Grade 1 program - Kennedy PressBack-to-Front Maths … · Web viewThis program has been created for use by a single teacher with students working from grade 1 ... not summative

Grade 1 program

ContentsGrade 1 program............................................................................................................................................................................................................................................................. 2

Regular consolidation and practice activities:......................................................................................................................................................................................................... 2

Assessment strategy:............................................................................................................................................................................................................................................... 2

Term 1:........................................................................................................................................................................................................................................................................ 4

Term 2:........................................................................................................................................................................................................................................................................ 8

Term 3:...................................................................................................................................................................................................................................................................... 12

Term 4:...................................................................................................................................................................................................................................................................... 16

© Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au

http://www.backtofrontmaths.com.au/

Grade 1 programThis program has been created for use by a single teacher with students working from grade 1 in a single class. It is designed to maximise the effectiveness of teaching and make use of the connections between related concepts. In addition to the focus concepts included within this program it is expected that certain concepts will be covered regularly in the course of normal teaching. These concepts are listed below.

Regular consolidation and practice activities:Play number sense games, match representations, make and partition numbers, create arrays and fill in blank number charts. Also organise shapes into groups, play shops and look regularly at times on the clock, the class timetable and calendar, and talk about directions to known locations. Make halves and quarters of various 2D shapes, 3D objects, lengths and groups and play chance and data sorting games. Use non-standard measurements and order lengths, volumes, masses and areas and talk about “how big” attributes are.

Assessment strategy:Throughout the year you should assess on numerous occasions. Please find below a suggested schedule for your assessment tasks from Back-to-Front Maths. Remember that you will need to include your own assessment for Fluency, and also for mental mathematics. A content test would be an appropriate assessment for these.

Semester 1: Early in semester 1 complete the first moderation task and the diagnostic tasks. This will give you baseline measurements for students’ proficiencies in problem-solving,

reasoning and understanding. It will also help explain the standards to you in a more meaningful manner. This should be formative only, not summative. During semester 1 try to examine 3-5 students per lesson during Journal problems in order to gauge their improvements. These should be formative only. Towards the end of semester 1, mark the last 3-4 Journal problems for each student using the tick-and-flick box. Use these observations to mark the criteria sheet in this

document. In your content test you will also need to include some application questions for students who are in the C/D/E category, which may be selected from those suggested in the lesson plans.

Towards the end of semester 1 complete the second moderation task. Final grade for reporting: Compare the results from your criteria sheet and the second moderation tasks to check that they align. If there is a discrepancy, then you will

need to use your judgement to grade the student appropriately. Be aware that the moderation tasks only exist to help illustrate the criteria. You may find that you have been marking too easily or too hard, so adjust your marking accordingly.

Semester 2: Consider using an investigation throughout the semester and using this as an additional assessment piece. If using these, never use the first investigation as a summative

piece as both students and teachers need time to get used to the requirements. Continue marking 5 students per lesson on Journal problems as formative tasks. Towards the end of semester 1, mark the last 3-4 Journal problems for each student using the tick-and-flick box. Use these marks in combination with the Blasts book to

mark the criteria sheet. You will also need to include some application questions for students who are in the C/D/E category, which may be selected from those suggested in the lesson plans.

Towards the end of semester 2 complete the third moderation task.



Final grade for reporting: Compare the results from your investigations, criteria sheets and the third moderation tasks to check that they align. If there is a discrepancy, then you will need to use your judgement to grade the student appropriately.



Term 1:

Focus concepts: Number names and concepts (to 20), counting, ordering, addition and subtraction including partitioning, (to 20) joining and separating (to 20), 2D and 3D shapes

Australian Curriculum statements These need to be achieved by the end of the year, not completed this term. In this term we will be focusing heavily on numbers to 20 so that next term we can focus on two digit numbers.

ACMNA012 - Develop confidence with number sequences to and from 100 (we are only going to 20 this term) by ones from any starting point. Skip count by twos, fives and tens starting from zeroACMNA013 - Recognise, model, read, write and order numbers to at least 100 (we are only going to 20 this term). Locate these numbers on a number lineACMNA014 - Count collections to 100 (we are only going to 20 this term) by partitioning numbers using place valueACMNA015 - Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging partsACMMG022 - Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious features

This is what your term focus looks like:Week 1 – Diagnostic testingWeeks 2-3 – Building numbers to 10 in lots of different ways. Building numbers to 20 if appropriate.Week 4 – Relative size of numbers to 10 with number linesWeeks 5 – Counting in twos and fives to 20Weeks 6-9 – Partitioning of single digit and teen numbers leading to formal addition and subtractionWeek 10 – 2D shapes



Teaching Sequence:Week 1: Diagnostic testingNumber conservation and partitioning – these build in complexity, so stop when a child gets stuck

1. Count six different coloured counters. Arrange into a line and ask the student to count. Next, ask students to start counting from the second counter and see if they think the number of objects changes. Watch for students to get all counters and count correctly. Drop number of counters to 4 if needed for this test and the following ones.

2. Move the counters in plain sight by picking up the counter at one end of the line and moving to the other end then ask the students how many there are now. Watch to see if they need to recount them. Mess them up. Ask how many now. Watch to see if they need to recount. Ask if the number could have changed or if it would always be six.

3. Arrange six counters into a circle and ask the students to count them. Check to see that they get them all once only.4. Count six objects into an opaque cup. Shake the cup. Ask students to show you how many counters would be in the cup after shaking it. Repeat three times. Get them

to show you with their fingers, with their eyes closed.5. Ask kids to show you 5 fingers. Then ask them to make 5 fingers with some fingers on each hand. For students who can, pair up and make 5 with their partner’s fingers

as well (2, 3 and 4 hands).6. Give 8 unifix cubes to each student. Ask the students to draw the 8 cubes. Then ask the students to break the 8 into two parts and draw these. Ask the students to find

as many different ways as possible to break the 8 into two parts and draw these.7. Start with 8 cubes on the ground. Move your hands over them and grab some without the kids being able to see how many you grabbed. Ask the kids to work out how

many you have.

Weeks 2 and 3: Consolidate numbers to 10, and build numbers to 20 if appropriateTargeted teaching:Consolidate numbers to 10, and build numbers to 20 if appropriate.

Make sure that kids understand: How to make a quantity (e.g. Please get me 6 blocks) Numbers don’t change when they move (e.g. 6 in a

circle is still 6) Colours don’t change numbers (watch for kids who

want to get counters or blocks of all the same colour)

Resources:

Back to Front Maths: JP.1 Counting in ones to 5 JP.2 Number names

Possibly: JP6 Teen numbers (if appropriate)

Other:

Regular tasks or indirect learning:

Homework suggestions:



Week 4: Number lines and ordering to 10Targeted teaching:Relative size of numbers to 10 (e.g. How big is 7 on a number line from 1-10)

Make sure that kids understand: There is space between numbers (they aren’t all

squashed up) Numbers are spaced out based on how big they are

rather than on making all the spaces equal irrespective of size (e.g. on a number line from 1-10, if we just put the numbers 2 and 8 on they shouldn’t be equally spaced – 8 is further from 10 than 2 is from 1, and there should be a pretty big space in the middle)

Resources:

Back to Front Maths: JP.3 Number lines to 10

Other:



Week 5: Counting and counting patternsTargeted teaching:Count in 1s, 2s and 5s. Consolidate counting and counting patterns

Make sure that kids understand: Counting does not always need to start at 1 Counting can go forwards or backwards Counting is about the QUANTITY, not about saying

numbers in order

Resources:

Back to Front Maths: JP.4 Counting in 2s and 5s

Other:





Weeks 6-9: Addition and Subtraction as partitioning to 20Targeted teaching:Partitioning of single digit and teen numbers.Focus on getting lots of different combinations to make a number first before using formal recording of the addition and subtraction sign.Follow up with lots and lots of practice partitioning of numbers to 20. Partitioning is one of the most important concepts to understand in early primary.

Make sure that kids understand: Doubles do not make all numbers (e.g. just because

3 and 3 makes 6, 4 and 4 doesn’t also make 6) Tens facts do not make all numbers Focus on gap questions (e.g. if I start with 6 objects

on the floor and pick up some so that there are 2 left, how many did I pick up?)

Make numbers to 10 in different ways with your fingers (e.g. 5 can be made with 2 fingers on one hand and 3 on the other)

Resources:

Back to Front Maths: JP 9 (joining), JP 10 (partitioning) JP.11 (separating) JP.12 Tens facts

Don’t use problem 12 until partitioning of lots of numbers has been completed and is solid

Other:



Week 10: 2D shapesTargeted teaching:Naming and properties of 2D shapes.

Make sure that kids understand: Triangles do not have to have the point facing up.

Squares can still be squares when they are on funny angles.

Triangles, hexagons, etc do not have to be regular – they can have different length sides and still be triangles

Resources:

Back to Front Maths: JP 31 – 2D shapes

Other:





Term 2: Focus concepts: Counting patterns, Money, Fractions, Multiplication and Division including arrays and sharing, Time, Length and Volume

Australian Curriculum statements (to achieve by the end of the year)

Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zeroRecognise, describe and order Australian coins according to their valueRecognise and describe one-half as one of two equal parts of a whole. Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zeroMeasure and compare the lengths and capacities of pairs of objects using uniform informal unitsACMMG020 Tell time to the half-hourACMMG021 Describe duration using months, weeks, days and hours

This is what your term focus looks like:Weeks 1 – Fractions – One HalfWeeks 2-3 – Money - note, coins and spendingWeek 4-5 – Time – clocks and calendarsWeeks 6-7 - Measurement: length and volumeWeeks 8-10 – Operations - multiplication and division


ACMNA012ACMNA017ACMNA016ACMNA012ACMMG019


Teaching Sequence:

Week 1: Fractions - HalvesTargeted teaching:One half

Make sure that kids understand: You can’t have a big half and a small half A half refers to the size of the portion rather than

what it looks like. The two halves may look different even though they are equal in size.

Halves do not need to be symmetrical

Resources:

Note: If your kids are having trouble with numbers to 20, consider skipping this concept altogether as they can pick it up easily in later grades.

Back to Front Maths:JP.8: Simple fractions

Other:



Weeks 2-3: Money and purchasingTargeted teaching:Recognising coins, purchasing small amounts of money, making money in different ways

Make sure that kids understand: An amount of money can be made in different ways

using collections of coins. One coin can be used to be the same amount as several other coins (e.g. 10 lots of 10c coins is the same amount as $1, not more)

Having lots of coins doesn’t mean that there is lots of money – it depends on the value of the coin

Resources:

Back to Front Maths:Problem 17: MoneyProblem 18: Purchase

Other:





Weeks 4-5: TimeTargeted teaching:Hours, half hours, time between events (elapsed time – how long does something take), calendars and days of the week

Make sure that kids understand: One minute is always exactly the same length You can tell the time just using the hour hand (see the

link in the resources column) The time of the day is not dependent on what you are

doing – just because you have a sleep during the day doesn’t mean that it is morning when you wake up

Morning, afternoon and night time are set – they don’t change

Resources:

Read this article on how to teach analogue time first:

http://www.backtofrontmaths.com.au/recent-news-articles/timely-thoughts-on-analogue-time

Back to Front Maths:

Adjust these to use only what you need – you might not need as much if you are looking at clocks and calendars regularly in class

Problem 25: TimetablesProblem 26: Elapsed time

Other:



Weeks 6-7: Measurement: length and volumeTargeted teaching:Using non-standard units for lengthComparing large and small volumes and capacities

Make sure that kids understand: Use the same unit of measurement when comparing

objects (e.g. the same sized block) You have to fit in as many units as possible when

measuring, ensuring that there are no gaps or overlaps. Parts of units are used where a whole unit cannot fit. We

use fractional language to describe these parts.

Resources:

Back to Front Maths:JP.22 - LengthJP.23 - Volume

Other:








Weeks 8-10: Multiplication and division

Investigation idea:Give each student 12 counters to arrange into as many different arrays as possible. Draw the arrays.

Targeted teaching:Lining up objects into arrays to represent multiplication in a 2D structure (e.g. 2 rows of 3 rather than 2 groups of 3) and the links to division and sharing

Make sure that kids understand: Multiplying means “lots of”, “groups of”, “rows of” or

“columns of” Division means “how many” (groups, lots, rows or

columns)

Resources:

Back to Front Maths:JP.15 ArraysJP.16 Sharing

Other:





Term 3: Focus concepts: Two digit numbers, formal operations, chance and data, position and direction

Australian Curriculum statements (to achieve by the end of the year)ACMNA012 Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zeroACMNA013 Recognise, model, read, write and order numbers to at least 100.ACMNA015 Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging partsACMNA016 Recognise and describe one-half as one of two equal parts of a whole.ACMSP024 Identify outcomes of familiar events involving chance and describe them using everyday language such as ‘will happen’, ‘won’t happen’ or ‘might happen’ACMSP262 Choose simple questions and gather responsesACMSP263 Represent data with objects and drawings where one object or drawing represents one data value. Describe the displaysACMMG023 Give and follow directions to familiar locations

This is what your term focus looks like:Weeks 1-3 – Two digit numbersWeek 4 – Calendars and days of the weekWeeks 5-6 – Formal operations and inverse operationsWeeks 7-8 – Chance and DataWeeks 9-10 – Position and Direction



Teaching Sequence: Weeks 1-3: Two digit numbersTargeted teaching:Build numbers to 100

Make sure that kids understand: Numbers can be broken into other smaller numbers

(partitioned). A collection of objects can be organised into groups so

that it is easier to tell how many there are (e.g. tens and ones).

One ten and ten ones are the same amount (e.g. if you cut a “ten” MAB up into the ones cube, there would really be 10 of them)

Resources:

Read this article before you start introducing two-digit numbers so that kids understand why we bundle in tens:

http://www.backtofrontmaths.com.au/recent-news-articles/introducing-two-digit-numbers

Back to Front Maths:JP.7 Two digit number namesJP.5 Numbers to 100

Other:



Week 4: Calendars and days of the weekTargeted teaching:Understand how days are put together to form weeks, months and the year. Understand that seasons are made up of different months.

Make sure that kids understand: Every week has the same number of days in it Every week has a consistent order of days in it Months can have different numbers of days and weeks Seasons last for 3 months. Know the four seasons, what

they mean in terms of weather and when they happen.

Resources:

Back to Front Maths:Problem 27: Calendars

Other:








Weeks 5-6: Formal operations and inverse operationsTargeted teaching:The relationship between addition and subtraction.Formal use of written operations for addition and subtraction.

Make sure that kids understand: Numbers have a constant value in operations and do not

require a link to real world objects (e.g. 3 + 4 will always give you 7 and the numbers can be rearranged or counted in different ways but still give you 7).

Facts can be related (e.g. 3 + 3 = 6 so 3 + 4 would equal 7). The inverse relationship between addition and subtraction

can help solve problems and calculate answers. Partitioning numbers helps with difficult calculations (e.g. 6

+ 5 is the same as 6 + 4 +1 or 10 + 1).

Resources:

Back to Front Maths:JP 13 Related factsJP 14 Addition and Subtraction

Other:



Weeks 7-8: Chance and DataTargeted teaching:Some events are more likely than others and can be described using everyday language such as ‘will happen’, ‘won’t happen’ or ‘might happen’.Information can be gathered, counted and grouped. We can use that information to answer questions.

Make sure that kids understand: All events have some kind of likelihood but very few things

are absolutely certain. Some things are more likely than others. Having two options doesn’t make them both the same

(e.g. It could rain or not rain, but that doesn’t make them both 50/50 – the chance of rain depends on the season)

Data can be collected or found for the purpose of answering questions

Data needs to be classified or organised in a way that best fits the question to be answered.

Data can be organised in different ways for different purposes.

Resources:

Back to Front Maths:JP.28 ChanceJP.29 Grouping DataJP.30 Using Data if time

Other:





Weeks 9-10: Position and DirectionInvestigation ideas:Create a map of the school or part of the school (such as the playground). Give directions to different locations as a “treasure hunt”.

Targeted teaching:Give and follow directions to familiar locations. Represent locations visually.

Make sure that kids understand: Directions are described using position (forwards,

backwards, left, right) and distance (how many steps, describing an object in the distance)

Resources:

Back to Front Maths:Problem 35: PositionProblem 36: Directions

Other:





Term 4: Focus concepts: 3D objects, Symmetry and Transformations, Mass, Patterns and Functions

Australian Curriculum statements (to achieve by the end of the year)ACMNA018 Investigate and describe number patterns formed by skip counting and patterns with objectsACMMG022 Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious features

This is what your term focus looks like:Weeks 1-3 – 3D objects, symmetry and transformationsWeek 4 – MassWeeks 5-8 – Patterns and functionsWeeks 9-10 – Catching up and preparing for next year



Teaching Sequence:

Weeks 1-3: 3D objects, symmetry and transformations of 2D shapes

Investigation idea:Create mosaics from tiling shapes. Preferably have the students attempt to replicate the shapes for tiling, and talk about flipping, sliding and turning as you complete the task.

Targeted teaching:Names and properties of 3D objects.Symmetry is about reflection across a line or on a rotation.2D shapes can be transformed using flips, slides and turns.

Make sure that kids understand: 3D objects are not called “squares” or “triangles” – they might

have square or triangular faces but have names reflecting their 3D nature (e.g. cube, pyramid)

2D shapes can be transformed with flips (reflections), slides (translations) and turns (rotations).

2D shapes can be symmetrical or not. Symmetry is created by reflections.

Resources:

Back to Front Maths:Problem 32: 3D objectsProblem 33: Flip, slide, turnProblem 34: Symmetry

Other:



Week 4: MassTargeted teaching:Hefting an object in each hand can be used to compare the mass of two objects.

Make sure that kids understand: Mass is about how heavy something is, not how much space it

takes up. Sometimes small objects can be very heavy – it depends on

what they are made from. The same amount of mass can be differently shaped and take

up significantly different amounts of space (e.g. a kg of metal vs a kg of feathers)

Resources:

Back to Front Maths:JP 24: Mass

Other:





Weeks 5-8: Patterns and functions

Investigation ideas:

Play games using repeating patterns and sequences, such as where one action provokes a repetition (e.g. when the leader claps two times all the followers clap two times) or provokes a different action (e.g. when the leader claps two times everyone has to jump in the air).

Create beading patterns using different shapes and patterns of beads.Play “what is missing”: The teacher creates a repeating or growing pattern using coloured counters. The students cover their eyes and the teacher removes part of the pattern (can be a whole repeating segment, or the end of one and start of another for added complexity). The students have to make what is missing.

Targeted teaching:Help kids to notice similarities and differences in the way objects or numbers are arranged. Identify and describe patterns and what happens to create, continue or change them.

Make sure that kids understand: Patterns can be comprised of colour, shape, size, actions and

numbers. How the pattern begins and how to get from one position in

the pattern to the next (identify the pattern – whether it repeats or grows, and what is similar each time) is really important.

Differences between items within a pattern and between patterns are also important.

We can make generalisations about the rule that is used to make the pattern. In order to be a rule, it should be true for every step in the pattern.

We can test a rule against subsequent steps in the pattern to check if it is right.

Resources:

Back to Front Maths:JP.19 Repeating patternsJP.20 Growing patternsJP.21 Function

Other:



Weeks 9-10: Catch up and preparation for next year



Documents

Grade 1 program - Kennedy PressBack-to-Front Maths … · Web viewThis program has been created for use by a single teacher with students working from grade 1 ... not summative