Algebraic Thinking

Expanded Form

break apart each digit in the number and show the digits' true value

Example.

4,358→4000+300+50+84,358→4000+300+50+8

Left-to-Right Subtraction

Algorithm for solving subtraction. Subtract each place value separately beginning with the largest and working to the smallest

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Function Table

a table that describes a function by displaying inputs and corresponding outputs in a table format

Column Division

Algorithm for solving division. Separate the problem into columns and work with each place value separately

Like Terms

terms with the same variable and exponent combination

Example.

2x2x and 5x5x

Trade First

Algorithm for solving subtraction. Align numbers vertically based on place value and then ensure all top numbers are equal or larger than the bottom numbers

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Same Change Rule

Algorithm for solving subtraction. Add or subtract the same amount from both numerals and then subtract

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Partial Products

Algorithm for solving multiplication. Expand each factor into hundreds, tens, ones, etc. and then multiply and add

Counting Up

Algorithm for solving subtraction. Start with the number that is being subtracted and count up to the original amount with each step looking for the next base-10 number

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Geometric Sequence

A sequence whose terms are generated by multiplying each term by the same common ratio.

Opposite Change Rule

Algorithm for solving addition. Add a number to one addend to make a number ending in zero and subtract the same amount from the other addend.

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Place Value

The value of each digit in a number based on its location, or place

Algorithm

a specific set of steps that allows the user to reach the correct answer every time

Area Models

Using the expanded form of a number, each number is multiplied together and the products are added to find the final answer

Independent Variable

a variable that determines the value of another variable

Arithmetic Sequence

A sequence that has the same common difference between terms.

Partial Quotients

Algorithm for solving division. First estimate the answer using base-10 numbers and then keep estimating until the remainder is less than the dividend

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Column Addition

Algorithm for solving addition. Align numbers based on place value and then add each column

Partial Sums Addition

Algorithm for solving addition. Add each place value separately and then find the total

Linear Relationship

a relationship with a constant rate of change that creates a straight line when graphed

Dependent Variable

a variable that changes in response to another variable

Lattice Multiplication

Algorithm for solving multiplication.

• Draw a lattice with diagonals in each box

• Write one factor across the top and one along the right side (58 x 213)

• Multiply each number and write the answer in the box with the tens digit on top (Top left box is 5 x 2 = 10)

• Add the diagonals beginning in the bottom right corner (4)

• If the sum is greater than 10, move the 1 to the next diagonal

• The answer will be along the left side and bottom

Modified Repeated Addition

Algorithm for solving multiplication. Using the concept that multiplication is repeated addition, students use base-10 numbers to multiply and add

Rectangular Arrays

dots or objects that show the end product of 2 numbers; the objects are arranged so there are an equal number of items in each row and column

Example.

These _____ show 4 × 3