number bonds to 10 reasoning and problem solving

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One Big Triangle

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One Big Triangle printable sheet

Once you've finished making the big triangle, think about these questions: How did you get started? What did you do next? You can print out the sheet at the top of this page and cut the triangles out, then try arranging them.   If you prefer, you can also use a printable version of  the triangles with numbers represented on tens frames .

Alternatively, you might like to use this interactivity, which allows you to drag each triangle onto the large triangle.

Why do this problem?

This problem is useful for consolidating number bonds to 10 and the corresponding subtraction facts. The novel context is likely to appeal to learners and encourage them to persevere. Children who are fluent with number bonds to 10 will still be challenged as the approach is not obvious, but logical reasoning will help them become more efficient in their search for a solution. The task will also draw on learners' geometrical reasoning too as they visualise triangles in different positions and orientations in order to solve the problem.

Possible approach

Key questions.

Can you find a different card with that number on it? What might be helpful to try next?  

Possible extension

Children could be asked whether they can find more than one solution. How will they know whether another solution is the same or different to any they have already got? How will they know that they have found all the solutions? Learners could also use the cards to make a shape (not necessarily a triangle) where the touching numbers add to 9 (or 8 or 11). Alternatively, they could add their own choice of numbers to  blank triangular pieces  to create their own activity.  

Possible support

Children could use the cards to make a different shape (not necessarily a triangle) where the touching numbers add to 10, and/or  the tens frame cards  could be used to provide more support. Some children may find it difficult to cope with matching more than one pair of numbers at a time, in which case a domino activity would be more accessible. A set of nine-spot dominoes would be useful for this and you can find one on our  printable resources page . The task could be to join the dominoes together so that the 'match' adds to 10 or any other number of the children's choice. This will then give them plenty of practice in identifying number bonds.  

Are you on the lookout for a dynamic resource to reinforce number bonds to 10 in your maths lessons? Dive into the "Make 10" worksheet, a free resource tailored for foundation, grade 1, and grade 2 students. Designed to foster understanding and fluency in number bonds, this engaging worksheet offers an interactive approach to mastering essential maths skills.

Exploring "Make 10"

The "Make 10" worksheet presents students with a series of 10 frames, each containing a varying number of counters. Students are tasked with completing each 10 frame by drawing additional counters to make a full set of 10. As they engage with the worksheet, students reinforce their understanding of number bonds to 10 in a hands-on and interactive manner.

How to Use the Worksheet:

Observation: Begin by examining each 10 frame on the worksheet. Take note of the number of counters already present in each frame.

Completion: Using a pencil or crayon, draw additional counters in each 10 frame to make a total of 10. For example, if a frame contains 3 counters, draw 7 more to complete the set.

Number Sentence: Beneath each 10 frame, students will find a space to write the corresponding number sentence. Record the addition equation that represents the completion of each 10 frame. For instance, if 3 counters are already present, the number sentence would be "3 + 7 = 10".

Reflection: Encourage students to reflect on the concept of number bonds as they complete each 10 frame. Discuss strategies for identifying combinations of numbers that add up to 10.

Benefits of "Make 10"

Hands-On Learning: Through drawing and completing 10 frames, students actively engage with the concept of number bonds, fostering a deeper understanding of addition and number relationships.

Visual Representation: The visual nature of the worksheet allows students to visualize and conceptualize number bonds to 10, enhancing their mathematical reasoning and problem-solving skills.

Personalized Learning: Students have the opportunity to work at their own pace, drawing on their existing knowledge and skills to complete each 10 frame and corresponding number sentence.

Download Now and Enhance Learning!

Ready to empower your students with a dynamic resource for mastering number bonds to 10? Click the button below to download the "Make 10" worksheet and ignite a journey of mathematical exploration and discovery!

Don't forget to explore all the other free resources available on our website!

From engaging games to interactive worksheets, there's something for every learner. Dive into the world of mathematics and literacy and unlock even more educational treasures!

Number Bonds

Number bonds show how numbers are split or combined. An essential strategy of Singapore maths, number bonds reflect the ‘part-part-whole’ relationship of numbers.

What is a number bond?

Number bonds let students split numbers in useful ways. They show how numbers join together, and how they break down into component parts. When used in Year 1, number bonds forge the number sense needed for early primary students to move to addition and subtraction. As students progress, number bonds become an essential mental problem-solving strategy.

Why are number bonds part of Singapore mathematics?

Number bonds are an essential component when teaching the Singapore method of maths for mastery . They foster number sense in students, and are an important concept within the Singapore primary curriculum. However so-called ‘Singapore Number Bonds’ are not a specifically Singaporean method — the term has been around since the 1920s.

How do number bonds work?

Number bonds are represented by circles connected by lines. The ‘whole’ is written in the first circle, while the ‘parts’ are in the adjoining circles.

How to teach number bonds

Children are usually introduced to number bonds through the Concrete, Pictorial, Abstract (CPA) approach . Here’s just one way to introduce and teach number bonds.

Concrete step

Children start out by counting familiar real-world objects that they can interact with. They then use counters to represent the real-world objects. From here, they progress to grouping counters into two groups.

By putting five counters into two groups, children learn the different ways that five can be made. For example, 3 and 2 as illustrated below. With further exploration, children work out other ways to break numbers into two groups.

Pictorial step

Now that they understand the concept with hands-on objects and experience, children progress to writing number bonds in workbooks or on whiteboards. Early number bond explorations might simply reflect the two groups of counters that they created during the concrete step, along with other combinations.

Abstract step

With the concrete and pictorial steps done and dusted, children progress to representing abstract problems using mathematical notation (for example, 3 + 2 = 5).

Taking the concept a step further

Number bonds also develop problem-solving strategies such as ‘making ten’ with ten frames, multilink or unifix cubes.

By mastering number bonds early on, pupils build the foundations needed for subsequent learning and are better equipped to develop mental strategies and mathematical fluency. By building a strong number sense, pupils can decide what action to take when trying to solve problems in their head.

This example shows how a pupil would develop their number sense, or mathematical fluency, by using number bonds to perform a mental calculation.

Find out how number bonds, proven mastery strategies, and world-class training can make maths better for everyone in your school.

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Bonds to 10 – Reasoning and Problem Solving

Bonds to 10 - Reasoning and Problem Solving

This worksheet includes a range of reasoning and problem solving questions for pupils to practise the main skill of using bonds to 10.

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What's included in the pack?

Bonds to 10 reasoning and problem solving worksheet Answer sheet

National Curriculum Objectives: Mathematics Year 1: (1C1) Represent and use number bonds and related subtraction facts within 20 Mathematics Year 2: (2C1) Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100

This resource is available to download with a Premium subscription.

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Number Bonds Worksheets to 50 and 100

Welcome to our Number Bonds Worksheets page. Here you will find a wide range of free printable Math Fact Worksheets, which will help your child learn their number bonds to 50 and 100.

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Quicklinks to ...

• What is a Number Bonds to 100?
• Number Bonds to 10
• Number Bonds to 20
• Number Bonds to 50 Worksheets

Number Bonds to 100 Worksheets

• More related resources

Number Bonds to 50 and 100 Online Quiz

Here you will find a range of free printable math worksheets to help your child learn their number bonds to 50 or 100.

These sheets are carefully graded so that the easier sheets come first and give extra support.

Using these sheets will help your child to:

• learn and practice their bonds to 50 or 100.

Want to test yourself to see how well you have understood this skill?.

• Try our NEW quick quiz at the bottom of this page.

What is a number bond to 100?

We can look at number bonds to 100 as pairs of numbers with a total of 100.

However, knowing your number bonds to 100 is more than just being able to quickly recite pairs that have a total of 100.

We would also expect children to know all the facts related to the pair of numbers that have a total of 100.

In other words:

• If we know that 63 + 37 = 100, we should also know
• 37 + 63 = 100
• 100 - 63 = 37
• 100 - 37 = 63
• And if we switch the equation on either side of the equals sign, we could add to this...
• 100 = 63 + 37
• 100 = 37 + 63
• 37 = 100 - 63
• 63 = 100 - 37

So there would be a total of 8 facts for every number bond fact that we would want children to be able to find!

The sheets below will help you child to learn their number bonds to 100 and accompanying facts!

Number Bonds to 50

• Number Bonds to 50 Sheet 1
• PDF version
• Number Bonds to 50 Sheet 2

Number Bonds to 100 with Blocks

These sheets use place value blocks partially filled to help find out the missing number bond to 100.

• Number Bonds to 100 with Blocks Sheet 1
• Number Bonds to 100 with Blocks Sheet 2

Number Bonds Worksheets to 100 - Bar Model missing facts

These number bonds worksheets involve working out the 4 related facts for each bar model.

• Number Bonds to 100 Sheet 1
• Number Bonds to 100 Sheet 2

Numbers Bonds to 100 - Related Facts

• Number Bonds to 100 Sheet 3
• Number Bonds to 100 Sheet 4

Numbers Bonds Worksheets to 100 - Quick Practice

• Number Bonds to 100 Sheet 5
• Number Bonds to 100 Sheet 6

Numbers Bonds Worksheets to 100 - Mastery

• Number Bonds to 100 Sheet 7

Number Bonds to 100 Walkthrough Video

This short video walkthrough shows several problems from our Number Bonds to 100 Worksheet 5 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, check out the video!

More Recommended Math Worksheets

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

Online Number Bonds Practice

In our Number Bonds Practice area, you can practice your number bonds to a variety of numbers. Test your numbers bonds to 10, 20 , 100 or even 1000. Want to try decimals - you can do that too!

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

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

• Number Bonds Practice Zone
• Number Bonds Printable Worksheets Generator

Our new number bonds worksheet generator will allow you to create your own printable number bonds worksheets.

You can choose from a range of values from whole numbers to decimals.

You can also choose to use addition questions, subtraction questions or both.

Graded Number Bond Sheets

If you are looking for more easier sheets, then have a go at the sheets in this section.

The sheets on this webpage focus on number bonds to 10 and 12.

• Decimal Number Bonds to 1

Third Grade Place Value Worksheets

Here you will find a range of Free Printable 3rd Grade Place Value Worksheets.

The following worksheets involve different Third Grade place value activities such as counting in thousands, hundreds, tens and ones, reading, writing and ordering numbers to 10,000, and know what number each digit represents.

• learn their place value with 4 digit numbers;
• use place value models to understand how to combine thousands, hundreds, tens and ones;
• understand the value of each digit in a 4 digit number;
• Place Value Models 4 Digits
• Place Value 4 Digit Numbers Worksheets (conversion)
• Ordering 4-Digit Numbers
• 3rd Grade Math Puzzles

Here you will find a range of printable 3rd grade math puzzles for your child to enjoy.

The puzzles will help your child practice and apply their addition, subtraction and multiplication 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 and practice their addition facts to 100;
• practice adding multiples of 10;
• practice their subtraction facts to 100;
• practice multiplication and division facts;
• develop problem solving skills and reasoning.

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

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We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.

This quick quiz tests your knowledge and skill with Number Bonds to 50 and 100.

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Number Bonds 10 and 20 Word Problems

Subject: Mathematics

Age range: 5-7

Resource type: Worksheet/Activity

Last updated

13 November 2020

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Number Bonds 10 and 20 Word Problems. Addition and subtraction word problems. KS1

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