Content Area:  Math
Unit Title: Numeration
Unit Authors:    Gail Stallings                                                                                   Date:  12/12/2010
Unit Summary
This unit, Numeration, represents one of two Number and Operations in Base Ten standards in the 2009 Common Core and one of two (Numeration) units in envision MATH, Grade 5.  Numeration focuses on base ten place value concepts in whole numbers and decimals, and provides the foundation for Unit 9 (Fractions and Decimals). This class of inclusion students has a wide range of abilities (and needs) in this topic.
In this unit, students will review and expand on previous knowledge and experience (with whole number place value concepts), learning to work with larger numbers (billions.) They will find examples of very large numbers in the real world and situations that create the need to compare numbers.  They will explore place value concepts and relationships by problem solving and working with manipulatives, place value charts and templates, calculators, digital representations, and print, working individually, in pairs and groups.
Students will extend their knowledge of how to read, write, compare, order and round whole numbers to numerals through the billions. They will recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left (to 1,000,000,000).
Following their work with whole numbers, students will review and expand on previous knowledge and experience (with decimal place value concepts), learning to work with decimals to the thousandths. They will read, write, compare and order decimals.
The final topic will call on students to observe and explain patterns in whole numbers and decimals.
Primary interdisciplinary connections: Social Studies, Science, Language Arts
21st century themes: Communication and Collaboration, Life and Career Skills, Financial, Economic, Business,  and Entrepreneurial Literacy
Unit Rationale:  Understanding numeration and how our number system works is the foundation for all math that follows, including everyday math (life skills.)

Standards:    4.NBT      Number and Operations in Base Ten
5.NBT      Number and Operations in Base Ten
Content Statements:

• Generalize place value understanding for multi-digit numbers. (4)
• Understand the Place Value System (5)

Cumulative Progress Indicator (CPI):    The student will:

4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.  For example, recognize that 700/70 = 10 by applying concepts of place value and division (to 1,000,000).
5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left (to 1,000,000,000)
4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form (through billions).
4.NBT.3 Use Place Value understanding to round multi-digit whole numbers to any place.
5.NBT.2 Explain patterns in the number of  zeros of the product when multiplying a number by powers of 10.
Compare and Order (whole) Numbers  1-2
5.NBT.3.a.  Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, eg., 347.392= 3 x 100 + 4 x 10 +7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1,000).
5.NBT.3.b.  Compare two decimals to the thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
5.NBY.4Use place value understanding to round decimals to any place.
5.NBT.2  Explain patterns in the placement of the decimal point when the decimal is multiplied or divided by powers of 10.

Unit Essential Questions

• How can we read, write and compare large numbers (through billions)?
• How can we read, write and compare decimals (through hundredths)?

What is the relationship among the various place values?
Unit Enduring Understandings

• Our number system is based on groups of ten. Whenever we get 10 in one place value, we move to the next greater place value. (A digit in in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.)
• Numbers can be used to tell how many.

Place value can be used to compare and order whole numbers and decimals.
Unit Learning Targets
Students will ...

• Demonstrate and understanding of place value concepts (including value, order, place, magnitude and relationships to other numbers/digits.)
• Read and write whole numbers to the billions, and decimals to the thousandths.
• Compare, order and round whole numbers and decimals.
• Explain the relationship between a digit in one place and the digit to its right or left.

Evidence of Learning
UNIT  Summative Assessment (last day)   (after 6-9 days)
Topic 1 Test (Page 18,19)   This is a diagnostic, multiple-choice test to assess students’ understanding of geometric concepts and skills presented in Topic 1. An Item Analysis for Diagnosis and Intervention is provided in the Teacher Edition. The Intervention System materials are provided in a separate box.  Administer test questions in Senteo format (see below), five to a page.
Alternative tests (for differentiation) – Free Response Test, Multiple Choice Test
Equipment needed (for assessment): Computer w/SmartBoard/ Smart Response software and peripherals; Senteo Question Set (Unit Test questions); print copies of test questions (provide larger print,(or magnifying glasses); and space for those students who need it;  provide sticky notes or small squares of paper for blocking); manipulatives;
(Base ten blocks, play money, number tile sets, overlapping place value number sets, E-tools
large digit cards (8x10),
place-value charts, place value chart templates, graph paper cut into blocks of three
communicators, markers, erasers,)
Teacher Resources:
enVisionMATH, Grade 5, TE, Topic 1
http://www.primaryresources.co.uk/maths/mathsB4.htm#1
http://www.ronblond.com/MathGlossary/
http://teacher.scholastic.com/maven/index.htm
http://www.watchknow.org/Category.aspx?CategoryID=2214
http://teachingtoday.glencoe.com/videos/view/place-value
“Bully” as numbers 5 – 9 for rounding
Illuminations.com
Envisions
Number Devil (book, CD)

Unit Formative Assessments

• Independent Work
• Create own place-value chart
• Quick Checks
• Games and Activities
• Observation
• Projects
• Homework
• Group work
• Bell work
• Quizzes
• Exit cards

Lesson Plans
Lesson

Lesson 1
Place Value
1-2 days (80 min/day)

Lesson 2
Comparing and Ordering Whole Numbers
1 day

Lesson 3
Decimal Place Value
1-2 days

Lesson 4
Comparing and Ordering Decimals
1 day

Lesson 5
Look for a Pattern
1 days

Teacher Notes:
Writing large numbers: build up from known place values; always write from ones, one period at a time;
Use BTB/money to demonstrate magnitude, patterns, values and rounding
Show students overall structure and patterns; make sure students are able to create their own chart with their own symbols when they need it
Use lined or grid paper
When rounding, write new digits above original digits (use manipulatives such as money)
Do all the steps
Be able to copy rounding rule (or big enough to “bully” rounded digit?)
Block all but two focus numbers; (think in tens)
Copy digits in greater place values, put in zeros, decide about remaining digit
Standard to expanded – deconstruct in layers below
Expanded to standard – stack and construct as column problem
Written to standard – construct over respective words
Standard to written – break down ( list in periods) – write numerals next to  numbers
Value – relate to expanded form
Use standard/expanded foldables/overlapping numbers
Bank checks to reinforce standard/word form
Bank questions to reinforce other  place-value concepts
Emphasize word problems, practical applications
Videos (music)
Blank place value charts
Decimals  show fraction/decimal/name/abbreviation
Demo concept with decimal squares
Show rainbow pattern
Have student write and read fraction for decimal
Place value Puzzler
Virtual manipulatives
Place value game
Experiment with adding and subtracting large numbers to see how to get greatest and smallest sums and differences
Dictate period by period, allowing students time to record one period before moving on to the next.
Use number tiles, or graph squares cut in sets of three.)
Curriculum Development Resources
enVisionMATH, Grade 5, TE, Topic 1