Oxford Mathematics Primary Years Programme
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Questions and Answers

Partitioning 23 into two parts, if one part is 7, the other part is ______.

16

Which of the following equations represents a valid partition of the number 16 into two parts?

  • $16 = 10 + 8$
  • $16 = 5 + 9$
  • $16 = 2 + 13$
  • $16 = 12 + 4$ (correct)
  • If you have 20 counters and you partition them into two groups, which combination is NOT possible based on the provided content?

  • 2 and 18
  • 7 and 12 (correct)
  • 5 and 15
  • 10 and 10
  • Which of the following is the most accurate description of 'partitioning' in a mathematical or conceptual context?

    <p>Dividing a whole into distinct, non-overlapping parts or subsets. (A)</p> Signup and view all the answers

    When counting on from a larger number, you begin with the ______ number and increment by the ______ number.

    <p>larger, smaller</p> Signup and view all the answers

    What is the result of counting on 9 from 23?

    <p>32 (A)</p> Signup and view all the answers

    When presented with the addition problem 5 + 16, it is more efficient to start counting from 5 and add 16.

    <p>False (B)</p> Signup and view all the answers

    Calculate the result of adding 12 to 65 using mental math strategies.

    <p>77</p> Signup and view all the answers

    Which of the following is the most accurate description of the strategy of 'counting on'?

    <p>Starting with the larger addend and incrementing by the value of the smaller addend. (C)</p> Signup and view all the answers

    Applying the 'count on' strategy to determine how much is 8 more than 86, you would start at ______ and progress by ______ steps.

    <p>86, 8</p> Signup and view all the answers

    Which of the following mathematical strategies is most closely aligned with the concept of 'partitioning' as described in the content?

    <p>Decomposition (B)</p> Signup and view all the answers

    When adding 9 and 3 using the count-on strategy, which number should you start with and why?

    <p>Start with 9 because it is the larger number, requiring fewer counts to reach the sum. (A)</p> Signup and view all the answers

    When using the count-on strategy, it is always more efficient to start counting from the smaller number, regardless of the difference between the two numbers.

    <p>False (B)</p> Signup and view all the answers

    Explain how the 'count on' strategy simplifies addition, especially when dealing with numbers that have a significant difference in value.

    <p>The 'count on' strategy simplifies addition by starting with the larger number and adding the smaller number incrementing one by one, which reduces the effort required to count from one.</p> Signup and view all the answers

    To efficiently add 16 and 3 using the count-on method, begin with ______ and count up three times.

    <p>16</p> Signup and view all the answers

    In a problem where you need to add 12 and 11, which initial step demonstrates the most efficient use of the 'count on' strategy?

    <p>Starting at 12 and counting up 11 numbers. (D)</p> Signup and view all the answers

    What is the primary advantage of using a number line in conjunction with the 'count on' strategy?

    <p>It provides a visual representation of the addition process, which can improve understanding and accuracy. (D)</p> Signup and view all the answers

    Explain a scenario where the 'count on' strategy might not be the most efficient method for addition. What alternative strategy could be used?

    <p>When adding numbers with a small difference, the 'count on' strategy may be less efficient than other methods, such as memorizing addition facts or using mental math strategies.</p> Signup and view all the answers

    When presented with an addition problem, the first step in effectively applying the 'count on' strategy involves identifying the ______ of the two numbers.

    <p>larger</p> Signup and view all the answers

    Which of the following methods is LEAST efficient for finding the difference between two numbers, especially when dealing with larger values?

    <p>Using a pre-calculated difference table for common number pairs. (B)</p> Signup and view all the answers

    Finding the difference between two numbers is always the same as determining how many units need to be added to the smaller number to reach the larger number.

    <p>True (A)</p> Signup and view all the answers

    Explain a real-world scenario where knowing the difference between two quantities is crucial for decision-making.

    <p>Budgeting, determining profit/loss, measuring temperature changes, calculating speed, figuring out discounts.</p> Signup and view all the answers

    When finding the difference between 25 and 18 by counting back, you start at 25 and count back ______ units to reach 18.

    <p>7</p> Signup and view all the answers

    Match the number pairs with their corresponding differences:

    <p>14 and 18 = 4 9 and 12 = 3 17 and 9 = 8 27 and 21 = 6</p> Signup and view all the answers

    A student is asked to find the difference between two numbers. They consistently count up from the larger number to the smaller one. What fundamental concept are they misunderstanding?

    <p>The relationship between addition and subtraction. (A)</p> Signup and view all the answers

    Which calculation strategy would be most appropriate and efficient to find the difference between 102 and 98?

    <p>Counting up from 98 to 102. (A)</p> Signup and view all the answers

    Given three numbers A, B, and C, where A > B > C, which expression represents the largest difference?

    <p>$A - C$ (A)</p> Signup and view all the answers

    Based on the data provided for skip counting, which of the following sequences demonstrates consistent incremental jumps?

    <p>a: 2s -&gt; 38, 40, 42, 46, 50, 56 (A)</p> Signup and view all the answers

    In skip counting by 5s, the sequence 35, 40, 50, 65, 75 demonstrates a consistent arithmetic progression.

    <p>False (B)</p> Signup and view all the answers

    If a student is skip counting by 10s and starts at 10, identifying 30 and 70 as subsequent numbers in the sequence, what is the likely next number if the student understands the pattern?

    <p>100</p> Signup and view all the answers

    When skip counting by ______, the difference between consecutive numbers is constant and equal to the skip count value.

    <p>2s, 5s, or 10s</p> Signup and view all the answers

    Match the skip counting sequence with their respective skip values:

    <p>38, 40, 42, 46, 50, 56 = Skip counting by 2s 35, 40, 50, 65, 75 = Skip counting by 5s 10, 30, 70, 100 = Skip counting by 10s</p> Signup and view all the answers

    Consider the skip counting chart provided. Which skip counting sequence contains an error?

    <p>All sequences are correct (B)</p> Signup and view all the answers

    Following the 'Skip count by 2s' directions, '73, 66, 65, 56' is a correct path for the koala to get to the tree.

    <p>False (B)</p> Signup and view all the answers

    Given the last segment of skip counting by 5s to find the secret number includes 48 and 94, what would be the whole number average between the two values?

    <p>71</p> Signup and view all the answers

    Which of the following pairs does NOT represent a valid partition of 28 as demonstrated in the provided examples?

    <p>38 and -10 (B)</p> Signup and view all the answers

    Partitioning numbers is MOST strategically employed to enhance which of the following mathematical skills?

    <p>Simplification of complex arithmetic problems (D)</p> Signup and view all the answers

    True or False: For any given whole number, there exists only a single, unique way to partition it into exactly two whole number parts.

    <p>False (B)</p> Signup and view all the answers

    True or False: When a number is partitioned, each resulting part must invariably be of a lesser value than the original number.

    <p>False (B)</p> Signup and view all the answers

    Demonstrate a partition of the number 57 into three parts, ensuring that one of these parts is precisely 25.

    <p>Example answers: 25, 20, 12 or 25, 15, 17 or 25, 30, 2. Many combinations are possible.</p> Signup and view all the answers

    Articulate in your own words the fundamental advantage of employing number partitioning as a strategy when dealing with calculations involving larger numerical values.

    <p>Example answer: Partitioning larger numbers simplifies complex calculations by breaking them down into smaller, more manageable parts. This allows for easier mental arithmetic or step-by-step problem-solving by working with less intimidating numbers.</p> Signup and view all the answers

    Complete the following four-part partition of the number 57: ___ and 5 and 20 and 7.

    <p>25</p> Signup and view all the answers

    Match each number with the set of partitions that accurately represents it.

    <p>14 = 7 and 7; 10 and 4 28 = 20 and 8; 14 and 14 57 = 30 and 27; 40 and 17 11 = 6 and 5; 7 and 4</p> Signup and view all the answers

    Flashcards

    Counting On

    A strategy where you start from a larger number and count upwards to find the answer.

    Bigger Number

    The larger of two numbers you begin counting from.

    Addition of 9 and 3

    Counting on from 9, you add 3 to get 12.

    Addition of 11 and 6

    When counting on from 11, adding 6 gives you 17.

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    Addition of 2 and 15

    Counting on from 2, you reach 17 after adding 15.

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    Circle the Bigger Number

    A practice method where you identify and focus on the larger number before adding.

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    Number Line Usage

    Using a visual representation of numbers to show and solve addition problems.

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    Drawing More Objects

    Adding a specific number of items to a group to find the new total.

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    Partitioning Numbers

    The process of dividing a number into two or more parts.

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    Example of Partitioning

    23 can be partitioned as 10 and 13, 20 and 3, or 15 and 8.

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    Number Pair

    A combination of two numbers that add up to a specific total.

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    Drawing Counters

    Using objects to represent and visualize numbers for partitioning.

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    Independent Practice

    Activities done alone to reinforce learning, such as partitioning numbers into parts.

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    Ways to Partition

    Different combinations or methods to break a number into parts.

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    Partition 28

    Finding different pairs or groups that total 28.

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    Partition 57

    Identifying sums that result in 57 when combined.

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    Same as Partition

    Using different numbers that equal the same total when partitioned.

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    Finding Multiple Ways

    Discovering various combinations to express a value.

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    Understanding Value Partitioning

    Comprehending why breaking down numbers is useful in math.

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    Smaller number

    The lesser of two numbers being compared.

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    Count on

    To add to a number by progressing sequentially.

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    Altogether

    The total when numbers are combined.

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    Partitioning

    The process of separating a whole into parts.

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    Counting more

    Finding how much more one number is than another.

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    Drawing numbers

    Visually representing numbers using colors for clarity.

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    Combined total

    The sum of two or more numbers after counting on.

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    Difference Between Numbers

    The result of subtracting one number from another.

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    Finding Differences

    Identify the gap between two values by counting.

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    Count Up Method

    A technique to find difference by counting from the smaller number to the larger one.

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    Counting Back Method

    A strategy where you start with a larger number and count backwards to find the difference.

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    Pairs with Difference of 3

    Two numbers that, when subtracted, give a result of 3.

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    Guided Practice

    Structured exercises led by a teacher to help students learn.

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    Number Line

    A visual tool for showing numbers in order and finding differences.

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    Skip Counting by 2s

    Counting numbers in increments of two, e.g., 2, 4, 6, 8.

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    Skip Counting by 5s

    Counting numbers in groups of five, e.g., 5, 10, 15.

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    Number Pattern

    A sequence of numbers that follow a specific rule or formula.

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    Counting Sequence

    A specific order of numbers used in counting.

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    Colouring Squares

    Using colors to represent or highlight numbers in a sequence.

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    Secret Number

    A number you find by following a clue, often in skip counting.

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    Count to Find Quantity

    The action of counting objects to determine how many there are.

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    Koala and the Tree

    A visual problem-solving scenario using skip counting to reach a goal.

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    Study Notes

    Oxford Mathematics Primary Years Programme

    • This book is a student book for the Primary Years Programme (PYP)
    • The book is published by Oxford University Press
    • It is written by Annie Facchinetti
    • The book covers the mathematical scope and sequence for the PYP
    • The book is meant to be supported by teacher resources
    • The series is designed to offer clear, comprehensive and easy-to-use materials for teachers
    • The student books include guided practice, independent practice, and extended practice on each topic
    • Differentiation is important in the series to ensure every student can access the curriculum at their point of need
    • Further activities and support are available in teacher resources to cater for different learning needs
    • The book includes topics like numbers, measurement, shape, space, data handling, chance and patterns
    • The student books cover topics including 2-digit numbers, counting to 100, reading and writing numbers, ordering numbers, counting on, counting back, partitioning numbers
    • Different practice types are included to help students learn and consolidate their understanding and skills in mathematics

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    Description

    Student book for the Primary Years Programme (PYP) published by Oxford University Press, written by Annie Facchinetti. Covers mathematical scope and sequence for the PYP, supported by teacher resources. Includes guided practice, independent practice and covers topics like numbers, measurement, shape, space, data handling, chance and patterns.

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