Accelerating progress in mathematics and statistics – Teacher guidance
 

Targeted teaching to accelerate learning is provided by the classroom teacher, with support (as needed) by school leadership. For more information, see Accelerating progress – Leadership guidance.

In Aotearoa New Zealand, we draw on the Te Tūāpapa o He Pikorua model to ensure the right levels of support are in place for students.

Targeted support builds on high-quality universal (tier 1) classroom teaching, accelerating the progress of students who need extra support to reach the expected year level. Effective universal classroom teaching that includes small group work targeted to specific needs is part of the same continuum as targeted teaching.

Targeted teaching involves providing additional focused, intensive, adaptable small-group lessons designed to accelerate student progress. Typically, targeted small-group support:

• provides more focused, intensive teaching to help students engage with the curriculum content for their year level
• builds on and connects with the general classroom mathematics and statistics programme
• offers frequent and explicit instruction
• is informed by teachers’ noticing, understanding, and responding to misconceptions and core conceptual understanding.

Strategies that accelerate learning include:

• pre-teaching key concepts to build confidence and prepare students for upcoming content
• focusing on essential learning by teaching critical skills and concepts rather than re-teaching everything
• teaching precise mathematical vocabulary with clear definitions and encouraging its use in discussions to help students communicate mathematical ideas effectively. Successful interventions include vocabulary walls, cards, and graphic organisers to support understanding (Gillon et al., 2024, p. 57).
• engaging, hands-on learning to help students retain and apply concepts and procedures
• scaffolding and support designed to student needs to help them engage with year level progressions
• building confidence through positive learning and experiencing success
• connecting new content to prior knowledge to make learning more accessible
• ongoing assessment and feedback to monitor progress and uncover misconceptions.

“Students learn best when teachers inquire into their progress and respond by adapting their teaching practice” (Ministry of Education, 2023).

Students have diverse learning needs and backgrounds. Adopting an inclusive, responsive teaching approach ensures that all students have the support they need to succeed.

Students needing accelerated learning benefit from explicit teaching in relevant and engaging situations that encourage a positive relationship with maths. Using the acceleration framework, along with the elements of the comprehensive teaching and learning programme described in the sections below, underpin the lesson examples provided in this resource.

Gillon et al. (2024) conclude that to help your students succeed in math, focus on clear, step-by-step instruction. Teach concepts explicitly and systematically, using hands-on materials and visual models to make abstract ideas more concrete. Encourage students to use problem-solving strategies so they feel confident tackling challenges.

Regular formative assessments and progress checks help you understand where students are at and what they need next. These assessments guide your teaching and ensure students get the right support at the right time.

Create opportunities for small group work and peer-assisted learning, where students can talk through their thinking and learn from each other. Use flexible groups so students aren’t stuck in one ability level – this keeps learning dynamic and responsive to their progress (Gillon et al., 2024, p. 59). Strong relationships with maths matters. Help students develop a positive attitude toward maths by celebrating effort, encouraging a growth mindset, and making connections to real-life situations. When students see maths as something they can succeed in, they’re more likely to engage and persist in learning.

By combining structured teaching, regular progress monitoring, and a focus on building confidence, you can create supportive and effective maths learning environments for all students.

Your class includes students with differing strengths and learning needs. Knowing your students and building relationships with parents and whānau helps you to identify students needing targeted support and plan effectively.

Early identification and teaching support is key

The progress outcomes describe what students will understand, know, and do by the end of each phase. It is important to notice, recognise, and respond where students need help to fully engage with the teaching sequence statements within a phase rather than waiting until the end of the phase. Intervene early before gaps grow.

For those who are already fully engaging with the teaching sequence statements for their year level, continue to monitor student’s progress and take action to increase support if needed.

Effective targeted teaching begins with a clear process of noticing, recognising, and responding to the diverse needs of students. The key to selecting students for additional support lies in careful observation and assessment, ensuring you can provide timely, targeted interventions to accelerate learning.

• Notice, recognise, and respond: Pay close attention to the concepts and procedures for the year-level teaching sequence. Look across the year-level sequences to identify which prerequisite concepts and procedures students will need from prior year levels.
• Informal notice and recognise: Look for signs that indicate the need for further support. This could include challenges in problem-solving, fluency, recalling and using basic facts applying mathematical operations, or mathematical vocabulary understanding. Identifying these indicators across each phase of the curriculum allows you to respond quickly with targeted help before gaps widen.
• Assessment types and purpose: Use formative and diagnostic assessments to monitor student progress and pinpoint misconceptions. These tasks assess confidence with concepts or procedures, guide planning decisions, and identify areas needing additional support, ensuring teaching is adapted to student needs.
• Ongoing progress monitoring: Regular monitoring of student progress tracks how well students are responding to targeted interventions. By continuously assessing their understanding, you can adjust your teaching methods, revisit key concepts, or introduce new concepts to ensure sustained progress.
• Don’t wait for schoolwide screening: If you notice a student needs additional support, conduct a relevant diagnostic skills assessment and provide immediate support. Observations, standardised screening assessment, and parent and whānau insights are all valuable for identifying students needing additional support.

Targeted support is about adapting your teaching, e.g., using scaffolds and reducing them over time so that your students can access the learning. It is not about differentiating the content or creating easier versions of a learning activity. It involves continually assessing the strengths and needs of your students and adapting your teaching to ensure all students can access teaching at their year level. Gillon et al. (2024, p. 57) emphasise the importance of ensuring suitable year-level learning content across all year levels and ensuring that students build a strong foundation and progressively advance their mathematical understanding.

To accelerate learning in mathematics, consider the six steps from The Acceleration Framework (Rollins, 2014):

• Generate thinking, purpose, relevance, and curiosity.
• Clearly articulate the learning goal and expectations.
• Scaffold and practice essential prerequisite skills.
• Introduce new vocabulary and review prior vocabulary.
• Dip into the new concept at the student’s year level.
• Conduct formative assessment frequently.

The approaches described in the acceleration framework can be used as a structure to plan your targeted sessions. See “Acceleration framework” tab above for detailed information on how to use this framework to accelerate progress in mathematics and statistics.

Planning for accelerating learning in mathematics and statistics

When developing a comprehensive teaching and learning programme, consider whether your students have opportunities to receive explicit teaching, apply new concepts and procedures through rich tasks, communicate in mathematics and statistics, and develop positive relationships with mathematics and statistics through the learning environment and tasks.

Explicit teaching

Explicit teaching is a structured and interactive approach where learning is broken into clearly explained and modelled manageable steps. It emphasises connecting new knowledge to prior learning, providing guided and independent practice, and offering regular feedback.

Through scaffolding, explicit teaching helps transfer new learning into long-term memory, reducing cognitive load and enabling students to engage in more complex tasks. Rich discussions, visual aids, and concise explanations ensure that students develop both conceptual and procedural understanding, fostering confidence and motivation.

Explicit teaching: Key guidance

Explicit teaching is clearly described in Gillon et al., (2024, p. 57) as segmenting complex skills, modelling content, structured prompting techniques (e.g., least to most prompting strategies), providing opportunities to respond with appropriate feedback, and creating purposeful practice opportunities. These approaches are effective at all year levels, helping to build a strong foundation and supporting proficiency in complex mathematical concepts in secondary education.

Explicit teaching involves:

• Structured steps: Break learning into manageable steps, explain and model clearly, and build on prior knowledge
• Interactive learning: Engage students with discussions, questions, and checks for understanding.
• Practice: Move from guided to independent practice to reinforce learning. Gillon et al. (2024) found that teaching focused on building fluency and automaticity is especially effective when paired with timed activities lasting between 1 and 5 minutes. These activities should be introduced once students have had sufficient practice with a concept, rather than during the initial introduction of new material.
   
  • Timed exercises help strengthen the automatic recall of basic arithmetic facts, freeing up cognitive resources for more complex problem solving. This approach is particularly helpful for students who lack self-confidence or have complex learning needs, as it offers success in small, manageable steps, boosting their sense of competence.
     

• Visual support: Use materials and visuals to develop understanding before introducing abstract concepts.

  • As outlined in step 3 above, the use of concrete materials and pictures to create visual images is crucial. Gillon et al. (2024) point to the importance of specific tools and in particular the research supports the use of number lines. They state that number lines are a valuable tool for teaching a variety of mathematical concepts, from basic number to understanding in primary years to more advanced topics like operations and data analysis in secondary years. They help students visualise numbers and improve problem solving skills.

• Reducing cognitive load: Present information clearly, focus on key points, and avoid unnecessary details.

Learning through rich tasks

Rich tasks engage students and foster critical thinking. Using problems and rich tasks provides opportunity to evaluate how students apply concepts to mathematical situations.

Providing intentional instruction on solving word problems enables students to connect mathematical concepts to real world situations. As teachers, focus on helping students recognise and categorize problems based on their underlying structures. Use real life contexts to make problems more engaging and accessible. Introducing algebraic reasoning further strengthens their ability to tackle word problems. These strategies are effective for all year levels, with increasing complexity and relevance as students advance (Gillon et al., 2024, p. 58).

The following guides you on using rich tasks:

• Purpose and planning: Use rich tasks to introduce or reinforce concepts, develop processes, and apply learning to new situations.
• Accessibility and challenge: Design tasks that are inclusive, with varying levels of challenge, and ensure students understand the learning purpose.
• Encouraging student agency: Provide choices in how tasks are approached to build confidence, motivation, and ownership.
• Facilitating collaboration: Plan for discussion, collaboration, and regular feedback during tasks.
• Active teacher role: Monitor students, prompt with questions, and encourage reasoning, connections, and deeper thinking.

Communicating – promoting student discourse
 

Good discussions help students think deeply, solve problems, and improve their conceptual understanding.

Chapin and O’Connor (2009) describe academically productive talk in mathematics as purposeful and structured conversations where students engage in meaningful dialogue to deepen their understanding of mathematical concepts. This type of talk encourages students to articulate their thinking, listen to others, ask questions, and build on each other’s ideas. It creates an environment where students can explore, refine, and challenge mathematical ideas collaboratively.

“Talk moves” are specific strategies that teachers can use to guide and facilitate academically productive talk. These moves help students develop a deeper understanding of mathematical concepts and foster a classroom culture of communication and inquiry. Some key talk moves include:

• revoicing – restating or summarising a student’s idea to ensure clarity and understanding
• asking for clarification – prompting students to elaborate on or clarify their thinking
• building on others’ ideas – encouraging students to connect their own thinking to the ideas of their peers
• prompting for reasoning – asking students to explain the reasoning behind their answers or solutions
• encouraging peer interaction – creating opportunities for students to discuss and debate ideas with their peers
• modelling thinking aloud – demonstrating the thought process involved in solving a problem to guide students in their own problem solving.

These strategies not only promote mathematical understanding but also help students develop communication skills, critical thinking, and a collaborative approach to learning.

Guidance to promote student communication includes:

• facilitating extended discussions where students share ideas, actively listen, critique, question, and extend their reasoning
• making thinking visible – use discussions to uncover students’ reasoning, identify misconceptions, and guide them toward accurate understanding
• developing mathematical language – support students in using precise vocabulary, symbols, and representations (e.g., graphic organisers) to articulate their thinking and reasoning.

Here are some practical ideas to build students' confidence to speak up in math classrooms:

Create a safe environment

Creating a safe classroom culture is essential for students to feel comfortable sharing their mathematical ideas. When students feel respected, valued, and supported in their learning environment, they are more likely to engage actively in discussions, take risks, and share their thinking without fear of judgement or failure. This is particularly important in mathematics, where students often need to express their reasoning, ask questions, and make mistakes as part of the learning process.

A safe classroom culture encourages:

• risk taking – students are more likely to try out new strategies or solutions if they know that making mistakes is part of the learning journey and will not lead to embarrassment or ridicule
• collaboration – when students feel safe, they are more willing to listen to and build on the ideas of others, fostering a collaborative learning environment where multiple perspectives are valued
• open dialogue – a culture of safety promotes open communication, where students can express their thoughts, ask questions, and engage in meaningful discussions without fear of their ideas being dismissed or misunderstood
• growth mindset – a supportive environment helps cultivate a growth mindset, where students understand that effort and persistence lead to improvement, encouraging them to embrace challenges and approach mathematical problems with confidence
• inclusive participation – in a safe classroom, all students regardless of their ability level, feel empowered to contribute to discussions, ensuring that a wider range of ideas and perspectives are shared and valued.

Scaffold discussion
 

To help students articulate their thinking, justify their reasoning, and engage in meaningful discussions, teachers can use “Talk moves” and sentence starters. For example:

• Provide sentence starters, e.g.:
  • "I noticed that..." 
  • "I wonder why..." 
  • "Can someone add to what [student] just said?" 
  • "Does anyone have a different way of thinking about this?" 
• Start with low-stakes questions: Begin with open-ended or simple questions that allow for multiple answers, ensuring all contributions are valued. 
• Celebrate all contributions: Highlight unique approaches or creative thinking, even if the answer isn’t correct. Show students that their input matters.

Positive relationships with mathematics

A positive relationship with mathematics enhances student learning and reduces anxiety. Here are key strategies to help build that relationship:

• Set high expectations: Encourage students with clear, achievable goals and a focus on effort over innate ability.
• Make learning accessible: Plan lessons with varied entry points and differentiated activities to ensure every student experiences success. Highlight and affirm their success.
• Incorporate students' interests and backgrounds: Design lessons to students' cultures, prior knowledge, and interests to make maths more relevant and engaging.
• Encourage exploration and critical thinking: Allow students to investigate problems, ask questions, and explore different solutions.
• Connect maths to the real world: Show students how maths helps solve real-world issues, from local challenges to global problems.
• Offer manageable challenges: Provide tasks that stretch students' abilities while building perseverance and confidence.
• Support students through anxiety: Recognise signs of stress and provide scaffolding or breaks to reduce cognitive overload.
• Involve whānau: Engage parents and caregivers in their children’s learning journey through communication and support.
• Model a positive attitude: Show enthusiasm and persistence with maths, demonstrating that learning is a process that requires effort

Andrade, H., & Heritage, M. (2017). Using formative assessment to enhance learning, achievement, and academic self-regulation. Routledge.

Black, P., & Wiliam, D. (2018). Inside the black box: Raising standards through classroom assessment. GL Assessment.

Chapin, S. H., & O'Connor, C. (2009) Classroom Discussions: Using Math Talk to Help Students Learn. Sausalito, CA: Math Solutions.  

Gillon, G., Everatt, J., McNeil, B., Clendon, S., LaVenia, M., Evans, T., Smith, J., Gath, M., Tufulasi, T. (2024). Accelerating Learning in Oral Language, Reading, Writing, and Mathematics: Report prepared for the Ministry of Education July 30, 2024. University of Canterbury | Te Whare Wānanga o Waitaha, Christchurch, New Zealand.

Marzano, R. J. (2004). Building background knowledge for academic achievement: Research on what works in schools. Ascd.

Ministry of Education. (2022). Te Tuapapa. Vimeo.

Ministry of Education. (2023). Te Mātaiaho | The refreshed New Zealand Curriculum Draft for Testing | March 2023. New Zealand Government.

Ministry of Education. (2024).Te Mātaiaho | The New Zealand Curriculum: Mathematics and statistics years 0-8, October 2024

Rollins, S. P. (2014). Learning in the Fast Lane: 8 Ways to Put ALL Students on the Road to Academic Success. ASCD.

In this important first step, teachers expose students, who have been identified as needing support, to the new concept, preparing them in advance of the upcoming lessons. Generating thinking, purpose, relevance, and curiosity is one way to develop positive relationships with mathematics and statistics.

Begin teaching a mathematics concept by sparking curiosity and relevance through hands-on, thought-provoking activities. This prepares students and helps them see the real-world connections, answering the question, “What does this have to do with me?” (Ministry of Education, 2024; Rollins, 2014). Encourage exploration in pairs or small groups by identifying patterns, discussing observations, and generating ideas.

Engage students in meaningful discussions that build knowledge through sharing, active listening, questioning, and reasoning. Effective activities for this step include:

• visual images
• number talks
• think boards
• brainstorming
• scavenger hunts
• sorting
• the first act of a three-act task
• picture books – e.g., Picture books with mathematical content
• games – e.g., Games | Tāhūrangi or search for games on Tāhūrangi
• Noticing and Wondering – e.g., Creative Math Prompts

Clearly articulated learning goals and expectations underpin explicit teaching. 

After sparking students’ curiosity, this step is crucial for effective learning, particularly for students needing support to meet year level expectations. Clearly stated goals provide direction and purpose. Wordy curriculum statements can be too complex, so use student friendly language and tools like concept maps to clarify goals and expectations. Explicit, understandable learning goals prevent confusion and keep students focused on the purpose of their work. 

Without specific objectives, lessons risk becoming a disconnected series of tasks rather than a cohesive journey toward meaningful learning outcomes. Prompt students to make connections between the learning purpose and previous lessons and learning. Set expectations that everyone can succeed and that mistakes are part of the learning process (Rollins, 2014). 

 Be specific and clear: The goal should clearly state what students are expected to learn or achieve by the end of the lesson.

• Instead of "understand addition," use specific goals such as "solve two-digit addition problems using regrouping." It is important to structure targeted lessons with clear objectives, step by step instructions, and regular reviews (see Gillon et al., p. 57). 

 Use action verbs: Frame the goal with measurable and observable action verbs. Words like "identify," "solve," "calculate," "apply," and "explain" provide clarity on what students should be able to do. 

• "We will be able to solve addition and subtraction problems with fractions." 

 Tie learning goals to real-world application: Whenever possible, connect the goal to real-life situations or practical applications to help students see the relevance of the learning. 

• "You will be able to calculate the total cost of items in the brochure using percentages." 

 State the success criteria: Describe how students will demonstrate their understanding of the concept. This could include the use of specific tools, methods, or strategies to show mastery. 

• "You will correctly multiply multi-digit numbers using the long multiplication method and explain this procedure." 

Keep goals student-centred: Frame the goal to focus on what the students will do, not what you will teach. This makes the goal meaningful and helps students take ownership of their learning. 

• "I will be able to break down word problems and apply the correct mathematical operations to solve them." 

Link to previous learning: When appropriate, explain how the current learning goal connects to previous lessons or builds on prior knowledge. 

• "Building on what we learned about adding fractions with the same denominator, we will now add fractions with different denominators." 

Alongside any work the teacher is doing on acceleration, they are working on building students' relationship with mathematics. See the guidance around developing positive relationships with maths at the start of the teaching sequence for each phase. 

Step 3 and 4 can be switched or undertaken together. 

In this step, identify high-priority prerequisite concepts and procedures that students haven’t learned and that present a barrier to further learning. 

To help teachers identify these high priority areas, the following statement from Rollins (2014, p. 14) is useful: “Students could master the new concept if they just knew _______________.”

Explicit teaching is key – start with clear explanations, demonstrations, and visual representations and materials. This structured approach ensures students develop a solid understanding of mathematical concepts and procedures. It involves clear explanations, guided practice, and immediate feedback to help students build their knowledge – step by step. 

Scaffolding in Mathematics 

Scaffolding supports students as they build confidence and independence. Plan for scaffolding in explicit teaching and practice activities, depending on the needs of your students. 

• Break down complex concepts: Large or abstract mathematical ideas are broken into smaller, manageable steps to support student understanding. 
• Use visual representations: Models such as number lines, arrays, bar models, or manipulatives (e.g., base-ten blocks) help students make sense of math concepts. 
• Connect to prior knowledge: Activating what students already know and linking new learning to familiar concepts enhances comprehension. 
• Guided practice and worked examples: Teachers provide step-by-step demonstrations and gradually shift responsibility to students through guided practice. 
• Sentence stems and mathematical language: Providing structured ways for students to articulate their thinking improves their ability to reason mathematically. 
• Questioning and prompts: Using open-ended and strategic questioning helps students think critically and reflect on their learning process. 

Skipping this step risks students engaging with new material enthusiastically but without foundational/conceptual understanding, leading to frustration and no payoff. By scaffolding prerequisite skills in context, students gain the confidence and preparation needed to succeed with new content. 

The goal is to support students’ mathematical reasoning, problem-solving, and independence while ensuring they engage successfully with year-level content. Review curriculum sequence statements to identify key prerequisite skills and how students will apply and demonstrate their learning. 

Encouraging students to use mathematical language strengthens their ability to communicate mathematical ideas effectively. Research highlights vocabulary walls, cards, and graphic organisers as effective strategies across all year levels (Gillon et al., 2024). Activating prior knowledge of key mathematics terms before introducing a new concept builds confidence, deepens understanding, and enhances engagement.

Encouraging meaningful mathematical discussions helps students think deeply, solve problems, and deepen their understanding. Academically productive talk involves structured conversations where students articulate their thinking, listen, question, and build on ideas (see Chapin and O’Connor, 2009). Teachers can facilitate this through “Talk moves”, such as revoicing, prompting for reasoning, and encouraging peer interaction. Creating a safe classroom environment promotes risk-taking, collaboration, and a growth mindset. Scaffolding discussions with sentence starters, low-stakes questions, and celebrating all contributions builds student confidence in sharing their ideas and deepens mathematical understanding.

Teaching vocabulary – Marzano's six steps for vocabulary learning

Marzano (2004) outlines six effective steps for teaching vocabulary across all learning areas:

• Introduce: Provide a clear explanation/example using illustrations, real-world contexts, or practical explanations.
• Rephrase: Have students restate the meaning in their own words, using personal word books or word lists.
• Visualise: Students create representations of the word (e.g., drawings, symbols, gestures).
• Refine and expand: Use activities like talk-alouds, posters, word walls, and think boards to deepen understanding.
• Discuss: Engage students in peer discussions using games like word sorts and barrier games for spaced practice.
• Practice and apply: Reinforce learning through repeated exposure using activities like Frayer models, card bingo, and think boards.

Students typically internalise a new word after about six meaningful exposures (Jenkins et al., 1984). Explicit instruction of precise mathematical vocabulary, combined with active engagement, supports learning.

Strategies for working with vocabulary include:

• TIP charts – a growing chart that includes terms, information (definitions), and pictures
• word games – activities like clines, grids and brainstorming
• graphic organisers – tools to visually connect concepts
• anchor charts and flashcards – reinforce key terms.

Key resources

• The language of mathematics and statistics. This section is located just above the glossary in each Phase of Learning.
• Taking up the challenge of mathematical language | Tāhūrangi
• NZC - Mathematics and statistics (Phase 1)
• NZC - Glossary of mathematics terms
• Mathematical Vocabulary | Dr Paul Swan
• “Building vocabulary and morphology knowledge” section in the Years 0-3 tab of Accelerating progress in literacy – Teacher guidance

In the first four steps, students establish the relevance of a new concept, clarify learning goals, address prerequisite skill gaps, and develop key vocabulary. In step 5, they begin applying their learning through structured, guided practice that reinforces recently taught concepts and procedures.

Students dip into the new concept through carefully designed activities such as scaffolded tasks, guided practice, or fluency building games. These activities help strengthen understanding, ensure students experience success early, and build confidence as they transition into more complex applications of the concept.

For example, to accelerate students' understanding of the relationship between perimeter and area begin by assessing their prior knowledge and identifying misconceptions, such as assuming a larger perimeter always means a larger area. Explicit teaching would introduce perimeter as the total distance around a shape and area as the space inside, using hands-on manipulatives, visual models, and real-world examples to highlight differences. Guided investigation would help students compare shapes with the same perimeter but different areas, and vice versa, encouraging discussion and reasoning. Structured practice with varied problems, including real-world applications like designing enclosures, would build fluency.

These activities are unique to acceleration and not repeated in the universal lesson to avoid redundancy. As students engage with the new concepts and procedures learned in the previous steps, through explicit teaching, they are leveraging the concepts and making connections within the learning for their year level.

In this step, teachers are noticing how students approach problems, adjusting instruction as needed to ensure mastery.

Key resources

The ALiM resources on Tāhūrangi provide a broad range of lessons appropriate for students to consolidate their new learning and practice new concepts and procedures.

Research highlights the importance of ongoing assessment, where teachers use learning evidence to adjust instruction and meet immediate learning needs (Andrade & Heritage, 2017; Black and Wiliam, 2018; Gillon et al., 2024). Rollins (2014) describes this as “just in time” teaching – providing students with the specific support they need at the moment they need it.

In acceleration, formative assessment is continuous and transparent, allowing for real-time instructional adjustments. Strategies like using whiteboards, sorting tasks, problem-solving on sticky notes, or working on chart paper stuck to the wall, help teachers monitor student understanding daily. Misconceptions are addressed immediately rather than waiting for a future lesson.

Effective formative assessment provides descriptive, actionable feedback from both teachers and peers, ensuring students stay on track. It enables teachers to refine instruction on the spot, maximising learning outcomes.

Possible formative assessment activities include:

• games
• agree and disagree statements
• always, sometimes, or never true
• card sorts (pictures, numbers, symbols, words)
• concept maps
• Frayer model
• concept cartoon
• clothesline maths
• Convince a sceptic
• 3-2-1 exit cards.

Andrade, H.L., & Heritage, M. (2017). Using Formative Assessment to Enhance Learning, Achievement, and Academic Self-Regulation (1st ed.). Routledge.

Black, P., & Wiliam, D. (2018). Classroom assessment and pedagogy. Assessment in Education: Principles, Policy & Practice, 25 [end italic] (6), 551–575.

Gillon, G., Everatt, J., McNeil, B., Clendon, S., LaVenia, M., Evans, T., Smith, J., Gath, M., Tufulasi, T. (2024). Accelerating Learning in Oral Language, Reading, Writing, and Mathematics: Report prepared for the Ministry of Education July 30, 2024. University of Canterbury | Te Whare Wānanga o Waitaha, Christchurch, New Zealand.

Ministry of Education. (2024). Te Mātaiaho | The New Zealand Curriculum: Mathematics and statistics years 0-8, October 2024.

Jenkins, J. R., Stein, M. L., & Wysocki, K. (1984). Learning vocabulary through reading. American Educational Research Journal, 21 (4), 767-787.

Rollins, S. P. (2014). Learning in the Fast Lane: 8 Ways to Put ALL Students on the Road to Academic Success. ASCD.

Work on building students' relationship with mathematics. See Mathematics and statistics learning area in the New Zealand Curriculum.

• Encourage students to have a go and take risks. Reinforce the idea that mistakes help us learn as we try new procedures or share ideas.

• Select highly interesting contexts based on knowledge of students’ personal experiences and backgrounds. Encourage students to connect with mathematics and statistics outside school by bringing in photos, resources, books, and other artefacts from home that link to mathematics and statistics learning.

Explicit teaching

Engage students in the mathematical and statistical processes – the Do practices (investigating situations, representing situations, connecting situations, generalising findings and explaining and justifying findings).

• Explicitly teach students to use these Do practices and demonstrate them regularly as part of the teaching.
• Teach connected concepts and procedures together. For example, when teaching time (in the measurement strand) connect with fractions (in number) and turns (in geometry). Point out connections within concepts (e.g., “If I know 3 + 4, then I know 4 + 3”).
• Demonstrate new concepts or procedures using clearly explained, manageable steps.
• Think aloud. Voice decision making (e.g., about which numbers or operations to use) while demonstrating a procedure or process.
• Engage every student in the active recall of previous learning (e.g., through games, matching activities, “think, pair, share"). Prompt students to make connections between previous and new learning.
• Plan ways for students to consolidate their mathematical and statistical learning and build procedural fluency. Use a range of guided and independent practice tasks, such as working on problems that use a procedure that has been demonstrated. Use songs, games, materials, families of facts, and digital tools to build fluency and for students to practice skip counting, addition, subtraction, multiplication, and division facts.

Communicating in mathematics and statistics

To support mathematical thinking through representations and language, use numbers, materials, and visual representations (e.g., diagrams, number lines) to help students express their thinking and understand new concepts. Select representations that align with the learning purpose, gradually guiding students toward using symbolic representations. Number lines are valuable for ordering, comparing, and demonstrating operations.

• Encourage pattern recognition and reasoning by engaging students in sorting, grouping, and partitioning activities. Guide them to notice connections, similarities, and differences.
• Develop mathematical and statistical vocabulary through games, songs, word walls, books, and digital tools. Connect informal language to precise mathematical and statistical terms, incorporating students’ first and heritage languages where possible.
• Promote discussion and reasoning by prompting students to explain their thinking, ask questions, and summarise ideas. Use questions, materials, and visual prompts to support connections between new and prior learning.

By integrating these strategies, students build a deeper understanding, communicate their ideas effectively, and strengthen their mathematical reasoning.

Teaching through rich tasks

Incorporate open-ended investigations to deepen students' understanding of mathematical and statistical concepts and extend their learning. Design investigations based on real-world contexts or mathematical scenarios (e.g., exploring different ways to partition 24 into smaller groups). By engaging in meaningful investigations, students develop critical thinking skills and a deeper understanding of mathematical and statistical structures and relationships.

• Select problems that highlight patterns and relationships, such as identifying the “odd one out” in a set of numbers or shapes.
• Explicitly teach problem-solving strategies, guiding students to interpret a problem, represent it through drawings or materials, develop a plan, apply their strategy, and check their results.
• Use the Mathematics Investigation Cycleon Tāhūrangi to explicitly teach problem solving strategies. 
• Use the Statistical Investigation Cycle  from CensusAtSchool to explicitly teach how to undertake a statistical enquiry.

Critical focus

In years 0-3, the critical focus of the New Zealand Curriculum is on creating rich learning environments where all students thrive in literacy and mathematics. To thrive in mathematics and statistics, students develop logical reasoning by exploring patterns, quantities, shapes, and data. They begin to generalise mathematical ideas, understand number properties and shape attributes, and use materials, number lines, and visual representations to make connections and explain their thinking. They learn to collect and use data to answer investigative questions of interest.  

Noticing and recognising where students need targeted support

• Read the teaching sequence horizontally – look at the previous year's statement as the learning that is foundational/prerequisite to your year’s learning.
• Build your diagnostic/formative assessment around these prerequisite concepts and procedures before you start teaching your new unit.
• Use this assessment information to recognise where students may not securely demonstrate the prerequisite concepts and procedures.
• Respond by stepping in with accelerative learning approaches, such as:
  • providing some pre-teaching before you embark on the new learning
  • planning 3–4 mini lessons with small groups in the lead up to your new lesson and/or as "in the moment” responses throughout the new learning
  • planning time throughout the lessons to work with individuals or small groups for targeted explicit teaching/scaffolding.

Concepts and procedures to notice in phase 1 (misconceptions)

The table below highlights some common misconceptions for phase 1 students, what they reveal about student thinking, and some possible responses.

These lesson planning examples are structured using the Rollins (2014) acceleration framework. They will help you accelerate progress for students identified as needing additional support to access the learning for their year level in the mathematics and statistics learning area (Ministry of Education, 2024).

The approaches can be used with individual students, small groups, or larger groups, depending on the purpose of learning. Remember, this is in addition to your universal classroom programme.

The six steps of the acceleration framework are:

1. generate thinking, purpose, relevance, and curiosity
2. clearly articulate the learning goal and expectations
3. scaffold and practice essential prerequisite skills
4. introduce new vocabulary and review prior vocabulary
5. dip into the new concept
6. conduct formative assessment frequently.

During your planning stage, consider potential barriers and misconceptions that might prevent your students from successfully engaging with the new concept. Anticipate the scaffolds students may need to support their learning and ensure success.

There are two mini lesson plan examples to download for each year level. You can find these in Materials that come with this resource.

Years 0-1

• Subitising (.doc) – students investigate the different number pairs that a given number can be broken into.
• Fractions as numbers (.doc) – students learn that fractions are numbers that can be represented using words, pictures, or symbols.

Year 2

• Place value with two-digit numbers (.doc) – students learn to understand the base-10 structure of two-digit numbers and how to operate with them.
• Understanding sequence of time (.doc) – students learn to name and order the months and seasons, and describe the duration of familiar events using months, weeks, days, and hours.

Year 3

• Place value with two-digit numbersm (.doc) – students create patterns by translating, reflecting, and rotating shapes and analysing patterns to see if a shape has been translated, reflected, or rotated.
• Using arrays for multiplication (.doc) – students learn that multiplication is repeated addition, that repeated addition can be visualised through an array, and that an a x b array has the same total number as a b x a array.

Work on building students' relationship with mathematics. See Mathematics and statistics learning area in the New Zealand Curriculum.

Support students to have a positive relationship with mathematics and statistics by fostering curiosity and by exploring mathematics and statistics through history, games, art, and puzzles.

Highlight students' mathematical thinking by sharing their strategies and approaches. Display their representations, drawings, or photos throughout the learning process to spark discussions about progress among students and with families.

Explicit teaching

Engage students in the mathematical and statistical processes – the Do practices, (investigating situations, representing situations, connecting situations, generalising findings and explaining and justifying findings).

• Incorporate warm-up routines that promote active recall and reinforce prior learning, such as quick challenges, thought-provoking questions, and games. Support fluency development through varied practice.
• Use worked examples and introduce new concepts in clear, manageable steps. Explain mathematical and statistical symbols, notation, and operations, ensuring students build both conceptual understanding and efficient problem-solving strategies.
• Link mathematical and statistical learning across different contexts, teaching related concepts together (e.g., multiplication and division with area and volume). Make these connections explicit by referencing prior applications in other subjects.
• Provide opportunities for students to consolidate their learning through prompts, questions, and real-world situations that integrate previously taught concepts. Emphasise connections between past and new learning to strengthen understanding.

Communicating in mathematics and statistics

To support student growth in mathematical and statistical thinking, create a learning environment that encourages collaboration, effective communication, and the use of various representations to deepen understanding.

• Encourage active discussion: Plan activities that prompt students to listen, reflect, and build on each other’s ideas. Use open-ended questions and discourse-based tools to guide meaningful discussions. Over time, help students justify their reasoning with evidence and examples.
• Use effective representations: Teach students to represent their thinking clearly using pictures, diagrams, and mathematical notation (e.g., equations, inequalities). Show them which representations best illustrate different concepts, such as number lines for operations and comparisons.
• Support visualisation and estimation: Encourage students to visualise mathematical ideas by estimating quantities, rounding, and recognising patterns in shapes, measurements, and data. Guide them to observe transformations like rotations and reflections.
• Develop mathematical language: Model precise mathematical and statistical vocabulary, ensuring it aligns with learning goals. Encourage students to explain their reasoning using correct terms and incorporate their first and heritage languages to deepen understanding.
• Promote reflection and recording: Set aside time for students to record their learning in an organised way, using words, symbols, and various representations. Provide opportunities for them to set goals and reflect on their progress.

Teaching through rich tasks

To deepen students' mathematical and statistical understanding, create opportunities for them to engage with rich, meaningful tasks that connect to real-world contexts and encourage the application of reasoning and problem-solving skills.

• Design contextual tasks: Develop tasks that use a variety of contexts or operations to help students apply their knowledge to different problems, such as using decimals in measurement situations.
• Encourage generalisation: Prompt students to think critically by asking questions like, "If I change this, what happens to that?" or "Is there another way to show this?"
• Teach problem-solving strategies: Support students in reading and understanding problems, using drawings or materials, identifying relevant knowledge, planning their solution steps, applying their plan, and checking their work.
• Provide opportunities for students to notice patterns, structures, and relationships, and encourage them to make observations and statements about what they find.
• Use the Mathematics Investigation Cycle on Tāhūrangi to explicitly teach problem solving strategies.  
• Use the Statistical Investigation Cycle from CensusAtSchool to explicitly teach how to undertake a statistical enquiry.

Critical focus

In years 4-6, the critical focus of the New Zealand Curriculum is for students to broaden their knowledge and enhance collaboration. They use various representations to model number operations and solve word problems. Students expand their understanding from whole numbers to fractions and decimals, visualise and classify angles, and use benchmarks to justify their classifications. Additionally, they apply their knowledge of number operations to explore perimeter, area, and variations in patterns, shapes, and data.

Noticing and recognising where students need targeted support

• Read the teaching sequence horizontally – look at the previous year's statement as the learning that is foundational/prerequisite to your year’s learning
• Build your diagnostic/formative assessment around these prerequisite concepts and procedures before you start teaching your new unit
• Use this information to recognise where students may not securely demonstrate the prerequisite concepts and procedures
• Respond by stepping in with accelerative learning approaches, such as:
  • providing some pre-teaching before you embark on the new learning
  • planning 3–4 mini lessons with small groups in the lead up to your new lesson or as "in the moment” responses throughout the new learning,
  • planning time throughout the lessons to work with individuals or small groups for targeted explicit teaching/scaffolding, e.g., vocab practice.

Concept and procedures to notice in phase 2 (misconceptions)

The table below highlights some common misconceptions for phase 2 students, what they reveal about student thinking, and some possible responses.

These lesson planning examples are structured using the Rollins (2014) acceleration framework. The framework will help you accelerate progress for students identified as needing additional support to access the learning for their year level in the mathematics and statistics learning area (Ministry of Education, 2024).

The guidance builds on your universal classroom programme (tier 1). The approaches can be used with individual students, small groups, or larger groups, as determined by the purpose of learning. Remember, this is in addition to your universal classroom programme.

The six steps of the acceleration framework are:

• generate thinking, purpose, relevance, and curiosity
• clearly articulate the learning goal and expectations
• scaffold and practice essential skills and concepts
• introduce new vocabulary and review prior vocabulary
• dip into the new concept
• conduct formative assessment frequently.

During your planning stage, consider potential barriers and misconceptions that might prevent your students from successfully engaging with the new concept. Anticipate the scaffolds students may need to support their learning and ensure success.

There are two mini lesson plan examples to download for each year level. You can find these in Materials that come with this resource.

Year 4

• Cuisenaire Rod Fractions (.doc) – the idea that fractions come from equi-partitioning of one whole: the size of a given length can be determined with reference to one whole.
• Using dot plots to show the distribution of a numerical variable (.doc) – students work through all stages of the statistical enquiry cycle, from posing the investigative question, through planning for and collecting data, to analysis and answering the investigative question.  

Year 5

• Multiplication with large numbers (.doc) – using word problems and rich tasks to teach students to multiply three-digit by one-digit numbers and two two-digit whole numbers.
• Exploring area (.doc) – supports students to develop their ideas about area using standard units.

Year 6

• Multiply multi-digit whole numbers (.doc) – multiplying multi-digit whole numbers and connecting multiplication to scaling and stretching.
• Features and properties of 3D shapes (.doc) – investigate a variety of three-dimensional shapes. By examining a wide range of shapes and looking at the relationship between the numbers of faces, edges and vertices, students see whether they can “discover” Euler’s famous formula.

Work on building students' relationship with mathematics. See the Mathematics and Statistics learning area in the New Zealand Curriculum.

Engage students with authentic tasks that connect to their own experiences, interests, and the world around them. When learning feels relevant, students are more likely to stay curious and involved. Alongside these meaningful tasks, model and teach strategies for perseverance—encourage them to try a different approach, sketch a diagram to clarify their thinking, or talk through the challenge with a classmate. These habits help build confidence and resilience, turning setbacks into opportunities for learning.

Explicit teaching

Engage students in the mathematical and statistical processes (investigating situations, representing situations, connecting situations, generalising findings, and explaining and justifying findings).

Break new learning into clear, manageable steps using worked examples, and model both efficient written and mental strategies. Include examples with deliberate errors or missing steps to help students build reasoning and analytical skills. Support learning through regular opportunities to actively recall, practise, and connect new concepts with prior knowledge. Begin with focused, repeated practice to build confidence and fluency, then gradually introduce mixed (interleaved) practice to strengthen flexibility and deeper understanding.

Communicating in mathematics and statistics

To support student growth in mathematical and statistical thinking, create a learning environment that encourages collaboration, effective communication, and the use of various representations to deepen understanding. Support students to communicate clearly by prompting them to articulate their thinking when using visualisation to represent relationships, patterns, shapes, and data.

• Provide opportunities for students to actively listen, reflect, and build on one another’s thinking through open-ended questions and structured discussion. Support them in forming and justifying claims based on observations and evidence, while maintaining a balance between teacher input and student dialogue.
• Encourage the use of appropriate representations—such as graphs, tables, diagrams, and equations—to support reasoning and problem-solving. Over time, guide students toward increased use of equations and visual models to express and extend their thinking.

Explicitly teach mathematical and statistical vocabulary within meaningful contexts, using tools like the Frayer model to strengthen understanding. Where appropriate, incorporate students’ first or heritage languages to support conceptual development.

Teaching through rich tasks

To deepen students' mathematical and statistical understanding, create opportunities for them to engage with rich, meaningful tasks that connect to real-world contexts and encourage the application of reasoning and problem-solving skills.

Design rich mathematical investigations that connect to real-life contexts, such as creating a savings plan, to help students apply their learning in meaningful ways. Support them in identifying suitable questions and selecting the mathematical concepts, strategies, and representations needed.

Include tasks with multiple entry and exit points, allowing for different approaches and solutions. Explicitly teach problem-solving strategies, such as drawing diagrams, using tables to find patterns, linking to prior knowledge, forming and solving equations, organising working clearly, and checking the reasonableness of results.

Noticing and recognising where students need targeted support

• read the teaching sequence horizontally – look at the previous year's statement as the learning that is foundational/prerequisite to your year’s learning
• build your diagnostic/formative assessment around these foundational concepts and procedures before you start teaching your new unit
• use this information to recognise where students may not securely demonstrate the prerequisite concepts and procedures
• respond by stepping in with accelerative learning approaches – see the examples below:
  • e.g. some pre-teaching before you embark on the new learning
  • e.g. plan 3–4 short sessions with small groups in the lead up to your new lesson OR as "in the moment” responses throughout the new learning,
  • e.g. planning time throughout the lessons to work with individuals or small groups for targeted explicit teaching/scaffolding. Vocab practice etc.)

Concepts and procedures to notice in Phase 3 (common misconceptions)

The table below highlights common misconceptions for phase 3, year 7-8, students, what they reveal about student thinking, and some possible responses.

These examples use the Rollins (2014) acceleration framework. It will help you plan mini lessons to accelerate progress for students identified as needing additional support to access the learning for their year level in the mathematics and statistics learning area (Ministry of Education, 2024).

The guidance builds on your universal classroom programme. The approaches can be used with individual students, small groups, or larger groups, as determined by the purpose of learning.

The six steps of the acceleration framework are:

• generate thinking, purpose, relevance, and curiosity
• clearly articulate the learning goal and expectations
• scaffold and practice essential prerequisite skills
• introduce new vocabulary and review prior vocabulary
• dip into the new concept
• conduct formative assessment frequently

During your planning stage, consider potential barriers and misconceptions that might prevent your students from successfully engaging with the new concept. Anticipate the scaffolds students may need to support their learning and ensure success.

There are two lesson plan examples for each year level. See Materials that come with this resource to download:

• Year 7 – Measuring area (.doc)
• Year 7 – Adding and subtracting decimals (.doc)
• Year 8 – Working with percentages (.doc)
• Year 8 – Solving equations (.doc)