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Grade 4 Mathematics Module 3, Topic G: Division of Thousands, Hundreds, Tens, and Ones

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Title:

Grade 4 Mathematics Module 3, Topic G: Division of Thousands, Hundreds, Tens, and Ones

URL:

https://www.engageny.org/resource/grade-4-mathematics-module-3-topic-g-overview

Content Source:

EngageNY
Type: Lesson/Unit Plan

Overview:

Module 3, Topic G extends to division with three- and four-digit dividends using place value understanding. Students begin the topic by connecting multiplication of 10, 100, and 1,000 by single-digit numbers from Topic B to division of multiples of 10, 100, and 1,000 in Lesson 26. Using unit language, students find their division facts allow them to divide much larger numbers. In Lesson 27, place value disks support students visually as they decompose each unit before dividing. This lesson contains a first-use script on the steps of solving long division using place value disks and the algorithm in tandem for three- and four-digit dividends (4.NBT.6). Students then move to the abstract level in Lessons 28 and 29, recording long division with place value understanding, first of three-digit, then four-digit numbers using small divisors. In Lesson 30, students practice dividing when zeros are in the dividend or in the quotient. Lessons 31 and 32 give students opportunities to apply their understanding of division by solving word problems (4.OA.3). In Lesson 31, students identify word problems as a number of groups unknown or group size unknown, modeled using tape diagrams. Lesson 32 allows students to apply their place value understanding of solving long division using larger divisors of 6, 7, 8, and 9. Concluding this topic, Lesson 33 has students make connections between the area model and the standard algorithm for long division.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 4
3. Determine and justify solutions for multi-step word problems, including problems where remainders must be interpreted.

a. Write equations to show solutions for multi-step word problems with a letter standing for the unknown quantity.

b. Determine reasonableness of answers for multi-step word problems, using mental computation and estimation strategies including rounding.

Unpacked Content
Evidence Of Student Attainment:
Students:
When given multi step word problems,
  • Solve a variety of multistep word problems involving all four operations on whole numbers including problems where remainders must be interpreted.
  • Explain and justify solutions using connections between the problem and related equations involving a single (letter) unknown.
  • Evaluate the reasonableness of solutions using estimation strategies.
Note: Multi step problems must have at least 3 steps.
Teacher Vocabulary:
  • Operation
  • Multi Step problem
  • Remainder
  • Unknown quantity
  • Equation
  • Rounding
  • Mental strategy
  • Partition
  • Estimation
  • Reasonableness
Knowledge:
Students know:
  • Context situations represented by the four operations.
  • How to calculate sums, differences, products, and quotients.
  • Estimation strategies to justify solutions as reasonable.
Skills:
Students are able to:
  • Solve multi-step word situations using the four operations.
  • Represent quantities and operations physically, pictorially, or symbolically.
  • Write equations to represent the word problem and use symbols to represent unknown quantities.
  • Use context and reasoning to interpret remainders.
  • Use estimation strategies to assess reasonableness of answers by comparing actual answers to estimates.
Understanding:
Students understand that:
  • Using problem solving strategies will help them determine which operation to use to solve a problem.
  • Remainders must be interpreted based on the context, and remainders are sometimes ignored, rounded up, or partitioned.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.4.3.1: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
M.4.3.2: Solve single-step word problems.
M.4.3.3: Recognize key terms to solve word problems.
Examples: in all, how much, how many, in each.
M.4.3.4: Solve division problems without remainders.
M.4.3.5: Recall basic addition, subtraction, and multiplication facts.

Prior Knowledge Skills:
  • Demonstrate computational understanding of multiplication and division by solving authentic problems with multiple representations using drawings, words, and/or numbers.
  • Identify key vocabulary words to solve multiplication and division word problems.
    Examples: times, every, at this rate, each, per, equal/equally, in all, total.
  • Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
  • Recall basic multiplication facts.
  • Add and subtract within 20.
  • Represent repeated addition, subtraction, and equal groups using manipulatives.
  • Distinguish between rows and columns.
  • Use repeated addition to solve problems with multiple addends.
  • Count forward in multiples from a given number.
    Examples: 3, 6, 9, 12; 4, 8, 12, 16.
  • Recall doubles addition facts.
  • Model written method for composing equations.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.1 Solve one-step word problems involving real-life situations using the four operations within 100 without regrouping and select the appropriate method of computation when problem solving.


Mathematics
MA2019 (2019)
Grade: 4
12. Use strategies based on place value, properties of operations, and/or the relationship between multiplication and division to find whole-number quotients and remainders with one-digit divisors and up to four-digit dividends.

a. Illustrate and/or explain quotients using equations, rectangular arrays, and/or area models.
Unpacked Content
Evidence Of Student Attainment:
Students:
When given division problems with one-digit divisors and up to four-digit dividends,
  • Find quotients with remainders using strategies based on place value, properties of operations, and the relationship between multiplication and division.
  • Illustrate quotients using a rectangular array and/or area model, and explain the connection of the visual model to the equation.
Teacher Vocabulary:
  • Quotient
  • Dividend
  • Divisor
  • Divide
  • Multiply
  • Multiple
  • Equation
  • Remainder
  • Area model
  • Greatest multiple
  • Decompose
  • Compose
  • Array
  • Properties of operations
  • Unknown factor
  • Partial quotient
Knowledge:
Students know:
  • How to decompose and compose numbers in a variety of ways using place value and the properties of operations to demonstrate a variety of strategies for division.
  • Division can be described as an unknown factor problem.
  • A variety of contextual situations can be represented with a division equation.
Skills:
Students are able to:
  • Use strategies based on place value to find whole number quotients and remainders.
  • Use the properties of operations to find whole number quotients and remainders.
  • Use arrays and area models to find whole number quotients and remainders.
  • Illustrate division situations with rectangular arrays and area models.
  • Write an equation to represent a division situation.
Understanding:
Students understand that:
Division expressions represent
  • The number of objects in each group when the total number is partitioned evenly into a given number of groups.
  • The number of groups when the total number is partitioned into groups that each contain a given number.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.4.12.1: Define fraction, numerator and denominator.
M.4.12.2: Recognize fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts.
M.4.12.3: Identify the parts of a fraction a/b as the quantity formed by a parts and size 1/b.
M.4.12.4: Recognize fractions as numerals that may represent division problems.
M.4.12.5: Label numerator, denominator, and fraction bar.
M.4.12.6: Identify parts of a whole with two, three, or four equal parts.
M.4.12.7: Recognize that equal shares of identical wholes need not have the same shape.
M.4.12.8: Distinguish between equal and non-equal parts.

Prior Knowledge Skills:
  • Recognize fractions as lengths from zero to one.
  • Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
  • Identify a number line.
  • Recognize whole numbers as lengths from zero to one.
  • Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
  • Identify a number line.
  • Label the fractions on a pre-made number line diagram.
  • Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
  • Recognize a number line diagram with equally spaced points.
  • Compare length using non
  • standard units to determine which is longer.
Tags: arrays, divide, dividends, divisor, equations, operations, place value, quotients, remainders, word problems
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There are eight lessons in this topic.

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  This resource provided by:  
Author: Hannah Bradley