$4th grade build and decompose fractions$

$4th grade build and decompose fractions$

For example, 4132 is less than 50 is greater than 5000, so 4132 is less than 6200.

$4th grade build and decompose fractions$

Benchmark numbers can be used to compare quantities.Knowing that the unit 'kilometres' is greater than the unit 'metres', and knowing that 625 is greater than 75, one can infer that 625 kilometres is a greater distance than 75 metres. Sometimes numbers without the same unit can be compared, such as 625 kilometres and 75 metres.Numbers that do not show a unit are assumed to have units of ones (e.g., 75 and 12 are considered as 75 ones and 12 ones). Numbers with the same units can be compared directly (e.g., 7645 kilometres compared to 6250 kilometres).Numbers are compared and ordered according to their “how muchness” or magnitude.Exposure to this larger pattern and the names of the periods – into millions and beyond – satisfies a natural curiosity around “big numbers”, although students at this grade do not need to work beyond thousands. Going from left to right, a “hundreds-tens-ones” pattern repeats within each period (ones, thousands, millions, billions, and so on).For example, 500 is 10 times greater than 50, 50 is 10 times greater than 5, and 5 is 10 times greater than 0.5. The value of the digits in each of the positions follows a “times 10” multiplicative pattern.For example, 189 means 1 hundred, 8 tens, and 9 ones, but 1089 means 1 thousand, 0 hundreds, 8 tens, and 9 ones. It serves as a placeholder, holding the other digits in their correct “place”. A zero in a column indicates that there are no groups of that size in the number.To determine the value of a digit in a number, multiply the value of the digit by the value of its place. The 5 in 511, for example, has a value of 500, not 5.

$4th grade build and decompose fractions$

The place (or position) of a digit determines its value ( place value).The number 385 describes a different quantity than the number 853. The order of the digits makes a difference.It is important for students to understand key aspects of place value.Open number lines can be used to show the composition of large numbers without drawing them to scale.Partial number lines can be used to show the position of a number relative to other numbers.Depending on the number, estimation may be needed to represent it on a number line.

$4th grade build and decompose fractions$

Closed number lines with appropriate scales can be used to represent numbers as a position on a number line or as a distance from zero.Composing and decomposing numbers in a variety of ways can support students in becoming flexible with their mental math strategies.For example, 587 could be decomposed as 58 tens and 7 ones or decomposed as 50 tens and 87 ones, and so on. There are non-standard but equivalent ways to decompose a number using place value, based on understanding the relationships between the place values.When a number is decomposed and then recomposed, the quantity is unchanged.Every strand of mathematics relies on numbers.They express magnitude and provide a way to answer questions such as “how much?” and “how much more?”. Most often, numbers describe and compare quantities. Numbers are used throughout the day, in various ways and contexts.For example, 1362 may be represented as the sum of 136 ten-dollar bills and 1 toonie or 13 base ten flats, 6 base ten rods, and 2 base ten units. Tools may be used when representing numbers.For example, 5125 can be decomposed into 5000 and 100 and 25. Numbers are decomposed when they are represented as a composition of two or more smaller numbers.For example, 1300, 200, and 6 combine to make 1506. Numbers are composed when two or more numbers are combined to create a larger number.Numbers can be composed and decomposed in various ways, including by place value.Any quantity, no matter how great, can be described in terms of its place value. Each place value column repeats the 0 to 9 counting sequence. There are patterns in the way numbers are formed.For example, in the number 4107, the digit 4 represents 4 thousands, the digit 1 represents 1 hundred, the digit 0 represents 0 tens, and the digit 7 represents 7 ones. They are referred to as the digits in a number and each digit corresponds to a place value. The numerals 0 to 9 are used to form numbers.Reading numbers involves interpreting them as a quantity when they are expressed in words, in standard notation, or represented using physical objects or diagrams.

$4th grade build and decompose fractions$