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# Planning Sheet

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```									                                                               Five daily lessons
Unit 8
Properties of numbers and reasoning about numbers

Year 4                                                                                                           This unit plan is designed to
Spring term                                                                                                      guide your teaching.
Unit Objectives
Year 4                                                                            You will need to adapt it to
meet the needs of your class.
 Recognise negative numbers in context (e.g. on a number line, on a              Page 14
temperature scale).
 Recognise and extend number sequences formed by counting from any               Page 16
number in steps of constant size, extending beyond zero when counting                                    Resources needed to teach this unit:
back.
 Make and investigate a general statement about familiar numbers by finding                                  Resource sheet 8.1
examples that satisfy it.                                                                                   Resource sheet 8.2
 Explain methods and reasoning about numbers orally and in writing.              Page 76                     Resource sheet 8.3
   Resource sheet 8.4
   Resource sheet 8.5
Link Objectives                                                                      Resource sheet 8.6
   Resource sheet 8.7
Year 3                                        Year 5                                                 Activity sheet 8.1
    Order whole numbers to at least 1000          Order a given set of positive and negative                 OHT 8.1
and position them on a number line.            integers (e.g. on a number line, on a temperature          OHT 8.2
    Describe and extend number                     scale).                                                    Large number cards, -5 to 5
sequences: count on or back in tens           Recognise and extend number sequences formed               Whiteboards
or hundreds starting from any two- or          by counting from any number in steps of constant           Number fans
three-digit number.                            size, extending beyond zero when counting back.            Counting stick
    Investigate a general statement about          For example: count in steps of 25 to 1000, and then        Thermometer Interactive Teaching
familiar numbers by finding examples           back; count on or back in steps of 0.1, 0.2, 0.3…           Program downloadable from website
that satisfy it.                              Make and investigate a general statement about              (www.standards.dfes.gov.uk)
    Explain methods and reasoning orally           familiar numbers by finding examples that satisfy it.      OHP calculator
and, where appropriate, in writing.           Explain a generalised relationship (formula) in            Class set of calculators
words.                                                     Thermometers
   Explain methods and reasoning.

(Key objectives in bold)
NNS Unit Plans
Planning      Day One                                       Unit 8 Properties of numbers and reasoning                                      Term: Spring                    Year Group: 4
sheet                                                       about numbers
Oral and Mental                                             Main Teaching                                                                                                   Plenary
Objectives and        Teaching Activities                   Objectives and            Teaching Activities                                                                   Teaching Activities/Focus Questions
Vocabulary                                                  Vocabulary
Read and write            Display Resource sheets 8.1      Recognise negative                                                                                                  Discuss the activity and check the answers.
whole numbers up           to 8.5 in the following way:     numbers in context e.g.   Q Where would you see/use negative numbers?
to 10 000 presented                                                                                                                                                             Using the interactive thermometer, ask children
8.3
in words and digits.         8.1                            on a number line           Introduce negative numbers through the context of temperature. Compare                   to look at the third thermometer on Activity
8.2         8.5          on a temperature scale.     temperatures of different resources, central heating, a fridge, a freezer.               sheet 8.1. Ask questions such as the following
8.4
Compare climates and discuss times of year when temperature was below                    for them to answer orally, demonstrate their
zero. Look at a room and other thermometers together, pointing out the                   responses with the interactive thermometer.
Say a number and point to                                    negative values.
the words on the display:                                                                                                                         Q What will the temperature be if it rises by 3oC?
 Draw a vertical number line on the board with zero marked in the middle
e.g. ‘Three hundred and fifty-                               and 5 divisions above, 5 divisions below. Ask children to count on from              Q What will it be if it drops by 2oC?
six’; ‘Six thousand, nine                                    zero as you point to the appropriate divisions above it on the line, then back
hundred and one’.                                            to zero. Point to the –1 position.                                                   Q What temperature is 3 degrees below zero or
freezing point?
Ask children to write the                                  Q What does this mark represent?
numbers in digits on their                                                                                                                        Q What temperature is 2 degrees above
whiteboards.                                                  Establish it is a negative one and repeat for the other negative values.              negative 6 degrees?
Explain that numbers above zero are positive numbers, numbers below
Write a number in digits on                                   zero are negative numbers. Give examples of above and below freezing.
the board, ask children to                                    Write all the numbers (-5 to 5) alongside the line. Ask the class to count
say the number and a                                          back from 5 to –5, then up to 5.
volunteer to point to the
By the end of the lesson the children should
words on the display. Write                                 Draw a horizontal line:                                                              be able to:
a number in digits and ask
children to write the number
in words on their                                                                                                                                      Order a set of positive and negative
whiteboards.                                                                                                                        5                   numbers;
-5
     Locate positive and negative numbers
on a number line;
Q Which whole numbers lie between –5 and 5?                                                 Use negative numbers in the context of
temperature.
In response to each suggestion, point along the line, asking children to tell
you when to stop.                                                                   (Refer to supplement of examples, section 6,
VOCABULARY
negative                                                                                                         page 14.)
positive                   Extend the line to –6 and 6. Ask the class to count back from 6 to the other
above and below zero        end of the line. Hand out cards –5 to 0 inclusive. Ask the children to come
out and position themselves in order. Repeat with cards, from –5 to 5 using
different children to order themselves.

RESOURCES                  Give out Activity sheet 8.1. Ask children to complete the number lines.
RESOURCES                                                   Thermometers                Collect answers.
Resource sheet 8.1                                          Activity sheet 8.1
Resource sheet 8.2                                          Large number cards –5        Discuss the four thermometers. Explain that each thermometer tells the
Resource sheet 8.3                                          to 5                         temperatures in degrees Celsius and 0oC is freezing point.
Resource sheet 8.4                                          Thermometer
Resource sheet 8.5                                          Interactive Teaching         Ask children to fill in the missing temperatures.
Whiteboards                                                 Program

NNS Unit Plans
Planning                       Day Two                        Unit 8 Properties of numbers and reasoning                                            Term: Spring                              Year Group: 4
sheet                                                         about numbers
Oral and Mental                                               Main Teaching                                                                                                                   Plenary
Objectives and        Teaching Activities                     Objectives and               Teaching Activities                                                                                Teaching Activities/Focus
Vocabulary                                                    Vocabulary                                                                                                                      Questions
Recognise negative          Use a counting stick held        Make and investigate a         Draw a 3 x 3 grid on the board and              Model how to start the process of                 Look again at the first grid.
numbers in context.          vertically to revise counting    general statement about         write in the numbers 1 to 9 as shown:           investigation using a different set of
between positive and             familiar numbers by                                                             numbers, e.g. 6–14.                                Ask the children in pairs to discuss
negative numbers.                finding examples that                                                                                                              the following:
satisfy it.                             1        2       3                      Ask children to investigate this
     Use program ‘Thermometer’                                                                                        statement using Resource sheet 8.6.              Q Are any of the statements made
or display OHT 8.1. Discuss                                                                                                                                         true for all sets of numbers?
the scale on the thermometer,                                            4        5       6                     When children have investigated the
identify zero and the value of                                                                                   statement and satisfied themselves                 Remind the children of the initial
the intervals on the scale.                                                                                      that this is a general statement, ask:             general statement.
Point to a value and ask                                                 7        8       9
children to write it on their                                                                                    ’Using the numbers 1, 1, 1, 2, 2, 2, 3,           After a few minutes, choose pairs of
whiteboards to show. Repeat                                                                                      3, 3, can you fill in a grid where all the         children to share their ideas with the
for different values.                                                                                            rows, columns and diagonals total the              class.
Point out that 1-9 are consecutive
same?’
numbers and show how they are
Q What will this temperature                                       arranged in the grid in order.
be after a rise of 3 degrees,                                                                                    Ask the children to investigate this
a fall of 4 degrees?                                                                                             statement using Resource sheet 8.6.              By the end of the lesson the
Ask children to total the middle row
and the middle column, then each                                                                 children should be able to:
Demonstrate using the                                                                                            After the children have had a few tries           Investigate a given statement by
diagonal.
thermometer to confirm the                                                                                       ask the following questions.                       finding and testing examples;
children’s answers.                                            Q What do you notice?                                                                               Understand the term ‘general
Q Will it work with 2 in the middle? 3               statement’.
in the middle?
Discuss and agree a statement and
record it on the board, e.g.                                                                     (Refer to supplement of examples,
Q Where do the even numbers need                   section 6, page 80.)
In this grid the middle row, the middle         to be?
column and each diagonal have a
total of 15.                                    When the majority of the class are
convinced it can’t be done, ask:
Q What other statements could you
make?                                         Q Can you explain why?
VOCABULARY
positive                                                                                      e.g. All the corner numbers are odd
negative                                                                                      etc…
above/below zero
minus                                                                                        Tell the children you are going to give
VOCABULARY                      them a general statement to
total                           investigate.
next, consecutive
RESOURCES                                                     general statement              Write on the board:
OHT 8.1
Thermometer                                                                                   ’When nine consecutive numbers are
Interactive Teaching                                                                          arranged in order in a 3 x 3 grid, the
Program                                                       RESOURCES                       middle row and column have the
Counting stick                                                Resource sheet 8.6              same total as each diagonal’.

NNS Unit Plans
Planning                     Day Three                            Unit 8 Properties of numbers and reasoning Term: Spring                                                                     Year Group: 4
sheet                                                             about numbers
Oral and Mental                                                   Main Teaching                                                                                                               Plenary
Objectives and      Teaching Activities                           Objectives and          Teaching Activities                                                                                 Teaching Activities/Focus
Vocabulary                                                        Vocabulary                                                                                                                  Questions
Read and write            Return to the display of Resource      Make and                  Write 1 + 2 + 3 on the board.                                                                      Discuss children’s findings
numbers up to              sheets 8.1 to 8.5. Point to a          investigate a                                                                                                                  and agree statements for
10 000.                    number and ask children to read        general statement        Q What sort of numbers are these?                                                                     each case.
the number aloud as you point.         about familiar
Round three-digit          Ask children to write the number in    numbers by finding         Ask children to find the total. Record it then write:                                             Q Can you think of a
numbers to the             digit form on the board.               examples that                                                                                                                  statement for the sum of
nearest 10 or 100.                                                satisfy it.                2+3+4=                                                                                              any odd number of
Q What is 1000 more/100 less than                                   3+4+5=                                                                                              consecutive numbers?
this?                                                             4+5+6=
5+6+7=                                                                                              Discuss, allowing time for
Q What do you get when you add                                                                                                                                          children to collectively
200/subtract 1000/take away 50                                    Ask children to describe the list, copy the list and, record each total. Ask children to            formulate the wording for the
from this number?                                                 continue the pattern of calculations by three lines or more.                                        statement, with your help if
necessary.
Ask children to say the answers                                  Ask them to look at the totals.
aloud and to point to the numbers                                                                                                                                   Q What numbers could we
on the display as they do so.                                   Q Is there a pattern in the totals? Can you describe it?                                              use to test the statement?

     Remind children about the rules for                             Q How might you explain it to someone?                                                                Collect answers and check
rounding to the nearest 10, then                                                                                                                                      the children’s calculations.
the nearest 100.                                                  Establish that the totals are consecutive multiples of 3, starting at 6.

     Write on the board a three-digit                                 Agree the general statement: ‘The sum of any three consecutive numbers is a multiple of           By the end of the lesson the
multiple of 10, e.g. 370. Ask                                     3’ and write it on the board.                                                                     children should be able to:
children to suggest numbers that                                                                                                                                     Find examples that match
when rounded to the nearest 10                                    Ask the children to find further examples to satisfy the statement. Encourage them to try           a general statement;
would give that number. Record                                    larger numbers.                                                                                    Make and explain a
them on the board.                                                                                                                                                    general statement.
     Discus results, ask for some examples and establish that the general statement appears to
Repeat for a three-digit multiple of                              be true.                                                                                          (Refer to supplement of
100, asking children to give                                                                                                                                        examples, section 6, page
numbers that would make that                                    Q Is it true for every set of three consecutive numbers? Can we see any relationships?              80.)
number when rounded to the
nearest 100.                                                    Q Is there a relationship between the totals and the numbers in each set?
     Provide other numbers for children                               Encourage children to offer reasons and explanations. Look at the adding of 1 to each
to use number fans to show                                        number to get the next three consecutive numbers and the property that the sum of three
numbers that would round to them.                                 consecutive numbers is 3 x the middle number.
VOCABULARY
nearest ten
Q How many possible numbers are                                   Q Can you use the rule to work out the sum of 29 + 30 + 31 without adding them together?
nearest hundred
there that would round to 460?
round up
round down                                                                                   Ask children to add groups of five consecutive numbers 1 + 2 + 3 + 4 + 5, 2 + 3 + 4 + 5 + 6
Q What about 300?                        VOCABULARY                 etc. and look for any patterns. Encourage them to make a general statement and test it by
consecutive                using other examples, e.g. 101 + 102 + 103 + 104 + 105.
Collect answers and discuss            multiple
RESOURCES                  strategies.                            example
Number fans                                                       pattern

NNS Unit Plans
Planning                      Day Four                   Unit 8 Properties of numbers and reasoning about                                             Term: Spring                              Year Group: 4
sheet                                                    numbers
Oral and Mental                                          Main Teaching                                                                                                                          Plenary
Objectives and         Teaching Activities               Objectives and          Teaching Activities                                                                                            Teaching Activities/Focus
Vocabulary                                               Vocabulary                                                                                                                             Questions
Recall multiplication         Play ‘Ping Pong’ for      Make and                  Write a starting number on the board, e.g. 4.             Identify the rule for the sequence x 4.            Draw on the board:
facts in the 3 and 4        x4 facts. The teacher        investigate a
times table.                sets a rhythm with the       general statement          Write ‘the rule is + 3’.                                  Statement
children as shown            about familiar                                                                       1st cross → 1 + (1 x 4)                                      ,        …
Begin to recall             below, then gives a          numbers by finding         Discuss the rule and how to generate the                  2nd cross → 1 + (2 x 4)
multiplication facts        number for children to       examples that              sequence using the rule.                                  3rd cross → 1 + (3 x 4)
in the 6 times table.       give the x 4 product         satisfy it.                                                                                                                            Q Which table will generate
within the rhythm set.                                  Get children to recite the sequence formed, i.e.          Test                                                this sequence?
Repeat the start number      Recognise and              4, 7, 10, 13, 16, 19, 22.                                 10th cross → 1 + (10 x 4)
twice to consolidate the     extend number                                                                                                                             Write on the board:
product.                     sequences.               Q Is 34 in our sequence?                                   In pairs get children to investigate and record
in the same way, the number of posts needed          1 + (‫ ٱ‬x ?)
Teacher       Children                                  Continue counting to establish 34 is in the               to make a fence.
ping          pong                                    sequence.                                                                                                      Test suggestions.
ping          pong
ping          pong                                    Write 34 = 4 + (‫ ٱ‬x 3).                                        ,              ,                        …
Q What shape or symbol could
3              12                                                                                                                                                  we use to generate a
3              12                                    Discuss this with the children and establish 10                                                               sequence using the 6 times
7              28                                    goes in the box. Emphasise that you are                Q Where have you seen a sequence like this             table?
7              28                                    adding on a multiple of 3.                               before?
5              20                                                                                                                                                   Give children two minutes to
5              20                                    Repeat for other sequences.                            Q Can we write each statement as                        work in pairs with
1 + (‫ ٱ‬x 4)?                                          whiteboards.
   Repeat for 3 x facts.                                  Present this problem to the class:
Introduce the 6 times                                                                                            Ask children to investigate the numbers of           Collect ideas from the class
table. Start in order 1 to                            Q How many squares will there be in the 10th                posts used to build these huts:                      and discuss, e.g.
10, then randomly.                                      cross?

,          ,             ,               …
HOMEWORK – Practise six times
Q What is the rule for the huts?                     table.
What statement can we make?
How do we test it?
By the end of the lesson the
children should be able to:
Give children time to read the question and                                                                   Investigate a problem by
with the class work through the stages shown                                                                   using the following skills:
below.                                                                                                         - recording
- identifying a sequence
Recording                                                                                                      - making a general
statement
VOCABULARY                                                                                                                                - testing the statement.
Cross        Squares
sequence
VOCABULARY                                               multiple                         1             5
2             9                                                                                        (Refer to supplement of
multiply                                                 rule                                                                                                                                    examples, section 6, pages 76
product                                                  predict                          3            13
4            17                                                                                        and 80.)

NNS Unit Plans
Planning      Day Five                                         Unit 8 Properties of numbers and                              Term: Spring                                                        Year Group: 4
sheet                                                          reasoning about numbers
Oral and Mental                                                Main Teaching                                                                                                                     Plenary
Objectives and        Teaching Activities                      Objectives and          Teaching Activities                                                                                       Teaching Activities/Focus
Vocabulary                                                     Vocabulary                                                                                                                        Questions
Recall                      Get the class to chant the 2      Make and                  Remind children of homework.                        ‘In the first table the sum of three numbers         Discuss the activity, ask for
multiplication facts         times table, saying each          investigate a                                                                  in an L-shape always has factors 5 and 3.’            examples and record them on
in 2, 3, 4 and 6             number statement twice.           general statement          Ask the class to count in 6s from zero to                                                                 the board.
times tables.                                                  about familiar             60. Show OHT 8.2 and ask class to                  Ask children to cover three numbers of their
Repeat the chant this time        numbers by finding         count in 6s again.                                  own using the L-shape, and sum them.                Q If we extend the table to
saying the 2 times table          examples that                                                                                                                        numbers larger than 100, will
followed by the 4 times table,    satisfy it.              Q How does OHT 8.2 help you with this               Q Are your numbers multiples of 5 and                   our statement still work?
i.e.                                                         counting?                                           multiples of 3?
Explain methods                                                                                                                      Use an example from the
1 x 2 = 2;        1x4=4           and reasoning.             Establish that the last column in the table         Collect responses and get the class to                extended table and with the
2 x 2 = 4;        2x4=8                                      helps as these numbers are multiples of             amend the statement, using calculators to             children work through using the
3 x 2 = 6;        3 x 4 = 12…                                6.                                                  confirm that the numbers are not always               OHP calculator.
multiples of 5.
Highlight the doubling                                     Q What can you say about the other                                                                         Remind the children about their
process.                                                     columns?                                            ’The sum of three numbers in an L-shape is            learning in this unit by asking
always a multiple of 3.’                              them the following question.
Q What table could help us                                     Establish that the 2nd, 4th and 6th
learn our six times table?                                   columns are multiples of 2, the 3rd and             Ask children to find other examples that test       Q Tell me three things you have
6th columns are multiples of 3.                     this.                                                 learnt in this unit?
     Get the class to chant the 3
times table, saying each                                    Give out Resource sheet 8.7.                        Collect some examples to confirm the
number statement twice.                                                                                          statement.
Q What can you say about columns in the
Repeat the chant but saying                                  first and second table?                            Explain that you want the children to use the       By the end of the lesson the
the 3 times table, followed by                                                                                   second table and this time cover four               children should be able to:
the 6 times table, i.e.                                      Identify the columns that have multiples            numbers using a 2 x 2 square. Demonstrate            Find examples that match a
of 2, 4 and 5. Explain that you are going           using:                                                general statement;
1 x 3 = 3;        1x6=6                                      to use an L-shape to cover three numbers                                                                 Explain methods and
2 x 3 = 6;        2 x 6 = 12                                 on the first table and then add these three                       43   44                                 reasoning orally and record
3 x 3 = 9;        3 x 6 = 18…                                numbers. Demonstrate using the three                                                                      work systematically.
numbers:                                                          48   49
Remind the children that the                                                                                                                                         (Refer to supplement of
numbers in the 6 times table                                            22                                                                                           examples, section 6, pages 76
are double the numbers in the                                                                                    and add the numbers with the OHP                    and 80.)
3 times table.                                                          26   27                                  calculator. 43 + 44 + 48 + 49 =

     Play ‘Ping Pong’ to practise 2,   VOCABULARY                                                                     Ask children to find sums of their own and
With the OHP calculator show children
3, 4 and 6 times tables. Set a    multiple                                                                       make a statement they can test using
how to find the sum of 22 + 26 + 27 = 75.
rhythm then give numbers for      factor                                                                         examples of their own.
children to respond with                                   Q What do we know about this number?
products as shown below:                                                                                         Collect children’s statements and gather
Identify the number on the other two                them into a common statement that children
(x 3)   Teacher       Children    RESOURCES                                                                      can test with their own examples e.g.
tables to establish that 75 has factors 5
ping          pong       OHT 8.2
and 3. Use the OHP calculator to confirm
ping          pong       Resource sheet 8.7                                                             ’In the second table the sum of four
this. Make the statement:
ping          pong       OHP calculator                                                                 numbers in a 2 x 2 square always has a
5              15       Class set of                                                                   factor of 4’.
9              27       calculators

NNS Unit Plans

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