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FREE RESOURCES
Here you will find a range of free posters, activities, and games which will help you teach various topics in the mathematics curriculum. Each activity has an instructional video which you can use in the classroom or at home.
These activities will help students:
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Develop their number skills and facts
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Connect and apply their knowledge in other areas
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Engage in problem based situations
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Think critically
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Communicate their ideas and learn to reason mathematically
Be sure to check this space regularly as new ideas will be added each month.
How Many Ways?
Explore how numbers are modelled on the Linear Abacus® using base 10 notation, and discover how to rename numbers (i.e., find equivalent names for numbers) using the Linear Abacus® as a calculating device to model the arithmetic.
© 2023 Linear Abacus
© 2023 Linear Abacus
The Maths in French Numerals
Task ages 7-14 years
Counting in French can be tricky when you reach the numbers 70-99, as the system for naming numbers within this range counts by 20s. Some examples are provided below:
The numeral 78 is read aloud as "soixante-dix-huit". This is connected to the expression 60+18.
The numeral 83 is read aloud as "quatre-vingt-trois". This can be connected to the expression (4x20)+3.
The numerals 99 is read aloud as "quatre-vingt-dix-neuf". This is connected to the expression (4x20)+10+9.
To help students recognise how these expressions are equivalent to 71, 83 and 99 respectively, you could model the processes on the abacus string as shown on the task card.
Key Mathematical Ideas
1. Understanding that a number is a place in an order.
2. Place value- understanding the role of digits in a numeral.
3. Renaming and equivalence- understanding how two expressions can show the same number.
4. Number operations and order of operations- understanding which operations to use and how to perform these actions on the abacus string.
5. Mathematical argument- reasoning with calculations and models.
Key Mathematical Skills
1. Making connections between concrete representations, numerals, and calculations.
2. Applying known facts to solve problems.
3. Reasoning- using colour to highlight different ideas and to explain their thinking behind their methods.
© 2023 Linear Abacus
Counting in French can be tricky when you reach the numbers 70-99, as the system for naming numbers within this range counts by 20s. Some examples are provided below:
The numeral 78 is read aloud as "soixante-dix-huit". This is connected to the expression 60+18.
The numeral 83 is read aloud as "quatre-vingt-trois". This can be connected to the expression (4x20)+3.
The numerals 99 is read aloud as "quatre-vingt-dix-neuf". This is connected to the expression (4x20)+10+9.
To help students recognise how these expressions are equivalent to 71, 83 and 99 respectively, you could model the processes on the abacus string as shown on the task card.
Key Mathematical Ideas
1. Understanding that a number is a place in an order.
2. Place value- understanding the role of digits in a numeral.
3. Renaming and equivalence- understanding how two expressions can show the same number.
4. Number operations and order of operations- understanding which operations to use and how to perform these actions on the abacus string.
5. Mathematical argument- reasoning with calculations and models.
Key Mathematical Skills
1. Making connections between concrete representations, numerals, and calculations.
2. Applying known facts to solve problems.
3. Reasoning- using colour to highlight different ideas and to explain their thinking behind their methods.
© 2023 Linear Abacus
Additive vs. Multiplicative Number Systems
Activity ages 9-14 years
Ancient civilisations in the past used different systems of numeration. These number systems had different ways to arrange symbols to form numerals. Some used additive or subtractive notation whilst others used multiplicative or positional notation. In this activity (which is part of the place value unit) students will explore ancient Roman numeration and compare this with the Hindu-Arabic numeration system that we use today. The activity card includes instructions and follow up activities.
Key Mathematical Ideas
1. Understanding the meaning of a numeral, digit and number.
2. Modelling additive and multiplicative processes on the Linear Abacus®.
3. Matching models with written calculations.
4. Place value- understanding positional notation, base 10 groupings, and the role of digits in a number.
Key Mathematical Skills
1. Reasoning and making connections between concrete representations, numerals, and calculations.
2. Applying known facts when calculating and modelling on the abacus string.
3. Describing the efficiency of number systems.
© 2023 Linear Abacus
Ancient civilisations in the past used different systems of numeration. These number systems had different ways to arrange symbols to form numerals. Some used additive or subtractive notation whilst others used multiplicative or positional notation. In this activity (which is part of the place value unit) students will explore ancient Roman numeration and compare this with the Hindu-Arabic numeration system that we use today. The activity card includes instructions and follow up activities.
Key Mathematical Ideas
1. Understanding the meaning of a numeral, digit and number.
2. Modelling additive and multiplicative processes on the Linear Abacus®.
3. Matching models with written calculations.
4. Place value- understanding positional notation, base 10 groupings, and the role of digits in a number.
Key Mathematical Skills
1. Reasoning and making connections between concrete representations, numerals, and calculations.
2. Applying known facts when calculating and modelling on the abacus string.
3. Describing the efficiency of number systems.
© 2023 Linear Abacus
Free Poster
Numbers 0-20
Free Poster
Numbers 0-20
Download the free number poster below. This can be displayed on the numeracy wall or be used as flashcards to help students count to 20 on the Linear Abacus®.
© 2023 Linear Abacus
What's the difference?
Here is a task card for grades 2 - 5. This is from our Number Games Book.
Additive Thinking Flashcards
Activity ages 7-12 years
This lesson is a rich activity which is from the Additive Thinking Flash Cards set. This is linked to question 27 in the set and can be used as a main task and formative assessment piece.
How to use the cards
Children need to solve the full Additive Triple to see the connections between the DIFFERENCE, ADDITION and SUBTRACTION simple number sentences, word problems, and models on the Linear Abacus®. The cards are divided into 3 related problems labelled (a), (b) and (c). An information card has been provided which provides you with answers, explanations, and ideas for assessment. All triples in the set encourage children to coordinate language, models, and descriptive calculations. The three concepts: DIFFERENCE, ADDITION, and SUBTRACTION, are all taught simultaneously in each triple. The questions in the set increase in difficulty, this is one of the more challenging questions in the set.
Sample Question
There are 3 parts to this question. It starts with a Linear Abacus® model which includes specific numerals. Students need to copy the model on their own abacus string and determine if the model is representing the DIFFERENCE, ADDITION, or SUBTRACTION problem. This means they learn to talk about simple number sentences and concepts. For instance, a child might state:
“if I know both count-numbers then I am solving for the DIFFERENCE”.
“if I know one count-number and the relation (the DIFFERENCE) then I am either solving the ADDITION or SUBTRACTION problem”.
Next, student use a picture prompt to help them write a word problem for the model. Included are characters (one or two actors) and discrete items (countable things). Once children write the story and SNS for the model, they have to generate the other 2 stories and SNS in the triple and explain the connections between all three. You can access these sample cards for FREE!
Key Mathematical Ideas
1. Understanding the meaning of numerals in a number sentence.
2. Connecting models with descriptive calculations, and word problems.
3. Building number facts for addition and subtraction.
Key Mathematical Skills
1. Reasoning and making connections between concrete representations, numerals, and calculations.
2. Applying known facts when calculating and modelling on the abacus string.
3. Developing the skills to interpret and write word problems.
© 2024 Linear Abacus
This lesson is a rich activity which is from the Additive Thinking Flash Cards set. This is linked to question 27 in the set and can be used as a main task and formative assessment piece.
How to use the cards
Children need to solve the full Additive Triple to see the connections between the DIFFERENCE, ADDITION and SUBTRACTION simple number sentences, word problems, and models on the Linear Abacus®. The cards are divided into 3 related problems labelled (a), (b) and (c). An information card has been provided which provides you with answers, explanations, and ideas for assessment. All triples in the set encourage children to coordinate language, models, and descriptive calculations. The three concepts: DIFFERENCE, ADDITION, and SUBTRACTION, are all taught simultaneously in each triple. The questions in the set increase in difficulty, this is one of the more challenging questions in the set.
Sample Question
There are 3 parts to this question. It starts with a Linear Abacus® model which includes specific numerals. Students need to copy the model on their own abacus string and determine if the model is representing the DIFFERENCE, ADDITION, or SUBTRACTION problem. This means they learn to talk about simple number sentences and concepts. For instance, a child might state:
“if I know both count-numbers then I am solving for the DIFFERENCE”.
“if I know one count-number and the relation (the DIFFERENCE) then I am either solving the ADDITION or SUBTRACTION problem”.
Next, student use a picture prompt to help them write a word problem for the model. Included are characters (one or two actors) and discrete items (countable things). Once children write the story and SNS for the model, they have to generate the other 2 stories and SNS in the triple and explain the connections between all three. You can access these sample cards for FREE!
Key Mathematical Ideas
1. Understanding the meaning of numerals in a number sentence.
2. Connecting models with descriptive calculations, and word problems.
3. Building number facts for addition and subtraction.
Key Mathematical Skills
1. Reasoning and making connections between concrete representations, numerals, and calculations.
2. Applying known facts when calculating and modelling on the abacus string.
3. Developing the skills to interpret and write word problems.
© 2024 Linear Abacus
Naming and Counting Unit Fractions
Here is a task card linked to our video "Counting Fractions | Linear Abacus®"
Naming Numbers Below 100
Activity ages 7-12 years
This activity card is linked to episode 1 of our maths series. This allows children to practice naming and expanding numbers below 100.
Key Mathematical Ideas
1. Model numbers below 100 on the Linear Abacus®.
2. Read and interpret numbers.
3. Understand the role of digits in a numeral.
4. Expand numbers using arrays and arithmetic.
5. Use colour to reason mathematically.
6. Define what a number, digit and numeral is.
Key Mathematical Skills
1. Reasoning and making connections between concrete representations, numerals, and calculations.
2. Applying known facts when calculating and modelling on the abacus string.
3. Describing the role of digits in numerals.
© 2024 Linear Abacus
This activity card is linked to episode 1 of our maths series. This allows children to practice naming and expanding numbers below 100.
Key Mathematical Ideas
1. Model numbers below 100 on the Linear Abacus®.
2. Read and interpret numbers.
3. Understand the role of digits in a numeral.
4. Expand numbers using arrays and arithmetic.
5. Use colour to reason mathematically.
6. Define what a number, digit and numeral is.
Key Mathematical Skills
1. Reasoning and making connections between concrete representations, numerals, and calculations.
2. Applying known facts when calculating and modelling on the abacus string.
3. Describing the role of digits in numerals.
© 2024 Linear Abacus
Free Poster
Modelling Numerals as Counts and Measures
Download the free poster below which is connected to the place value lesson on informal units of measurement. This poster demonstrates the distinction between additive and multiplicative thinking, and shows how arithmetic can be applied to discrete and continuous phenomena.
This can be displayed on the numeracy wall in the classroom.
© 2024 Linear Abacus
This can be displayed on the numeracy wall in the classroom.
© 2024 Linear Abacus
Renaming Whole Numbers
Here is a task card linked to our video "How to Rename Numbers | A creative activity for home and school using the Linear Abacus®"
French Numerals
Here is a task card linked to our video "Les nombres de 70 à 99 avec Boulier Linéaire'
Fractions greater than 1
Here is a task card linked to our video "Naming Fractions Greater than 1 | Improper Fractions and Mixed Numbers | Linear Abacus®"
Testimonial
"When I introduced the Linear Abacus to my Grade 1s, I found it to be a very interesting and user friendly tool to teach addition, subtraction, skip counting and counting. Students found it easy to use and engage with. The use of the two distinctive colours helps the students to visualise and comprehend numbers up to 10 effortlessly. It serves as an excellent visual aid and very effective in teaching the fundamental concepts of Maths".
Tiana D'Souza, Teacher St John the Apostle Catholic Primary School
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