2015-2016 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
3rd 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.
th
5 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?
Textbook Correlation
Recommended Instructional Sequence
Essential Vocabulary
*Be selective in choosing problems aligned to the standards
Step 1: Problem-Based Learning “Solve and Share”
 tenth
within the topic. Lessons and problems used for instruction
Problem-Based Learning Lesson Flow Map
 hundredths
and assessment should be determined through collaborative
Conceptual understanding is developed when mathematics is
 decimal
unit planning.
introduced in the context of solving a real problem in which
 decimal point
ideas related to the new content are embedded. Conceptual
understanding results because the process of solving a problem
Topic 12: Understand and Compare Decimals
requires students to connect their prior knowledge with the new
Lesson 12-1: Fractions and Decimals
concept or procedure (Charles, R., Bay-Williams, J., et al., 2016).
Lesson 12-2: Fractions and Decimals on the Number Line
Lesson 12-3: Compare Decimals
Each lesson in the book begins with a Solve and Share. See the
Lesson 12-4: Add Fractions with Denominators Of 10 and
links below for additional tasks to be used as needed:
100
Math Formative Assessment System (MFAS) Tasks by Standard
Lesson 12-5: Solve Word Problems Involving Money
Illustrative Mathematics Tasks by Standard
Lesson 12-6: Math Practices and Problem Solving: Look For
and Use Structure
Step 2: “Visual Learning Bridge”
Enhance student learning by connecting student thinking and
solutions from the Solve and Share to the new ideas of the
lesson through the use of the worked-out problem in the
textbook.
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.
 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.
 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.
 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.
 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.
MAFS.4.OA.1.a Determine whether an equation is true or false by using comparative relational thinking. For example, without adding 60 and 24, determine
whether the equation 60 + 24 = 57 + 27 is true or false.
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.
Additional Resources & Links
Georgia Units
Unit 5
 Decimal Line-Up
 Expanding Decimals with Money
EngageNY - Module 5
Topic A
Topic B
Topic C
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.
www.pearsonrealize.com
Home-School Connection Page
Reteaching Pages
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.
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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?
Marzano Proficiency Scales Bank
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.
Common Core Flip Books: Provides additional information and sample problems
for every standard
FSA Test Item Specifications
Spiral Review
*Consistent review of previously learned standards allows students multiple opportunities to master and build fluency with mathematical concepts and
procedures.
www.pearsonrealize.com
Daily Review 12-1 through 12-6