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Our

RICH TASKS

For Homeschooling

Our sequenced units of work are ideally suited for homeschooling environments, offering a structured yet flexible approach to mathematics education. Each unit provides a clear mathematical journey that allows homeschooling parents or tutors to easily plan and implement a comprehensive maths curriculum. The lesson plans can be readily adapted to suit individual learning paces and styles, making them perfect for personalised homeschool instruction. The Linear Abacus® tasks introduce innovative ways to explore mathematics, which can be particularly engaging in a home setting where hands-on, interactive learning is often emphasised. These tasks only require the use of 1 or 2 abacus strings, making them easy to implement at home. With provided objectives serving as clear learning goals and student worksheets offering opportunities for independent practice, this resource empowers homeschooling families to deliver high-quality mathematics education tailored to their child's unique needs and learning journey. Additionally, we offer support videos for parents on our YouTube channel, providing extra guidance and tips to help you make the most of these lessons in your homeschooling practice. To reinforce learning, follow-up task cards are available, allowing children to practice the concepts independently and further solidify their understanding. You can find all these resources in the Homeschooling  tab.

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For Schools

Each sequenced unit of work reveals a clear mathematical journey that the students will embark on as they explore different topics in mathematics. You and your team can determine a timeframe for each unit or individual lesson to ensure that students in your class have the chance to develop conceptual understanding of key ideas and mathematical proficiencies. The lesson plans are designed with teachers and schools in mind and aim to ease the workload for educators and can seamlessly integrate with any curriculum or school framework.  

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The difference with our sequenced units of work lies in their ability to guide you through concepts comprehensively from the start to end. Instead of offering standalone tasks, our designed units incorporate lessons that progressively build upon each another. 

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Additionally, the Linear Abacus® tasks are original and introduce innovative ways to explore mathematics with meaning. Each task is connected to various areas in number, arithmetic, and measurement, and is accompanied with a lesson plan and a student worksheet. These resources are designed to achieve the utmost level of quality, aiming to:

  • Highlight the key mathematical ideas connected to various topics in mathematics

  • Encourage sense making

  • Promote mathematical dialogue

  • Provide students with the chance to practice skills and develop their fluency with calculations and strategies

On each lesson plan you will find a list of lesson objectives which can be used as learning intentions or success criteria. These statements can be co-constructed with students.

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Over the course of the year, additional work units will be continually uploaded to this platform.

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Don't miss the opportunity to transform your classroom into a place of mathematical exploration and discovery. Elevate your teaching and empower your students with these sequenced units of work.  

AN INDUCTION TO FOUNDATIONAL NUMERACY

Place ValueUnit

NEW PRODUCT AVAILABLE SOON

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We have made some changes...stay tuned

ADDITIVE THINKING SEQUENCED LESSONS

Addtive Thinking Unit

Introducing a new approach to the teaching and learning of Additive Thinking: Connecting Models, language, and calculations.

Our innovative additive thinking unit transforms the way students aged 6-11 engage with whole number operations (+, -) by unveiling the deep connections between mathematics and language for the teaching and learning of arithmetic. Over the course of 3 weeks, with daily lessons of 1-1.5 hours, this unit will:

 

  1. Reveal the structure of additive thinking and not just teach how to do calculations.

  2. Introduce a groundbreaking coordination between mathematical structure and English grammar

  3. Empower students to construct, interpret, and reason with simple number sentences, and  to master the basic additive thinking concepts  DIFFERENCE, ADDITION, and SUBTRACTION.

  4. Introduce a color-coding system for numerals that  facilitates rich mathematical dialogue and deep understanding of how additive thinking is used in the world.

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"As both a teacher and mother, I have found these Additive Thinking Flashcards to be invaluable tools for enhancing the learning experiences of both my students and my own children. They thoroughly enjoy using these flashcards, and now that I have finished teaching them as part of our unit, I incorporate them regularly as a quick warm up- before each maths lesson. This practice effectively improves and stimulates their addition and subtraction skills. These flashcards are incredibly versatile, serving as effective warmups before lessons, as rich tasks in a unit, as rich assessment pieces, or as additional practice for students who need it. Since integrating these additive thinking flashcards into our routine, I've seen significant improvement in my children's addition and subtraction skills. They particularly enjoy the engaging illustrations and word problems featured on the flashcards. I highly recommend these additive flashcards if you are a teacher or mother of primary children".

 

Tram Nguyen, Teacher St Albans Heights Primary School

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For Teachers​

This document can be used as professional learning for teachers. It is a preface for the additive thinking unit. Here you will find information on how to teach operational arithmetic. This includes clear examples and diagrams to help you model ideas for students and build your confidence in using the mathematical resource. 

Our system will help you teach students how to coordinate Simple Number Sentences (SNS), Linear Abacus™ models, and word problems (wp), to understand a concept. The main aim is to help students understand what they are solving.

Suitable for ages 7 -15 years 

This number game is from our Linear Abacus™ Games Book. It is designed to help students learn the skills below prior to starting the additive thinking unit. 

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Number Skills and Techniques to Learn 

  • New mechanics on the abacus string, e.g., showing a DIFFERENCE.

  • How to develop new mathematical language to talk about an additive comparison and the gestures they perform on the abacus string. 

  • ​How to connect ideas from the place value unit.

  • How to transfer their thinking to a number line. 

  • How to use basic number facts e.g., bonds to 10, doubles, near doubles, etc. 

Suitable for ages 7 -15 years 

This number game is from our Linear Abacus™ Games Book. It is designed to help students learn the skills below prior to starting the additive thinking unit. 

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Number Skills and Techniques to Learn 

  • New mechanics on the abacus string e.g., showing ADDITION.

  • How to develop new mathematical language to talk about an additive situation and the gestures they perform on the abacus string. 

  • How to transfer their thinking to a number line. 

  • Use number properties such as the commutative property: 𝑎+𝑏=𝑏+𝑎, and the associative property: 𝑎+(𝑏+𝑐)=(𝑎+𝑏)+𝑐. 

Suitable for ages 7 -15 years 

This number game is from our Linear Abacus™ Games Book. It is designed to help students learn the skills below prior to starting the additive thinking unit. 

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Number Skills and Techniques to Learn 

  • New mechanics on the abacus string e.g., showing SUBTRACTION.

  • How to develop new mathematical language to talk about an additive situation and the gestures they perform on the abacus string. 

  • How to use place value ideas when subtracting and when partitioning numbers.

  • Learning to apply number bonds such as make 10 to simplify calculations. 

Suitable for ages 6 - 15 years

This lesson gives students the opportunity to develop their skills and techniques with the Linear Abacus™ and build their fluency with basic facts. 

Through this rich task students will learn how to talk about their models and reason mathematically about what they see or the actions they perform on the abacus string. In this process students will learn how to write a mathematical argument using calculations to match mathematical models, and find relationships between different number sentences in an additive triple. Students can learn to apply these skills when computing mentally or estimating.

Suitable for ages 7 - 15 years

This lesson gives students the opportunity to understand the role of numerals in a simple number sentence. This has a direct link to English grammar. They will learn how to differentiate between a count noun and mass noun and understand how these nouns in mathematics can be interpreted as countable things—discrete, or measurable stuff—continuous. Students will also learn how to model the two types of numerals on the Linear Abacus™. 

This rich activity will help students when solving and writing word problems in future lessons.

Suitable for ages 6 - 15 years

This lesson is a rich activity designed to help students coordinate calculations, word problems, and models on the Linear Abacus™. Students will learn about the triple of number sentences that are used to express additive thinking and how to interpret and write word problems linked to each SNS. They will also learn to recognise the numerals used to name counts or amounts and the numeral used to name the additive relation of DIFFERENCE between two numbers. They will first explore how to read, interpret and solve problems prior to writing their own.

Suitable for ages 6 - 10 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.

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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. 

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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!

Testimonial 

"Teaching the three additive concepts—difference, addition, and subtraction—together was beneficial. This approach allowed students to see connections between the concepts, making it easier for them to solve between different types of problems. The tasks really consolidated the concept of subtraction as a difference. Repeated exposure to phrases like "how many more" paired with the hands-on model of naming the beads on the Linear Abacus reinforced this understanding effectively. This consistent use of language and visual representation helped students understand the concept. Overall, in our formal summative assessment we saw students make progress, with growth ranging from 6 months to 2 years in their addition and subtraction post-assessments. Anecdotally, students demonstrated improved ability to reason with word problems, match operations to words, and explain their thinking clearly".

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Level 3/4 Teachers St Albans Heights Primary School

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