• # Elementary Mathematics Grade 4 Unit 1

Subject: Mathematics
Timeline: 9 days
Unit 1 Title: Multi-Digit Numbers

Unit Overview:

This unit will give students the opportunity to review expanded form, and rounding from previous years.  This skill will help them to master the skill of adding using partial sums and subtracting multi-digit numbers.  The unit will take students through the processes for rounding, adding, and subtracting multi-digit numbers.

Unit Objectives:

At the end of this unit, students must identify expanded form of multi-digit numbers.  They must be able to round numbers through the millions place.  The students must be able to add using partial sums, and subtract using trade-first subtraction.

Focus Standards:

PA.CCSS.Math.Content.CC.2.1.4.B.1  Apply place value concepts to show an understanding of multi-digit whole numbers. (4.NBT.2, 4.NBT.3)
PA.CCSS.Math.Content.CC.2.1.4.B.2   Use place value understanding and properties of operations to perform multi-digit arithmetic. (4.NBT.4)
PA.CCSS.Math.Content.CC.2.2.4.A.1   Represent and solve problems involving the four operations. (4.OA.3)
PA.CCSS.Math.Content.CC.2.4.4.A.1  Solve problems involving measurement and conversions from a larger unit to a smaller unit. (4.MD.2)

Mathematical Practice Standards:

#1 Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They monitor and evaluate their progress and change course if necessary. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?”

#2 Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships.  Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects

#3 Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades.

#5 Use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations.

Concepts - Students will know:
• expanded form
• rounding up to the millions place
• subtraction of large numbers
• number stories involving time
Competencies -Students will be able to:
• write numbers in expanded form
• round large numbers through millions
• use partial sums
• solve number stories

Assessments:
• Unit 1 Progress Check
• Daily RSA
• Optional Quizzes (3)

Elements of Instruction:

Learners in 4th grade will extend to 7 digits (millions) the previously taught common core standards focusing on decomposing numbers in sets to explain expanded form.  Students will round large numbers through the millions place.  Students will be able to add and subtract multi-digit numbers using a standard algorithm.  Students will apply their addition and subtraction understandings by solving number stories.

Differentiation:

Each lesson has differentiation options for each portion of the lesson. Additional differentiation options are listed with directions and student masters in the Teacher’s Guide.

Interdisciplinary Connections:
• Mental Math and Math message routines.

Students will play a variety of games that directly support the content of the lesson and the overall goals for the unit. Games for unit one included:
• Number Top-It (up to 7-digits)
• Fishing for Digits
• High-Number Toss
A constant practice with vocabulary words can be put on a math log, and given each day in addition to the mental math reflexes.

Example:

Number:  1,234,567 (read it, have the student write it)
The place of the 3 is?  Ten-Thousand
The value of the 2 is?  200,000
Which digit is in the tens place?  6
Expanded form:  1,000,000 + 200,000 + 30,000 + 4,000 + 500 + 60 + 7
Word form:  one million, two hundred thirty-four thousand, five hundred sixty-seven