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Grade 5 Mathematics Module 1, Topic A: Multiplicative Patterns on the Place Value Chart

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Title:

 Grade 5 Mathematics Module 1, Topic A: Multiplicative Patterns on the Place Value Chart

URL:

 https://www.engageny.org/resource/grade-5-mathematics-module-1-topic-overview

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

Module 1, Topic A begins with a conceptual exploration of the multiplicative patterns of the base ten systems. This exploration extends the place value work done with multi-digit whole numbers in Grade 4 to larger multi-digit whole numbers and decimals. Students use place value disks and a place value chart to build the place value chart from millions to thousandths. They compose and decompose units crossing the decimal with a view toward extending their knowledge of the 10 times as large and 1/10 as large relationships among whole number places to that of adjacent decimal places. This concrete experience is linked to the effects on the product when multiplying any number by a power of ten. For example, students notice that multiplying 0.4 by 1,000 shifts the position of the digits to the left three places, changing the digits’ relationships to the decimal point and producing a product with a value that is 10 10 10 as large (400.0) (5.NBT.2). Students explain these changes in value and shifts in position in terms of place value. Additionally, students learn a new and more efficient way to represent place value units using exponents (e.g., 1 thousand = 1,000 = 103) (5.NBT.2). Conversions among metric units such as kilometers, meters, and centimeters give students an opportunity to apply these extended place value relationships and exponents in a meaningful context by exploring word problems in the last lesson of Topic A (5.MD.1).

Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 5
5 ) Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. [5-NBT2]

NAEP Framework
NAEP Statement::
4A1b: Given a pattern or sequence, construct or explain a rule that can generate the terms of the pattern or sequence.

NAEP Statement::
4NPO3d: Describe the effect of operations on size (whole numbers).

NAEP Statement::
4NPO6a: Explain or justify a mathematical concept or relationship (e.g., explain why 15 is an odd number or why 7-3 is not the same as 3-7).

NAEP Statement::
8NPO1a: Use place value to model and describe integers and decimals.
Mathematics
MA2019 (2019)
Grade: 5
3. Using models and quantitative reasoning, explain that in a multi-digit number, including decimals, a digit in any place represents ten times what it represents in the place to its right and 1/10 of what it represents in the place to its left.

a. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, using whole-number exponents to denote powers of 10.

b. Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10, using whole-number exponents to denote powers of 10.
Unpacked Content
Evidence Of Student Attainment:
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.
Teacher Vocabulary:
  • Digit
  • Decimal
  • Decimal point
  • Thousandths
  • Hundredths
  • Tenths
  • Base-ten
  • Expanded form
  • Place value
  • Power of 10
  • Factor
  • Base
  • Exponent
  • Product
Knowledge:
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.
Skills:
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.
Understanding:
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.
Diverse Learning Needs:
Essential Skills:
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.

Prior Knowledge Skills:
  • 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.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.5.3 Compare base-10 models up to 99 and whole numbers up to 100 to determine symbols (<, >, =).
Mathematics
MA2019 (2019)
Grade: 5
17. Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real-world problems.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Convert different-sized measurement units within the same system.
  • Solve multi-step word problems involving conversion of metric or customary units.
Teacher Vocabulary:
  • Measurement system
  • US Customary
  • Metric
  • Unit
  • Conversion
  • Equivalent measurements
Knowledge:
Students know:
  • Strategies for converting a larger unit of measure to a smaller unit in the same system.
  • Relative size of customary and metric units of measure.
  • Strategies for converting between units of measure in the same system.
Skills:
Students are able to:
  • Convert measurement units.
  • Solve multi-step word problems involving measurement conversions.
Understanding:
Students understand that:
  • the multiplicative relationship between units of measures given in the same measurement system is essential when converting units to a larger or smaller unit.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.5.17.1: Identify relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; and hr, min, sec.
M.5.17.2: Express measurements in a larger unit in terms of a smaller unit.
M.5.17.3: Solve two-step word problems.
M.5.17.4: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).
M.5.17.5: Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
M.5.17.6: Recall basic addition, subtraction, multiplication, and division facts.

Prior Knowledge Skills:
  • Create a line plot with appropriate intervals.
  • Represent data on a line plot.
  • Apply strategies for solving problems involving all four operations with the fractional data.
  • Convert measurement units.
  • Solve mulit-step word problems involving measurement conversions.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.5.17 Using vocalization, sign language, augmentative communication, or assistive technology, to tell time using an analog or digital clock to the half or quarter hour.
M.AAS.5.17a Use standard units to measure the weight and length of objects.
M.AAS.5.17b Sort a collection of coin according to their value.

Tags: decimal, exponents, measurement, multidigit, patterns, powers of 10, realworld problems, zeros
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There are four lessons on this topic.

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Author: Hannah Bradley
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