2017-2018 Curriculum Blueprint
Grade: 4
Course: Mathematics
Topic 12 – Understand and Compare Decimals
Flexible Time
Line
7 days
Topic Overview
Students will use strategies such as visual models and number lines to understand the relationship between and compare fractions and decimals. Students
will be able to transfer their knowledge of decimals into solving real-world problems involving money.
Vertical Progression
Coherence Map
rd
3 Grade:
• Students learn that fractions are numbers that can represent a portion of a whole, or a point on the number line.
• Students work with fractions less than one as well as fractions greater than one.
5th Grade:
• Students will extend whole number place-value concepts to decimals and then use place-value understanding to compare and round decimals.
Learning Goal
Essential Question
Students understand the relationship between fractions and decimals and are able How can you write a fraction as a decimal?
to compare them.
How can you locate points on a number line?
Topic 12 Scale
How do you compare decimals?
Deconstructed Standards
MAFS.4.NF.3.5 (DOK 1) Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions
with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. [Conceptual Understanding; Procedural Skill
and Fluency]
• Rename and recognize a fraction with a denominator of 10 as a fraction with a denominator with 100.
• Recognize that two fractions with unlike denominators can be equivalent.
• Use knowledge of renaming tenths to hundredths to add two fractions with denominators 10 and 100.
MAFS.4.NF.3.6 (DOK 1) Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62
meters; locate 0.62 on a number line diagram. [Conceptual Understanding]
• Explain the values of digits in the decimal places.
• Read and write decimals through hundredths.
• Rename fractions with 10 and 100 in the denominator as decimals.
• Recognize multiple representations of fractions with denominators 10 and 100.
• Represent fractions with denominators 10 or 100 with multiple representations and decimal notation.
• Explain how decimals and fractions are alike.
MAFS.4.NF.3.7 (DOK 2) Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two
decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
[Conceptual Understanding; Procedural Skill and Fluency]
• Recognize that comparisons are valid only when the two decimals refer to the same whole.
• Compare two decimals to hundredths by reasoning about their size.
•
Justify the conclusions using visual models and other methods.
MAFS.4.MD.1.2 (DOK 2) Use the four operations to solve word problems involving distances, intervals of time and money, including problems involving
simple fractions or decimals. Represent fractional quantities of distance and intervals of time using linear models. [application]
• Express measurements given in a larger unit in terms of a smaller unit.
• Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
• Solve word problems involving distances, intervals of time and money.
• Solve world problems involving measurement that include simple fractions or decimals.
• Solve word problems that require expressing measurements given in a larger unit in terms of a smaller unit.
Math Practice Standard(s)
Link to Mathematical Practice Standards Rubric
MAFS.K12.MP.6.1 Attend to precision.
MAFS.K12.MP.7.1 Look for and make use of structure.
Suggested Learning Progression
The following learning progression provides students with an opportunity to
construct meaning and create connections through the CRA Method:
Concrete – Representational – Abstract.
*Collaborative teams should be selective in choosing standards-aligned tasks
for instruction and assessment. Teams may adjust the sequence and use
additional resources based on the needs of their students.
Topic 12: Understand and Compare Decimals
Sample Thinking Map: Understand & Compare Decimals
Teachers may use this map for professional development or as a teaching
tool. This map is a continuation from Topic 3. Teachers should be selective in
choosing strategies that they feel will benefit their students’ understanding
of the standard.
• Additional Resources:
o Georgia Units -- Unit 5-- Decimal Fraction Number Line (Use
as an introduction to decimals)
Lesson 12-1: Fractions and Decimals
• Additional Resource: EngageNY – Module 6 Topic A Lesson 2
Lesson 12-2: Fractions and Decimals on the Number Line
• Additional Resources:
Recommended Instructional Sequence
This instructional sequence is intended to provide a framework for student
learning. Various options are listed below each step in the sequence.
Collaborative teams may adjust the sequence as necessary to meet the needs
of their students.
Step 1: 5-Minute Spiral Review
• Pearson Daily Review
• Common Misunderstandings or Errors
Step 2: Problem-Based Learning
• Solve and Share
• Math Formative Assessment System (MFAS) Tasks by Standard
• Illustrative Mathematics Tasks by Standard
Step 3: Focus Lesson & Opportunities for Practice
• Visual Learning Bridge
• Guided Practice
• Thinking Map/Graphic Organizer
• Collaborative work
• Interactive Notebook
• Independent Practice
• Whole Group i-Ready Lesson
• Task Oriented Instruction
(additional opportunities for PBL)
Step 4: Differentiated Instruction
• Small group instruction
• Guided Practice
• Centers/stations (including i-Ready) • Intervention/Enrichment
Step 5: Student Debrief
• Thinking Map/Graphic Organizer
• Reflection
o So what? What did you
• Exit Ticket
learn?
• Interactive Notebook
o
o
i-Ready Lesson (Number & Operations): Renaming Fractions
as Decimals
EngageNY – Module 6 Topic A Lesson 1, Topic B Lesson 6
o
Lesson 12-3: Compare Decimals
• Additional Resources:
o Georgia Units Unit 5: “Decimal Line-Up”
o EngageNY – Module 6 Topic C Lessons 9 - 11
Lesson 12-4: Add Fractions with Denominators Of 10 and 100
• Additional Resource:
o i-Ready Lesson (Number & Operations): Fractions as Tenths
and Hundreths
o Georgia Units Unit 5: “Dismissal Duty Dilemma”
o EngageNY – Module 6 Topic D Lessons 12-14
Lesson 12-5: Solve Word Problems Involving Money
• Additional Resource: i-Ready Lesson (Number & Operations):
Decimal Notation Using Money
Lesson 12-6: Math Practices and Problem Solving: Look For and Use Structure
Professional Development
EngageNY Math Studio Talk: Common Core Instruction for
4.NF
This video addresses strategies for developing fraction
number sense. This segment focuses on denominators of 10
and 100. (12:40 – end of video) * YouTube must already be
opened on your browser before clicking the link.
Marzano Proficiency Scales Bank
Common Core Flip Books: Provides additional information
and sample problems for every standard
FSA Test Item Specifications
•
•
•
•
•
•
•
•
•
So why? Why is it
important?
Higher Order Questions & Writing Connections
Link to Webb’s DOK Guide
*Higher order questions should be utilized to foster a deep, conceptual
understanding of the topic. Encouraging students to express their
mathematical thinking in writing helps them solidify their learning.
How are decimal numbers and fractions related?
How can I write a decimal to represent a part of a group?
What are the characteristics of a decimal fraction?
What models can be used to represent decimals?
What patterns occur on a number line made up of decimal fractions?
When can tenths and hundredths be used interchangeably?
When is it appropriate to use decimal fractions?
When we compare two decimals, how do we know which has a greater
value?
Why is the number 10 important in our number system?
Resources
Pearson enVisionMath2.0
Home-School Connection Page
Reteaching Pages
Daily Review
Florida Interim Assessment Item Bank and Test Platform
Math Formative Assessment System (MFAS) Tasks by Standard
CPALMS - MFAS includes tasks and rubrics that the teacher can
implement with their students.
Illustrative Mathematics Tasks by Standard
The site illustrates standards with impeccably crafted tasks,
videos, lesson plans, and curriculum modules.
•
•
•
•
•
•
Essential Vocabulary
tenth
hundredths
decimal
decimal point
common
denominator
equivalent fractions