• Number Line up to 100 in Tens version 1a
• Number Line up to 100 in Tens version 1b
• Number Line up to 100 in Tens version 1c

My Number Line up to 100 in TENS (Portrait version)

• My Number Line up to 100 in Tens version 2a
• My Number Line up to 100 in Tens version 2b
• My Number Line up to 100 in Tens version 2c

Number Line up to 100 in ONES (Portrait version)

These number lines have been split into 5 separate lines of 20 numbers.

• Number Line up to 100 Version 3A
• Number Line up to 100 Version 3B
• Number Line up to 100 Version 3C
• Number Line up to 100 Version 3D

Number Line up to 100 in ONES (Landscape version)

• Number Line up to 100 Landscape Version 3A
• Number Line up to 100 Landscape Version 3B
• Number Line up to 100 Landscape Version 3C
• Number Line up to 100 Landscape Version 3D

Number Line up to 100 - Special Versions

Print & stick and small font versions.

• Number Line 0 to 100 Print and Stick Version 1A
• Number Line 0 to 100 Print and Stick Version 1B

This landscape version has all the numbers from 0 to 100, but with a tiny font which will be too small for most students to use!

• Number Line 0 to 100 Small font Version 1A
• Number Line 0 to 100 Small font Version 1B

Number Line up to 100 Worksheets

We also have some worksheets involving using number lines up to 100.

These sheets are aimed at 1st and 2nd graders and involve placing and reading numbers correctly on number lines.

• Number lines to 100 Worksheets

Looking for some more number line resources?

We have a range of both number line worksheets and printable number line resource pages to support place value and number learning.

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Appendix A: Applications

Using a problem-solving strategy to solve number problems, learning outcomes.

• Apply the general problem-solving strategy to number problems
• Identify how many numbers you are solving for given a number problem
• Solve consecutive integer problems

Now we will translate and solve number problems. In number problems, you are given some clues about one or more numbers, and you use these clues to build an equation. Number problems don’t usually arise on an everyday basis, but they provide a good introduction to practicing the Problem-Solving Strategy. Remember to look for clue words such as difference , of , and and .

The difference of a number and six is [latex]13[/latex]. Find the number.

https://ohm.lumenlearning.com/multiembedq.php?id=142763&theme=oea&iframe_resize_id=mom50

The sum of twice a number and seven is [latex]15[/latex]. Find the number.

Show Solution

https://ohm.lumenlearning.com/multiembedq.php?id=142770&theme=oea&iframe_resize_id=mom60

Watch the following video to see another example of how to solve a number problem.

Solving for Two or More Numbers

Some number word problems ask you to find two or more numbers. It may be tempting to name them all with different variables, but so far we have only solved equations with one variable. We will define the numbers in terms of the same variable. Be sure to read the problem carefully to discover how all the numbers relate to each other.

One number is five more than another. The sum of the numbers is twenty-one. Find the numbers.

https://ohm.lumenlearning.com/multiembedq.php?id=142775&theme=oea&iframe_resize_id=mom70

Watch the following video to see another example of how to find two numbers given the relationship between the two.

The sum of two numbers is negative fourteen. One number is four less than the other. Find the numbers.

https://ohm.lumenlearning.com/multiembedq.php?id=142806&theme=oea&iframe_resize_id=mom80

One number is ten more than twice another. Their sum is one. Find the numbers.

https://ohm.lumenlearning.com/multiembedq.php?id=142811&theme=oea&iframe_resize_id=mom90

Solving for Consecutive Integers

Consecutive integers are integers that immediately follow each other. Some examples of consecutive integers are:

[latex]\begin{array}{c}\phantom{\rule{0.2em}{0ex}}\\ \phantom{\rule{0.2em}{0ex}}\\ \phantom{\rule{0.2em}{0ex}}\\ \phantom{\rule{0.2em}{0ex}}\\ \hfill \text{…}1,2,3,4\text{,…}\hfill \end{array}[/latex] [latex]\text{…}-10,-9,-8,-7\text{,…}[/latex] [latex]\text{…}150,151,152,153\text{,…}[/latex]

Notice that each number is one more than the number preceding it. So if we define the first integer as [latex]n[/latex], the next consecutive integer is [latex]n+1[/latex]. The one after that is one more than [latex]n+1[/latex], so it is [latex]n+1+1[/latex], or [latex]n+2[/latex].

[latex]\begin{array}{cccc}n\hfill & & & \text{1st integer}\hfill \\ n+1\hfill & & & \text{2nd consecutive integer}\hfill \\ n+2\hfill & & & \text{3rd consecutive integer}\hfill \end{array}[/latex]

The sum of two consecutive integers is [latex]47[/latex]. Find the numbers.

Find three consecutive integers whose sum is [latex]42[/latex].

Watch this video for another example of how to find three consecutive integers given their sum.

• Ex: Linear Equation Application with One Variable - Number Problem. Authored by : James Sousa (Mathispower4u.com). Located at : https://youtu.be/juslHscrh8s . License : CC BY: Attribution
• Ex: Write and Solve an Equation for Consecutive Natural Numbers with a Given Sum. Authored by : James Sousa (Mathispower4u.com). Located at : https://youtu.be/Bo67B0L9hGs . License : CC BY: Attribution
• Write and Solve a Linear Equations to Solve a Number Problem (1) Mathispower4u . Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/izIIqOztUyI . License : CC BY: Attribution
• Question ID 142763, 142770, 142775, 142806, 142811, 142816, 142817. Authored by : Lumen Learning. License : CC BY: Attribution . License Terms : IMathAS Community License, CC-BY + GPL
• Prealgebra. Provided by : OpenStax. License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]

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Number Line to 1000 - Year 3

Subject: Mathematics

Age range: 7-11

Resource type: Lesson (complete)

Last updated

6 July 2023

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In this lower KS2 maths teaching resource, pupils identify, represent and estimate numbers to 1000 on a number line. These activities cover the year 3 curriculum objectives in the maths programme of study (Number - number and place value) and supports the White Rose small steps guidance for year 3 - Autumn - Block 1 - Place Value. Content includes:

• Activities containing varied fluency, reasoning and problem solving to reinforce and consolidate the children’s learning with 1 accompanying worksheet to use alongside the presentation
• 3 further differentiated varied fluency and reasoning and problem solving worksheets with answers

‘Number Line to 1000 - Year 3’ is editable so teachers can adapt the resource to meet their individual teaching needs.

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Get this resource as part of a bundle and save up to 45%

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

Year 3 Place Value Bundle

Year 3 Place Value Bundle This year 3 maths teaching bundle contains the following 9 PowerPoint teaching resources with accompanying worksheets: * Hundreds - Year 3 * Representing Numbers to 1000 - Year 3 * 100s, 10s and 1s - Year 3 * Number Line to 1000 - Year 3 * 10 and 100 More or Less - Year 3 * Comparing Objects up to 1000 - Year 3 * Comparing Numbers up to 1000 - Year 3 * Ordering Numbers up to 1000 - Year 3 * Counting in 50s - Year 3 Each of these maths teaching resources has been designed to help deliver lessons covering the curriculum objectives of the year 3 maths programme of study Number (Number and place value) and support the White Rose small steps guidance for year 3 - Autumn - Block 1 - Place Value. For a full description and preview of each resource please click on the images below. This bundle gives you a saving of 42% when compared to buying each resource individually.

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