In this Grade 5 Pengi Math lesson from Chapter 3, students learn how to add decimals mentally using the Commutative and Associative Properties to reorder and regroup addends. They practice identifying compatible numbers, applying compensation, and decomposing decimals into whole-number and fractional parts to simplify calculations. Students also explain their strategy choices and verify answers through estimation.
Section 1
Grouping Compatible Numbers Using Properties of Addition
The Commutative Property lets you add numbers in any order: .
The Associative Property lets you change the grouping of numbers being added: .
Together, these properties allow you to rearrange and group compatible numbers to simplify mental addition.
Section 2
Using Compensation for Addition
To mentally calculate the sum , you can change one addend by an amount to make it an easier number to work with, and then adjust the sum by subtracting .
Section 3
Adding Decimals Using Partial Sums
To add decimals using partial sums, add the values in each place value column separately. The total sum is the sum of these partial sums.
Section 4
Using Decomposition to Add Decimals
Decomposition breaks numbers into their place value parts to simplify addition. When adding a whole number and a decimal, the Associative Property can be used to group the whole numbers first: , where and are whole numbers and is the decimal part.
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Section 1
Grouping Compatible Numbers Using Properties of Addition
The Commutative Property lets you add numbers in any order: .
The Associative Property lets you change the grouping of numbers being added: .
Together, these properties allow you to rearrange and group compatible numbers to simplify mental addition.
Section 2
Using Compensation for Addition
To mentally calculate the sum , you can change one addend by an amount to make it an easier number to work with, and then adjust the sum by subtracting .
Section 3
Adding Decimals Using Partial Sums
To add decimals using partial sums, add the values in each place value column separately. The total sum is the sum of these partial sums.
Section 4
Using Decomposition to Add Decimals
Decomposition breaks numbers into their place value parts to simplify addition. When adding a whole number and a decimal, the Associative Property can be used to group the whole numbers first: , where and are whole numbers and is the decimal part.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter