ALEX Classroom Resource

Students:

• Use models to illustrate the relationship between two successive place values in whole numbers and decimals.
• Explain that a digit in one place represents 1/10 of what it represents to its left or the place value is 10 times the place value on the right.
• Use strategies to find products and explain patterns when multiplying by powers of 10.
  Example: The product of 420 x 200 = 42 x 10 x 2 x 100 is the same as (42 x 2) x (10 x 100) = 84 x 1000 = 84,000 shows multiplying by three powers of 10 shifts the digits in the product three place values greater (to the left.)
• Use strategies to find products and quotients and use place value understanding to explain patterns in the placement of the decimal point when involving a power of 10.
• Write powers of 10 in standard form and using exponential notation.

Students know:

• Each place value position represents 10 times what it represents in the place to its right.
  Example: In 433, the underlined 3 represents 3 tens and has a value of 30 which is ten times the value of the 3 ones to its right.
• Place value understanding is extended to apply reasoning that a place value position represents 1/10 of what it represents in the place value to its left.
  Example: In 433, the underlined 3 represents 3 ones and has a value of 3 which is one-tenth of the value of the 3 tens or 30 to its left.
• A given number multiplied by a power of 10 shifts the digits in the given number one place value greater (to the left) for each factor of 10. -A given number divided by a power of 10 shifts the digits in the given number one-tenth of the value (to the right) for each factor of 10.

Students are able to:

• Reason and explain the relationship between two successive place values.
• Explain patterns of zeros of the product when multiplying by powers of 10.
• Explain patterns in placement of decimals when multiplying or dividing by power of 10.
• Write powers of 10 using exponential notation.

Students understand that:

• The relationship of adjacent places values in the base ten system extend beyond whole numbers to decimal values.
• Multiplying or dividing by a power of 10 shifts the digits in a whole number or decimal that many places to the left or right respectively.

Learning Objectives:
M.5.3.1: Use place value understanding to round whole numbers to the nearest 10 or 100.
M.5.3.2: Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons.
M.5.3.3: Identify that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.

Students:

• Given a decimal number in one form (words, base-ten numerals, expanded), identify the number in another form.
• Read decimals with number names.

Example: Read 4.023 as "four and 23 thousandths."
• Write decimals using base-ten numerals and expanded form.

Example: 4.023 as 4 x 1 + 2 x 1/100 + 3 x 1/1000 or 4 x 1 + 2 x 0.01 + 3 x 0.001.
• Use place value understanding to compare two decimals.

Students know:

• How to read and write whole numbers in standard form, word form, and expanded form.
• How to compare two whole numbers using place value understanding.
• Prior place value understanding with whole numbers is extended and applied to decimal values.
• Recognize and model decimal place value using visual representations to compare.

Students are able to:

• Read and write decimal values in word form, standard form, and expanded form.
• Compare decimals to thousandths using <, >, or = .

Students understand that:

• the adjacent place value relationship in the base ten system extends to decimals and is used to write decimals in expanded form and compare decimals.

Learning Objectives:
M.5.4.1: Recognize decimals as parts of a whole.
M.5.4.2: Compare whole numbers.
M.5.4.3: Write whole numbers in words and expanded form.
M.5.4.4: Read whole numbers.
M.5.4.5: Define expanded notation and standard form.
M.5.4.6: Convert a number written in expanded to standard form.
M.5.4.7: Define hundredths and thousandths.
M.5.4.8: Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons.
M.5.4.9: Identify comparison symbols.
Examples: >, =, and <.

Students:

• Use strategies based on place value, properties of operations, and relationship between addition and subtraction to find sums and differences of decimals.
• Use strategies based on place value, properties of operations, and relationship between multiplication and division to find products and quotients of decimals.
• Use models to justify the sum, difference, product or quotient of decimals.
• Solve real-world problems with decimals to hundredths.

Note: Products are limited to thousandths and quotients are either whole numbers or decimals terminating at the tenths or hundredths place.

Students know:

• Strategies based on place value understanding, properties, and relationship between operations to find the sum, difference, product, and quotient of whole numbers.
• How to write decimal notation for fractions with denominators of 10 or 100.
• Use estimation strategies to assess reasonableness of answers.

Students are able to:

• Use concrete models, drawings, and strategies to add, subtract, multiply, and divide decimals.
• Relate strategies for operations with decimals to a written method and explain reasoning used.
• Solve real-world context problems involving decimals.

Students understand that:
Problems involving operations with decimals

• Can be solved using a variety of strategies based on place value, properties of operations, or the relationship between the operations.
• Can be illustrated using concrete models or drawings.

Learning Objectives:
M.5.8.1: Use decimal notation for fractions with denominators 10 or 100.
M.5.8.2: Multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations.
M.5.8.3: Add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
M.5.8.4: Apply properties of operations as strategies to multiply and divide.
M.5.8.5: Identify that 100 can be thought of as a bundle of ten tens, called a "hundred".
M.5.8.6: Identify that the numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
M.5.8.7: Recall basic addition, subtraction, multiplication, and division facts.