This document outlines Pennard Primary School's calculation policy. It provides strategies for teaching key calculation objectives in a concrete, pictorial, and abstract manner. The policy covers addition, subtraction, multiplication, and division and is intended as a working document that can be revised as needed.
This document discusses special cases of circle equations, including degenerate circles which represent a single point, and null sets which represent no points. It provides examples of converting circle equations to standard form, identifying degenerate and null sets, and finding the radius and equation of a circle given two points. Practice problems are also presented for students to identify circle equations as representing circles, points, or null sets, and to find the equation of a circle given its radius endpoints.
The document discusses different methods for dividing polynomials, including:
1) Dividing by a monomial by splitting the polynomial into fractions and reducing.
2) Performing long division of polynomials similar to long division of integers.
3) Using synthetic division as a shortcut for long division when the divisor is of the form x - k, where k is a number.
4) An example of using synthetic division to factor a polynomial completely when given one of its factors.
This document provides examples and explanations for solving equations with variables on both sides. It discusses adding or subtracting like terms to move all variable terms to one side of the equation. Several example equations are worked through step-by-step, including equations with multiplication, division, fractions, and parentheses. Students are reminded that some equations may have no solution or a solution of zero. The document concludes by assigning practice problems.
This document provides an overview of the different mathematical methods taught at Minchinhampton school. It explains that traditional methods are now used less to develop number skills and understanding. The methods are presented in a progressive order and are designed to aid conceptual understanding and support mental calculations. Pupils are taught methods appropriate to their level of understanding of numbers. Older pupils are creating videos to demonstrate the methods being used. The document then provides details on the specific methods used for addition, subtraction, multiplication and division.
This document provides an overview and agenda for a professional development session on the 1st Grade Math Expressions curriculum. It outlines the daily routines, materials, assessments, pacing guide, and teaching strategies for Units 1-8. Key concepts are highlighted for each unit, which focus on number sense, addition, subtraction, place value, measurement, and time. Non-essential lessons and quick quizzes are also noted. Contact information is provided for questions.
The document provides an overview of the Kindergarten Math Expressions curriculum covering Units 1-4, including daily routines, materials, teaching strategies, unit assessments, and a pacing guide. Key concepts introduced include numbers 1-10, patterns, story problems, partners, attributes, and teen numbers. Teachers are given guidance on routines, materials, and strategies to teach the essential skills and concepts in each unit.
This document discusses special cases of circle equations, including degenerate circles which represent a single point, and null sets which represent no points. It provides examples of converting circle equations to standard form, identifying degenerate and null sets, and finding the radius and equation of a circle given two points. Practice problems are also presented for students to identify circle equations as representing circles, points, or null sets, and to find the equation of a circle given its radius endpoints.
The document discusses different methods for dividing polynomials, including:
1) Dividing by a monomial by splitting the polynomial into fractions and reducing.
2) Performing long division of polynomials similar to long division of integers.
3) Using synthetic division as a shortcut for long division when the divisor is of the form x - k, where k is a number.
4) An example of using synthetic division to factor a polynomial completely when given one of its factors.
This document provides examples and explanations for solving equations with variables on both sides. It discusses adding or subtracting like terms to move all variable terms to one side of the equation. Several example equations are worked through step-by-step, including equations with multiplication, division, fractions, and parentheses. Students are reminded that some equations may have no solution or a solution of zero. The document concludes by assigning practice problems.
This document provides an overview of the different mathematical methods taught at Minchinhampton school. It explains that traditional methods are now used less to develop number skills and understanding. The methods are presented in a progressive order and are designed to aid conceptual understanding and support mental calculations. Pupils are taught methods appropriate to their level of understanding of numbers. Older pupils are creating videos to demonstrate the methods being used. The document then provides details on the specific methods used for addition, subtraction, multiplication and division.
This document provides an overview and agenda for a professional development session on the 1st Grade Math Expressions curriculum. It outlines the daily routines, materials, assessments, pacing guide, and teaching strategies for Units 1-8. Key concepts are highlighted for each unit, which focus on number sense, addition, subtraction, place value, measurement, and time. Non-essential lessons and quick quizzes are also noted. Contact information is provided for questions.
The document provides an overview of the Kindergarten Math Expressions curriculum covering Units 1-4, including daily routines, materials, teaching strategies, unit assessments, and a pacing guide. Key concepts introduced include numbers 1-10, patterns, story problems, partners, attributes, and teen numbers. Teachers are given guidance on routines, materials, and strategies to teach the essential skills and concepts in each unit.
This document provides an overview and agenda for a 2nd grade math expressions unit covering tools, strategies, routines, assessments, and pacing. It includes details on using the 120 poster, money flip chart, number path, and secret code cards for daily routines. It outlines the key ideas, teaching strategies, tools, and non-essential lessons for each unit 1-9. The goals are to explore addition and subtraction concepts, understand place value, add and subtract multi-digit numbers, and work with time, money, and data. Computational fluency is emphasized through daily quick practice activities.
The document provides information about a first grade math unit on subtraction from The Moffatt Girls math curriculum. It includes the standards covered in Unit 3, which focus on subtraction within 20, properties of operations, fluency with addition and subtraction within 10, the meaning of the equal sign, and solving word problems. It describes the unit's NO PREP practice pages and math centers to provide practice and application of skills in an engaging way. Pictures show examples of the practice pages and centers being used in the classroom.
This document provides information about numeracy teaching in Key Stage 2 (years 3-6). It discusses the progression of strategies taught for the four operations of number (addition, subtraction, multiplication and division). Mental and written calculation methods are outlined for each year group. The importance of numeracy in daily life and future careers is also highlighted. Parents are encouraged to support their child's numeracy learning at home.
The document provides materials and instructions for assessing 2nd grade math skills related to number sense. It includes checklists of skills students should be able to demonstrate such as skip counting, placing numbers on a number line, using objects to add and subtract within 1000, explaining addition and subtraction strategies, and quickly performing single-digit addition and subtraction. Sample problems, checklists, and solutions are provided. Teachers are instructed to have students explain their thinking and use manipulatives to show their work, rather than just getting the numerical answer.
This document provides a scheme of work for teaching mathematics at Stage 8. It includes 3 units per term that each focus on a different topic area like number, algebra, or data handling. Each unit lists learning objectives, example activities, and resources for teaching key concepts. It also provides problem-solving activities that can be incorporated across each unit to develop problem-solving skills. The purpose is to illustrate one way the curriculum could be planned and delivered over the school year in 3 terms with flexibility for teachers.
Spots for M.A.T.H. Professional Development Events Nechemia Weiss
This document provides an overview of the Spots for M.A.T.H. professional development program for the 2014-2015 school year. The program aims to help students develop real math wisdom through innovative tools like dot cards and open number lines. These tools make abstract math concepts more concrete and help students learn strategies for addition, subtraction, and problem solving. The program provides a predictable progression of lessons building math skills over multiple chapters and grades.
This document provides information from a Maths Information Evening for parents. It discusses what progress in maths entails, how maths is taught in key stages 1 and 2, and different maths concepts covered, including place value, addition, subtraction, multiplication, division, and problem solving. Parents are advised to praise their children's efforts, play maths games at home, and focus on building confidence rather than stressing workbooks or written methods.
This document contains summaries of key strategies and knowledge for stage 6 of the mathematics curriculum across several domains:
1) Addition and subtraction strategies including using number lines, place value, rounding and compensating, and standard algorithms.
2) Multiplication and division strategies such as recalling times tables, using distributive property, and solving word problems.
3) Ratio and proportion strategies like finding fractions, decimals, equivalencies, and solving division problems with fraction answers.
4) Algebraic thinking strategies including finding relationships in patterns and representing them using rules, tables, graphs, and equations.
This document contains an instrument for a basic mathematics skills diagnostic test for primary school students in a special education program in Johor, Malaysia. It outlines 18 skills to be tested in mathematics, from pre-number concepts to problem solving involving the four basic operations. For each skill, it provides sample test items and instructions for students to complete tasks related to number recognition, operations, time telling, and money. The test was developed by a panel of trainers for the special education program in the Johor State Education Department.
The document provides an overview of operations and algebraic thinking standards from kindergarten through 8th grade. It shows that in the early grades, standards focus on representing numbers, addition, subtraction and basic multiplication/division. In later grades, standards expand the scope of numbers and introduce concepts like ratios, proportions, expressions and patterns. Students are expected to apply mathematical operations to increasingly complex word problems and equations over time.
The teacher will lead lessons on comparing three-digit numbers using symbols like <, >, and =. Students will practice comparing numbers by plotting them on numbered number lines and determining which number is greater. Formative assessments include observing students during independent practice and reviewing work samples where they compare number pairs using number lines and write the correct symbol.
The document provides an overview of pre-algebra concepts including:
1) Six methods for solving "border problems" using algebra to determine the number of squares and those on the border.
2) Order of operations and the importance of PEMDAS.
3) Definitions of variables, expressions, and the substitution property of equality.
4) Properties of integers and how to add, subtract, and use counters to represent integer operations.
5) The number line and absolute value, and rules for adding and subtracting integers.
Conversion of fraction to decimal and vice versaJudePellerin
This document provides information and examples on rounding decimals and converting decimals to fractions. It discusses:
1) Rounding decimals by dropping numbers to the right of the place value being eliminated and adjusting the last digit if needed. Examples are provided such as rounding 25.4 to 25 and 0.3125 to 0.31.
2) Converting a decimal to a fraction by using 10 or a power of 10 as the denominator and reducing the fraction if possible.
3) Additional examples of rounding decimals to the nearest whole number, tenths, or hundredths.
This document discusses strategies for developing strong mental math skills in K-8 students. It defines mental math as using conceptual strategies to calculate without external aids. Several core strategies are described, such as making 10, using doubles, and the distributive property. The document emphasizes building number sense through repeated practice with games and discussion. Student progress in mental math is assessed through checklists, observations of strategy use, and sample work collection. Report cards evaluate if students can determine answers flexibly using strategies, make reasonable estimates, and apply estimation to daily life.
Here are the steps to solve this problem:
1) Kaleb bought 9 oranges
2) Ben bought the same number as Kaleb, which is 9 oranges
3) To find the total oranges they bought, we add the amounts:
9 oranges (Kaleb) + 9 oranges (Ben) = 18 oranges
4) The equation is: 9 + 9 = 18
5) I know I'm right because addition is commutative - the order of the addends doesn't matter. So adding Kaleb's 9 oranges and Ben's 9 oranges will give the total amount regardless of order.
The document provides an outline for a teaching week on functional mathematics for year 7 students. It includes topics such as numbers, fractions, decimals, measurement, and area/perimeter. The topics and outcomes are listed along with instructional approaches and strategies using examples, activities, and resources to explain key concepts in numbers, operations, and measurement.
The document provides an overview of topics and learning outcomes for a 7th grade functional mathematics teaching week. It includes instruction on:
1. Numbers - reading, writing, representing, and comparing numbers up to millions.
2. Fractions - representing, comparing, adding, and subtracting fractions.
3. Combined operations - performing multi-step calculations involving addition, subtraction, multiplication, and division.
The document outlines instructional approaches and strategies as well as recommended resources for teaching each topic.
The document provides lesson content on addition and subtraction of whole numbers. It includes examples and explanations of key concepts like finding the sum, carrying, borrowing, properties of addition/subtraction, and word problems. Practice problems are provided at the end to solve applications using the whole number operations and problem-solving process covered in the lesson.
Unit 6 presentation base ten equality form of a number with trainer notes 7.9.08jcsmathfoundations
The document discusses concepts related to base ten, equality, and forms of numbers. It defines these concepts, examines how students develop an understanding through research on cognitive development, and provides classroom applications and strategies for teaching these concepts effectively. Diagnostic questions are presented to assess student understanding, and examples show how to respond to common student errors or misconceptions in working with numbers.
The document covers various topics in patterns, fractions, algebraic expressions, equations, and numerical expressions. It includes examples of continuing number patterns, writing rules for patterns, using variables, evaluating expressions, solving equations by adding/subtracting and multiplying/dividing, using exponents, and more. It asks the reader to determine if statements are true or false, complete open sentences, write their own true/false sentences, and consider variables as unknown values in equations.
This document provides information about Pennard Primary School. It begins with welcoming messages from the headteacher and provides an overview of the school's vision, values, and aims. It describes the school's facilities and location. It explains that the school is committed to being a rights-respecting school and providing a high-quality education for all students in a supportive community environment.
Pennard Primary School is a school of approximately 210 pupils located in a rural village on the Gower Peninsula. The school aims to provide a high quality education in a stimulating environment to help every child reach their potential. It has a strong focus on values such as respect, responsibility, friendship and perseverance. The school day runs from 8:50am to 3:20pm with additional after school activities available. The school aims to prepare students to succeed in their education and future careers.
This document provides an overview and agenda for a 2nd grade math expressions unit covering tools, strategies, routines, assessments, and pacing. It includes details on using the 120 poster, money flip chart, number path, and secret code cards for daily routines. It outlines the key ideas, teaching strategies, tools, and non-essential lessons for each unit 1-9. The goals are to explore addition and subtraction concepts, understand place value, add and subtract multi-digit numbers, and work with time, money, and data. Computational fluency is emphasized through daily quick practice activities.
The document provides information about a first grade math unit on subtraction from The Moffatt Girls math curriculum. It includes the standards covered in Unit 3, which focus on subtraction within 20, properties of operations, fluency with addition and subtraction within 10, the meaning of the equal sign, and solving word problems. It describes the unit's NO PREP practice pages and math centers to provide practice and application of skills in an engaging way. Pictures show examples of the practice pages and centers being used in the classroom.
This document provides information about numeracy teaching in Key Stage 2 (years 3-6). It discusses the progression of strategies taught for the four operations of number (addition, subtraction, multiplication and division). Mental and written calculation methods are outlined for each year group. The importance of numeracy in daily life and future careers is also highlighted. Parents are encouraged to support their child's numeracy learning at home.
The document provides materials and instructions for assessing 2nd grade math skills related to number sense. It includes checklists of skills students should be able to demonstrate such as skip counting, placing numbers on a number line, using objects to add and subtract within 1000, explaining addition and subtraction strategies, and quickly performing single-digit addition and subtraction. Sample problems, checklists, and solutions are provided. Teachers are instructed to have students explain their thinking and use manipulatives to show their work, rather than just getting the numerical answer.
This document provides a scheme of work for teaching mathematics at Stage 8. It includes 3 units per term that each focus on a different topic area like number, algebra, or data handling. Each unit lists learning objectives, example activities, and resources for teaching key concepts. It also provides problem-solving activities that can be incorporated across each unit to develop problem-solving skills. The purpose is to illustrate one way the curriculum could be planned and delivered over the school year in 3 terms with flexibility for teachers.
Spots for M.A.T.H. Professional Development Events Nechemia Weiss
This document provides an overview of the Spots for M.A.T.H. professional development program for the 2014-2015 school year. The program aims to help students develop real math wisdom through innovative tools like dot cards and open number lines. These tools make abstract math concepts more concrete and help students learn strategies for addition, subtraction, and problem solving. The program provides a predictable progression of lessons building math skills over multiple chapters and grades.
This document provides information from a Maths Information Evening for parents. It discusses what progress in maths entails, how maths is taught in key stages 1 and 2, and different maths concepts covered, including place value, addition, subtraction, multiplication, division, and problem solving. Parents are advised to praise their children's efforts, play maths games at home, and focus on building confidence rather than stressing workbooks or written methods.
This document contains summaries of key strategies and knowledge for stage 6 of the mathematics curriculum across several domains:
1) Addition and subtraction strategies including using number lines, place value, rounding and compensating, and standard algorithms.
2) Multiplication and division strategies such as recalling times tables, using distributive property, and solving word problems.
3) Ratio and proportion strategies like finding fractions, decimals, equivalencies, and solving division problems with fraction answers.
4) Algebraic thinking strategies including finding relationships in patterns and representing them using rules, tables, graphs, and equations.
This document contains an instrument for a basic mathematics skills diagnostic test for primary school students in a special education program in Johor, Malaysia. It outlines 18 skills to be tested in mathematics, from pre-number concepts to problem solving involving the four basic operations. For each skill, it provides sample test items and instructions for students to complete tasks related to number recognition, operations, time telling, and money. The test was developed by a panel of trainers for the special education program in the Johor State Education Department.
The document provides an overview of operations and algebraic thinking standards from kindergarten through 8th grade. It shows that in the early grades, standards focus on representing numbers, addition, subtraction and basic multiplication/division. In later grades, standards expand the scope of numbers and introduce concepts like ratios, proportions, expressions and patterns. Students are expected to apply mathematical operations to increasingly complex word problems and equations over time.
The teacher will lead lessons on comparing three-digit numbers using symbols like <, >, and =. Students will practice comparing numbers by plotting them on numbered number lines and determining which number is greater. Formative assessments include observing students during independent practice and reviewing work samples where they compare number pairs using number lines and write the correct symbol.
The document provides an overview of pre-algebra concepts including:
1) Six methods for solving "border problems" using algebra to determine the number of squares and those on the border.
2) Order of operations and the importance of PEMDAS.
3) Definitions of variables, expressions, and the substitution property of equality.
4) Properties of integers and how to add, subtract, and use counters to represent integer operations.
5) The number line and absolute value, and rules for adding and subtracting integers.
Conversion of fraction to decimal and vice versaJudePellerin
This document provides information and examples on rounding decimals and converting decimals to fractions. It discusses:
1) Rounding decimals by dropping numbers to the right of the place value being eliminated and adjusting the last digit if needed. Examples are provided such as rounding 25.4 to 25 and 0.3125 to 0.31.
2) Converting a decimal to a fraction by using 10 or a power of 10 as the denominator and reducing the fraction if possible.
3) Additional examples of rounding decimals to the nearest whole number, tenths, or hundredths.
This document discusses strategies for developing strong mental math skills in K-8 students. It defines mental math as using conceptual strategies to calculate without external aids. Several core strategies are described, such as making 10, using doubles, and the distributive property. The document emphasizes building number sense through repeated practice with games and discussion. Student progress in mental math is assessed through checklists, observations of strategy use, and sample work collection. Report cards evaluate if students can determine answers flexibly using strategies, make reasonable estimates, and apply estimation to daily life.
Here are the steps to solve this problem:
1) Kaleb bought 9 oranges
2) Ben bought the same number as Kaleb, which is 9 oranges
3) To find the total oranges they bought, we add the amounts:
9 oranges (Kaleb) + 9 oranges (Ben) = 18 oranges
4) The equation is: 9 + 9 = 18
5) I know I'm right because addition is commutative - the order of the addends doesn't matter. So adding Kaleb's 9 oranges and Ben's 9 oranges will give the total amount regardless of order.
The document provides an outline for a teaching week on functional mathematics for year 7 students. It includes topics such as numbers, fractions, decimals, measurement, and area/perimeter. The topics and outcomes are listed along with instructional approaches and strategies using examples, activities, and resources to explain key concepts in numbers, operations, and measurement.
The document provides an overview of topics and learning outcomes for a 7th grade functional mathematics teaching week. It includes instruction on:
1. Numbers - reading, writing, representing, and comparing numbers up to millions.
2. Fractions - representing, comparing, adding, and subtracting fractions.
3. Combined operations - performing multi-step calculations involving addition, subtraction, multiplication, and division.
The document outlines instructional approaches and strategies as well as recommended resources for teaching each topic.
The document provides lesson content on addition and subtraction of whole numbers. It includes examples and explanations of key concepts like finding the sum, carrying, borrowing, properties of addition/subtraction, and word problems. Practice problems are provided at the end to solve applications using the whole number operations and problem-solving process covered in the lesson.
Unit 6 presentation base ten equality form of a number with trainer notes 7.9.08jcsmathfoundations
The document discusses concepts related to base ten, equality, and forms of numbers. It defines these concepts, examines how students develop an understanding through research on cognitive development, and provides classroom applications and strategies for teaching these concepts effectively. Diagnostic questions are presented to assess student understanding, and examples show how to respond to common student errors or misconceptions in working with numbers.
The document covers various topics in patterns, fractions, algebraic expressions, equations, and numerical expressions. It includes examples of continuing number patterns, writing rules for patterns, using variables, evaluating expressions, solving equations by adding/subtracting and multiplying/dividing, using exponents, and more. It asks the reader to determine if statements are true or false, complete open sentences, write their own true/false sentences, and consider variables as unknown values in equations.
This document provides information about Pennard Primary School. It begins with welcoming messages from the headteacher and provides an overview of the school's vision, values, and aims. It describes the school's facilities and location. It explains that the school is committed to being a rights-respecting school and providing a high-quality education for all students in a supportive community environment.
Pennard Primary School is a school of approximately 210 pupils located in a rural village on the Gower Peninsula. The school aims to provide a high quality education in a stimulating environment to help every child reach their potential. It has a strong focus on values such as respect, responsibility, friendship and perseverance. The school day runs from 8:50am to 3:20pm with additional after school activities available. The school aims to prepare students to succeed in their education and future careers.
The document provides information about Pennard Primary School. It outlines the school's vision to prepare students with knowledge, skills, and values to be responsible community members. It describes the school's facilities, staff, curriculum, and extracurricular activities. It emphasizes that the school aims to provide a happy, supportive learning environment where students' individual strengths are nurtured.
The PTA newsletter outlines upcoming events and changes to the PTA. The AGM was held where a new committee was elected and it was proposed that the PTA become more inclusive by changing its name to "Friends of Pennard Primary." Upcoming events include a book fair, EGM meeting, Halloween disco and pumpkin competition, and Christmas craft day and shopping evening. The newsletter provides details on these events and encourages parents to get involved with the PTA.
Pennard Primary School provides early years education for children ages 3 and up. The school offers a safe and caring environment where children can develop, enjoy learning, and achieve their goals. Teachers are highly experienced and passionate about caring for children and supporting their learning. Children experience vibrant and stimulating creative activities in an enriching environment designed to inspire growth and learning. Parents can secure a place for their child now by contacting the school office.
Dyslexia affects 1 in 10 people and is a neurological difference that impacts reading, writing, spelling, organization and time management. While dyslexia presents challenges, it is also associated with strengths like creativity, problem solving, entrepreneurship and being visual thinkers. Famous people like Picasso, Henry Ford and Keira Knightley have succeeded despite having dyslexia. With the right support and understanding of their differences, people with dyslexia can find ways to work with their strengths.
This document provides guidance and suggestions for parents to help children learn keywords and reading at home. It recommends making learning fun and engaging children's interests. Various game ideas are presented to reinforce learning keywords, such as snap, pairs, asking questions, making sentences and pictures, finding words in books, and sticking words around the house. Physical activities are also suggested for active learners. The document encourages parents to seek help from teachers if needed.
This document provides information for parents about a child starting school at Pennard Primary School in Wales. It aims to welcome parents and provide a happy and successful experience for children. The school believes that children thrive in a stimulating, creative and secure environment. It teaches a rich curriculum through play-based learning to develop children's skills and talents. The document outlines the school staff, medical procedures, curriculum areas including outdoor learning, and settling in process to help children adapt to school. It aims to build partnerships between school and home to support each child's learning and well-being.
The document discusses how to use VCOP skills (Vocabulary, Connectives, Openers, Punctuation) to improve boring sentences and make them more engaging. It provides an example of a simple sentence "The cat went along the wall" and shows how using different VCOP techniques can transform it into a more descriptive and interesting sentence. The techniques add adjectives, connectives, change the opener, and use different punctuation to create the final sentence "Whilst licking his lips, the fluffy ginger cat (who had sharp teeth) prowled along the red brick wall because he was spying on a juicy bird!"
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Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
Assessment and Planning in Educational technology.pptxKavitha Krishnan
In an education system, it is understood that assessment is only for the students, but on the other hand, the Assessment of teachers is also an important aspect of the education system that ensures teachers are providing high-quality instruction to students. The assessment process can be used to provide feedback and support for professional development, to inform decisions about teacher retention or promotion, or to evaluate teacher effectiveness for accountability purposes.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
Thinking of getting a dog? Be aware that breeds like Pit Bulls, Rottweilers, and German Shepherds can be loyal and dangerous. Proper training and socialization are crucial to preventing aggressive behaviors. Ensure safety by understanding their needs and always supervising interactions. Stay safe, and enjoy your furry friends!
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Calculation policy v2
1. Calculation Policy
This policy has been largely adapted from the White Rose Maths Hub Calculation Policy with further material added.
It is a working document and will be revised and amended as necessary.
2. Pennard Primary School Calculation Policy
P
Objective & Strategy Concrete Pictorial Abstract
Combining two
Use part part whole model.
Use cubes to add two num-
bers together as a group or
in a bar.
Use pictures to
add two num-
bers together
as a group or in
8 1 a bar.
4 + 3 = 7
5
3
Use the part-part
10= 6 + 4 whole diagram as
shown above to move
into the abstract.
parts to make a
whole: part- whole
model
Starting at the big-
ger number and
counting on Start with the larger number on the bead
string and then count on to the smaller num-
12 + 5 = 17
Start at the larger number on the number
line and count on in ones or in one jump to
find the answer.
5 + 12 = 17
Place the larger number in your head and
count on the smaller number to find your
answer.
ber 1 by 1 to find the answer.
Regrouping to make
10.
This is an essential skill for
column addition later.
6 + 5 = 11
Start with the
bigger number
and use the
smaller number
to make 10.
Use ten frames.
Use pictures or a number line. Regroup or
partition the smaller number using the part
part whole model to make 10.
7 + 4= 11
If I am at seven, how many more do I need to
make 10. How many more do I add on now?
Represent & use
number bonds and
related subtraction
facts within 20 2 more than 5.
Emphasis should be on the language
‘1 more than 5 is equal to 6.’
‘2 more than 5 is 7.’
‘8 is 3 more than 5.’
3. Pennard Primary School Calculation Policy
P
Objective &
Strategy
Concrete Pictorial Abstract
Adding multiples of
ten
50= 30 = 20
Model using dienes and bead strings
Use representations for base ten.
20 + 30 = 50
70 = 50 + 20
40 + □ = 60
Use known number
facts
Part part whole
Children ex-
plore ways of
making num-
bers within 20
Using known facts + =
+ =
Children draw representations of H,T and O
Bar model
3 + 4 = 7
7 + 3 = 10 23 + 25 = 48
4. Pennard Primary School Calculation Policy
P
Objective &
Strategy
Concrete Pictorial Abstract
Add a two digit
number and ones
17 + 5 = 22
Use ten frame to
make ‘magic ten
Children explore the pattern.
17 + 5 = 22
27 + 5 = 32
17 + 5 = 22
Use part
part whole
and number
3 2
line to
model.
20
17 + 5 = 22
Explore related facts
17 + 5 = 22
5 + 17 = 22
22
22—17 = 5
17 5
22—5 = 17
Add a 2 digit num-
ber and tens
25 + 10 = 35
Explore that the ones digit does not change
27 + 10 = 37
27 + 20 = 47
27 + □ = 57
Add two 2-digit
numbers
Model using dienes , place value counters
and numicon
Use number line and bridge ten using part
whole if necessary.
25 + 47
20 + 5 40 + 7
20 + 40 = 60
5+ 7 =12
60 + 12 = 72
Add three 1-digit
numbers
Combine to make 10 first if possible, or
bridge 1o then add third digit
+ +
Regroup and draw representation.
+ = 15
Combine the two numbers that make/
bridge ten then add on the third.
5. Pennard Primary School Calculation Policy
P
Objective &
Strategy
Concrete Pictorial Abstract
Column Addition—no
regrouping (friendly
numbers)
Add two or three 2 or 3-
digit numbers.
Model using
Dienes or nu-
micon
Add together the ones first, then the
tens.
Move to using place value counters
Children move to drawing the counters using
a tens and one frame.
tens ones
2 2 3
+ 1 1 4
3 3 7
Add the ones first, then the tens, then
the hundreds.
Column Addition with
regrouping.
Exchange ten ones for a ten. Model
using numicon and pv counters.
Children can draw a rep-
resentation of the grid to
further support their
understanding, carrying
the ten underneath the
line
Start by partitioning
the numbers before
formal column to
show the exchange.
6. Pennard Primary School Calculation Policy
Children continue to use dienes or pv
Objective &
Strategy
Concrete Pictorial Abstract
Y4—add numbers with
up to 4 digits
counters to add, exchanging ten ones for
a ten and ten tens for a hundred and ten
hundreds for a thousand.
Draw representations using pv grid.
Continue from previous work to carry
hundreds as well as tens.
Relate to money and measures.
Y5—add numbers with As year 4
tens ones tenths hundredths
Introduce decimal place value counters
and model exchange for addition.
more than 4 digits.
Add decimals with 2 dec-
imal places, including
money.
Y6—add several num-
bers of increasing com-
plexity
As Y5 As Y5
Including adding money,
measure and decimals
with different numbers
of decimal points.
Insert zeros for
place holders.
7. Pennard Primary School Calculation Policy
Objective &
Strategy
Concrete Pictorial Abstract
Taking away
ones.
Use physical objects, counters , cubes etc
to show how objects can be taken away.
6—4 = 2
4—2 = 2
7—4 = 3
16—9 = 7
Cross out drawn objects to show what has
been taken away.
Counting back
Move objects away from the group,
counting backwards.
Move the beads
along the bead
string as you count
backwards.
Count back in ones using a number line.
Put 13 in your head, count back 4. What number
are you at?
Find the
Difference
Compare objects and amounts
Lay objects to represent bar model.
Count on using a number line to find the
difference.
Hannah has12 sweets and her sister has 5. How
many more does Hannah have than her sister.?
8. Pennard Primary School Calculation Policy
Objective &
Strategy
Concrete Pictorial Abstract
Represent and use
number bonds and
related subtraction
facts within 20
Part Part Whole
model
Link to addition. Use
PPW model to model
the inverse.
If 10 is the whole and 6 is one of the arts,
what s the other part?
10—6 = 4 Use pictorial representations to show the part.
Move to using numbers within
the part whole model.
5
12
7
Make 10 14—9
Make 14 on the ten frame. Take 4 away
to make ten, then take one more away so
that you have taken 5.
13—7
Jump back 3 first, then another 4. Use ten
as the stopping point.
16—8
How many do we take off first to get to
10? How many left to take off?
Bar model
8 2
5—2 = 3
10 = 8 + 2
10 = 2 + 8
10—2 = 8
10—8 = 2
9. Pennard Primary School Calculation Policy
Objective & Strategy Concrete Pictorial Abstract
Regroup a ten into
ten ones
Use a PV chart to show how to change a
ten into ten ones, use the term ‘take and
make’
20—4 = 16
Partitioning to sub-
tract without re-
grouping.
‘Friendly numbers’
34—13 = 21
Use Dienes to
show how to par-
tition the number
when subtracting
without regroup-
ing.
Children draw representations of Dienes and
cross off.
43—21 = 22
43—21 = 22
Make ten strategy
Progression should be
crossing one ten, crossing
more than one ten, cross-
ing the hundreds. 34—28
Use a bead bar or bead strings to model
counting to next ten and the rest.
Use a number line to count on to next ten
and then the rest.
93—76 = 17
10. Pennard Primary School Calculation Policy
Objective &
Strategy
Concrete Pictorial Abstract
Column subtraction
without regrouping
(friendly numbers)
47—32
—
Use base 10 or Numicon to model
Intermediate step may
Darw representations to support under-
standing
be needed to lead to
clear subtraction under-
standing.
Column subtraction
with regrouping
Children may draw base ten or PV counters
and cross off.
Begin by parti-
tioning into pv
columns
Then move to
formal method.
Begin with base 10 or Numicon. Move to
pv counters, modelling the exchange of a
ten into tten ones. Use the phrase ‘take
and make’ for exchange.
11. Pennard Primary School Calculation Policy
Objective &
Strategy
Concrete Pictorial Abstract
Subtracting tens
and ones
234 - 179
Model process of exchange using Numi-
con, base ten and then move to PV coun-
ters.
Children to draw pv counters and show their
exchange—see Y3
Use the phrase ‘take and make’ for ex-
change
Year 4 subtract with
up to 4 digits.
Introduce decimal subtrac-
tion through context of
money
Year 5- Subtract
with at least 4 dig-
As Year 4 Children to draw pv counters and show their
exchange—see Y3
Use zeros
for place-
holders.
its, including money
and measures.
Subtract with decimal
values, including mixtures
of integers and decimals
and aligning the decimal
Year 6—Subtract
with increasingly
large and more
complex numbers
and decimal values.
12. Pennard Primary School Calculation Policy
Objective &
Strategy
Concrete Pictorial Abstract
Doubling Use practical activities using manip-
ultives including cubes and Numicon
to demonstrate doubling
Draw pictures to show how to double numbers Partition a number and then double each part
before recombining it back together.
+ = 32
Counting in multi-
ples
Count the groups as children are skip
counting, children may use their fin-
gers as they are skip counting.
Children make representations to show
counting in multiples.
Count in multiples of a number aloud.
Write sequences with multiples of num-
bers.
2, 4, 6, 8, 10
5, 10, 15, 20, 25 , 30
Making equal 2 x 4 = 8
13. Pennard Primary School Calculation Policy
groups and
counting the total
Use manipulatives to create equal groups.
Draw and make representations
14. Pennard Primary School Calculation Policy
lems
Objective &
Strategy
Concrete Pictorial Abstract
Repeated addition
Use different objects to add
equal groups
Use pictorial including number lines to solve
prob
Write addition sentences to describe objects
and pictures.
Understanding ar-
rays
Use objects laid out in arrays to find the an-
swers to 2 lots 5, 3 lots of 2 etc.
Draw representations of arrays to show under-
standing
3 x 2 = 6
2 x 5 = 10
15. Pennard Primary School Calculation Policy
Objective &
Strategy
Concrete Pictorial Abstract
Doubling Model doubling using dienes and PV
counters.
40 + 12 = 52
Draw pictures and representations to
show how to double numbers
Partition a number and then double
each part before recombining it back
together.
+ = 32
Counting in multi-
ples of 2, 3, 4, 5, 10
from 0
(repeated addition)
Count the groups as children are skip
counting, children may use their fin-
gers as they are skip counting. Use bar
models.
5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 40
Number lines, counting sticks and bar
models should be used to show repre-
sentation of counting in multiples.
Count in multiples of a number aloud.
Write sequences with multiples of
numbers.
0, 2, 4, 6, 8, 10
0, 3, 6, 9, 12, 15
0, 5, 10, 15, 20, 25 , 30
16. Pennard Primary School Calculation Policy
Objective &
Strategy
Concrete Pictorial Abstract
Multiplication is
commutative
Create arrays using counters and cu-
bes and
Numicon.
Pupils should understand that an array can
represent different equations and that, as
multiplication is commutative, the order of
the multiplication does not affect the answer.
Use representations of arrays to show different
calculations and explore commutativity.
12 = 3 × 4
12 = 4 × 3
Using the Inverse 2 x 4 = 8
This should be 4 x 2 = 8
taught alongside 8 ÷ 2 = 4
division, so pupils 8 ÷ 4 = 2
learn how they 8 = 2 x 4
work alongside
each other.
8 = 4 x 2
2 = 8 ÷ 4
4 = 8÷ 2
Show all 8 related fact family sentences.
17. Pennard Primary School Calculation Policy
Objective &
Strategy
Concrete Pictorial Abstract
Grid method Show the links with arrays to first intro-
duce the grid method.
Move onto base ten to move towards a
more compact method.
Move on to place value counters to show
how we are finding groups of a number. We
are multiplying by 4 so we need 4 rows
Fill each row with 126
Add up each column, starting with the ones
making any exchanges needed
Then you have your answer.
Children can represent their work with place
value counters in a way that they understand.
They can draw the counters using colours to
show different amounts or just use the circles in
the different columns to show their thinking as
shown below.
Bar model are used to explore missing numbers
Start with multiplying by one digit num-
bers and showing the clear addition
alongside the grid.
Moving forward, multiply by a 2 digit number
showing the different rows within the grid
method.
18. Pennard Primary School Calculation Policy
lumn, starting with theon
Objective & Strategy Concrete Pictorial Abstract
Grid method recap
from year 3 for 2
digits x 1 digit
Move to multiplying
3 digit numbers by
1 digit. (year 4 ex-
pectation)
Use place value counters to show how we
are finding groups of a number. We are mul-
tiplying by 4 so we need 4 rows
Fill each row with 126
Add up each co es
making any exchanges needed
Children can represent their work with place
value counters in a way that they understand.
They can draw the counters using colours to
show different amounts or just use the circles in
the different columns to show their thinking as
shown below.
Start with multiplying by one digit num-
bers and showing the clear addition
alongside the grid.
Column multiplication Children can continue to be supported by
place value counters at the stage of multipli-
cation. This initially done where there is no
regrouping. 321 x 2 = 642
It is im-
portant at
this stage
that they
always
multiply
the ones
first.
The corresponding long multiplication is mod-
elled alongside
The grid method my be used to show how this
relates to a formal written method.
Bar modelling and number lines can support
learners when solving problems with multiplica-
tion alongside the formal written methods.
327
x 4
28
80
1200
1308
This may lead
to a compact
method.
19. Pennard Primary School Calculation Policy
Objective &
Strategy
Concrete Pictorial Abstract
Column Multiplication for
3 and 4 digits x 1 digit.
It is im-
portant at
this stage
that they
always
multiply
the ones
first.
Children can continue to be supported by
place value counters at the stage of multipli-
cation. This initially done where there is no
regrouping. 321 x 2 = 642
327
x 4
28
80
1200
1308
This will lead to
a compact
method.
Column multiplication Manipulatives may still be used with the cor-
responding long multiplication modelled
alongside.
Continue to use bar modelling to support prob-
lem solving
18 x 3 on the
first row
(8 x 3 =24, carry-
ing the 2 for 20,
then 1 x 3)
18 x 10 on the
2nd row. Show
multiplying
by 10 by
putting
zero in
units first
20. Pennard Primary School Calculation Policy
Objective &
Strategy
Concrete Pictorial Abstract
Multiplying decimals
up to 2 decimal plac-
es by a single digit.
Remind children that the single digit belongs
in the units column. Line up the decimal
points in the question and the answer.
21. Pennard Primary School Calculation Policy
Objective &
Strategy
Concrete Pictorial Abstract
Division as sharing
Use Gordon ITPs for
modelling
I have 10 cubes, can you share them equally in
2 groups?
Children use pictures or shapes to share quanti-
ties.
8 shared between 2 is 4
12 shared between 3 is
4
22. Pennard Primary School Calculation Policy
Objective &
Strategy
Concrete Pictorial Abstract
Division as sharing
I have 10 cubes, can you share them equally in
2 groups?
Children use pictures or shapes to share quanti-
ties.
Children use bar modelling to show and support
understanding.
12 ÷ 4 = 3
12 ÷ 3 = 4
Division as grouping Divide quantities into equal groups.
Use cubes, counters, objects or place value
counters to aid understanding.
Use number lines for grouping
Think of the bar as a whole. Split it into the num-
ber of groups you are dividing by and work out
how many would be within each group.
28 ÷ 7 = 4
Divide 28 into 7 groups. How many are in
each group?
23. Pennard Primary School Calculation Policy
Objective &
Strategy
Concrete Pictorial Abstract
Division as grouping Use cubes, counters, objects or place value
counters to aid understanding.
24 divided into groups of 6 = 4
Continue to use bar modelling to aid solving
division problems.
How many groups of 6 in
24?
24 ÷ 6 = 4
Division with arrays
Link division to multiplication by creating an
array and thinking about the number sentenc-
es that can be created.
Eg 15 ÷ 3 = 5 5 x 3 = 15
15 ÷ 5 = 3 3 x 5 = 15
Draw an array and use lines to split the array
into groups to make multiplication and division
sentences
Find the inverse of multiplication and division
sentences by creating eight linking number
sentences.
7 x 4 = 28
4 x 7 = 28
28 ÷ 7 = 4
28 ÷ 4 = 7
28 = 7 x 4
28 = 4 x 7
4 = 28 ÷ 7
7 = 28 ÷ 4
24. Pennard Primary School Calculation Policy
Objective &
Strategy
Concrete Pictorial Abstract
Division with remain-
ders.
14 ÷ 3 =
Divide objects between groups and
see how much is left over
Jump forward in equal jumps on a number line
then see how many more you need to jump to
find a remainder.
Draw dots and group them to divide an amount
and clearly show a remainder.
Use bar models to show division with remain-
ders.
Complete written divisions and show the re-
mainder using r.
25. Pennard Primary School Calculation Policy
Objective &
Strategy
Concrete Pictorial Abstract
Divide at least 3 digit
numbers by 1 digit.
Short Division
96 ÷ 3
Use place value counters to divide using the
bus stop method alongside
42 ÷ 3=
Start with the biggest place value, we are
sharing 40 into three groups. We can put 1
ten in each group and we have 1 ten left over.
We exchange this ten for ten ones and then
share the ones equally among the groups.
We look how much in 1 group so the answer
is 14.
Students can continue to use drawn diagrams
with dots or circles to help them divide numbers
into equal groups.
Encourage them to move towards counting in
multiples to divide more efficiently.
Begin with divisions that divide equally with
no remainder.
Move onto divisions with a remainder.
Finally move into decimal places to divide the
total accurately.