Grade 4 Math Unit 4

4th Math Unit 4 Updated December 2, 2015 Page 1 of 19

Title Suggested Time Frame Unit 4 – Fractions, Measurement, and Data Analysis 4th and 5th Six Weeks

Suggested Duration: 30 days Big Ideas/Enduring Understandings Guiding Questions

• There is a need to be able to identify, read, write, and compare numbers beyond whole numbers.

• Measurement requires an understanding of the relationship among units.

• The number of weight or mass units can be determined by reading a measuring tool.

• What is the relationship between a fraction and decimal is as represented on a number line or in a pictorial model?

• How could you use a pictorial model to represent both a mixed number and an improper fraction?

• How can parts of a whole be useful in measuring length? • What are the standard units of measure in customary units? • What are the standard units of measure in metric units?

Vertical Alignment *TEKS one level below* *TEKS one level below*

TEA MATH VERTICAL ALIGNMENT—K-6th Grade

Sample Assessment Question Coming soon!

Grade 4 Math Unit 4

4th Math Unit 4 Updated December 2, 2015 Page 2 of 19

The resources included here provide teaching examples and/or meaningful learning experiences to address the District Curriculum. In order to address the TEKS to the proper depth and complexity, teachers are encouraged to use resources to the degree that they are congruent with the TEKS and research-based best practices. Teaching using only the suggested resources does not guarantee student mastery of all standards. Teachers must use professional judgment to select among these and/or other resources to teach the district curriculum. Some resources are protected by copyright. A username and password is required to view the copyrighted material. District Specificity/Examples TEKS clarifying examples are a product of the Austin Area Math Supervisors TEKS Clarifying Documents.

Ongoing TEKS

4.01 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

(A) apply mathematics to problems arising in everyday life, society, and the workplace; • Focus is on application

(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;

(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;

• Students should assess which tool to apply rather than trying only one or all

(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

(E) create and use representations to organize, record, and communicate mathematical ideas;

• Students should evaluate the effectiveness of representations to ensure they are communicating mathematical ideas clearly

• Students are expected to use appropriate mathematical vocabulary and phrasing when communicating ideas

(F) analyze mathematical relationships to connect and communicate mathematical ideas; and • Students are expected to form conjectures based on patterns or sets of examples and non-examples

(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication

• Precise mathematical language is expected.

Grade 4 Math Unit 4

4th Math Unit 4 Updated December 2, 2015 Page 3 of 19

Knowledge and Skills

with Student Expectations

District Specificity/ Examples

Vocabulary

Resources

Resources listed and categorized to indicate suggested uses. Any

additional resources must be aligned with the TEKS.

FRACTIONS---15 days

MAT.4.03 Number and operations. The student applies mathematical process standards to represent and generate fractions to solve problems. The student is expected to: (A) represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b > 0, including when a > b

Supporting vocabulary – decompose fractions, improper fraction, mixed number 4.03A A fraction with a numerator of one is called a unit fraction. When students investigate fractions other than unit fractions, such as 2/3, they should be able to join (compose) or separate (decompose) the fractions of the same whole. Example: 2/3 = 1/3 + 1/3 Being able to visualize this decomposition into unit fractions helps students when adding or subtracting fractions. Students need multiple opportunities to work with mixed numbers and be able to decompose them in more than one way. Students may use visual models to help develop this understanding. Example of word problems: Mary and Lacey decide to share a pizza. Mary ate 3/6 and Lacey ate 2/6 of the pizza. How much of the pizza did the girls eat together? Possible solution: The amount of pizza Mary ate can be thought of a 3/6 or 1/6 and 1/6 and 1/6. The amount of pizza Lacey ate can be thought of a 1/6 and 1/6. The total amount of pizza they ate is 1/6 + 1/6 + 1/6 +1/6 + 1/6 or 5/6 of the whole pizza.

• denominator • equal parts • fraction • numerator • sum of fractions • unit fractions • whole • distance • equal parts of a

whole • equivalent

fractions • identity

property • number line • equation/numb

er sentence • common

denominator • comparison

symbol • greater than (>) • less than (<) • equal to (=) • addition • subtraction • sum

HMH GoMath Modules 3, 4 & 5 Fractions as Numbers

• National Center on Intensive Intervention: Develop an understanding of fraction skills

Region 11 Livebinder http://illuminations.nctm.org/ 4.3A HMH GoMath Module 3.5 Motivation Math – Unit 9

Grade 4 Math Unit 4

4th Math Unit 4 Updated December 2, 2015 Page 4 of 19

(B) decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (C) determine if two given fractions are equivalent using a variety of methods

Example with mixed numbers: A cake recipe calls for you to use ¾ cup of milk, ¼ cup of oil, and 2/4 cup of water. How much liquid was needed to make the cake?

4.03B Students should justify their breaking apart (decomposing) of fractions using visual fraction models.

4.03C

• difference • equal

denominators • properties of

operations • benchmark

fraction • parts of a whole • reasonableness

Lesson Plan – Unit Fractions

• Lesson 5 specifically focuses on Unit Fractions

4.3B HMH GoMath Module 3.6 YouTube Video

• Decomposing fractions into addition

4.3C HMH GoMath Module 3.1-3.4

Grade 4 Math Unit 4

4th Math Unit 4 Updated December 2, 2015 Page 5 of 19

(D) compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <

This standard addresses equivalent fractions by examining the idea that equivalent fractions can be created by multiplying both the numerator and denominator by the same number or by dividing a shaded region into various parts.

4.03D This standard calls students to compare fractions by creating visual fraction models or finding common denominators or numerators. Students’ experiences should focus on visual fraction models rather than algorithms. When tested, models may or may not be included. Students should learn to draw fraction models to help them compare. Students must also recognize that they must consider the size of the whole when comparing fractions (ie, ½ and 1/8 of two medium pizza’s is very different from ½ of one medium and 1/8 of one large).

Motivation Math – Unit 10 Brain Pop Lessons Equivalent Fractions: It Means the Same

• Lesson plan Equivalent Fraction Maze Game 4.3D Motivation Math – Unit 11 Common Denominator War

Grade 4 Math Unit 4

4th Math Unit 4 Updated December 2, 2015 Page 6 of 19

(E) represent and solve addition and subtraction of fractions with equal

Example: There are two cakes on the counter that are the same size. The first cake has half of it left. The second cake has 5/12 left. Which cake has more left?

4.03E

Comparing with Common Denominators Lesson Comparing Fractions Game 4.3E

Grade 4 Math Unit 4

4th Math Unit 4 Updated December 2, 2015 Page 7 of 19

denominators using objects and pictorial models that build to the number line and properties of operations

A separate algorithm for mixed numbers in addition and subtraction is not necessary. Students will tend to add or subtract the whole numbers first and then work with the fractions using the same strategies they have applied to problems that contained only fractions.

4.03E Visual examples continued on next 2 pages…..

HMH GoMath Module 5 Motivation Math – Unit 12 Khan Academy Study Jams

• Add and subtract with common denominators

Grade 4 Math Unit 4

4th Math Unit 4 Updated December 2, 2015 Page 8 of 19

Grade 4 Math Unit 4

4th Math Unit 4 Updated December 2, 2015 Page 9 of 19

(F) evaluate the reasonableness of

sums and differences of fractions using benchmark

fractions 0, 1/4, 1/2, 3/4, and 1, referring to the same

whole

4.03F Students use benchmark fractions to estimate and examine the reasonableness of their answers. Students will recognize that comparisons are valid only when the two fractions refer to the same whole.

4.3F HMH GoMath Unit 5.4 Motivation Math – Unit 13

Grade 4 Math Unit 4

4th Math Unit 4 Updated December 2, 2015 Page 10 of 19

Estimating fractions using benchmark fractions

Grade 4 Math Unit 4

4th Math Unit 4 Updated December 2, 2015 Page 11 of 19

Grade 4 Math Unit 4

4th Math Unit 4 Updated December 2, 2015 Page 12 of 19

MEASUREMENT – 10 days

Although 4.5C is not a direct teach for the measurement unit, this is a prime opportunity to spiral and review area and perimeter.

MAT.4.08 Geometry and measurement. The student applies mathematical process standards to select

4.08A

• customary • length • liquid volume • mass • measurement

units

HMH GoMath Modules 15 & 16 Region 11 Livebinder

Grade 4 Math Unit 4

4th Math Unit 4 Updated December 2, 2015 Page 13 of 19

appropriate customary and metric units, strategies, and tools to solve problems involving measurement. The student is expected to: (A) Identify relative sizes of measurement units within the customary and metric systems (B) Convert measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table

Students develop benchmarks and mental images about meter and a kilometer and they also understand that “kilo” means a thousand, so 3000m is equivalent to 3km. Ex: … about the height of a tall chair, the length of 10 football fields, the distance a person might walk in about 12 min.

4.08B Students need ample opportunities to become familiar with these new units of measure and explore the patterns and relationships in the conversion tables that they create. Students may use a two-column chart to convert from larger to smaller units and record equivalent measurements. They make statements such as, if one foot is 12 inches, then 3 feet has to be 36 inches because there are 3 groups of 12.

• metric • relative size • equivalent

measures • larger unit to

smaller unit • measurements • smaller unit to

larger unit • table • addition • division • money • multiplication • perimeter • time • subtraction

http://illuminations.nctm.org/ 4.8A Activity - Relative size in metric system Activity – Matching relative sizes in customary system 4.8B Study Jam – Customary Units of Length Activity – Customary Units of Capacity (Conversion) Activity – Metric Units of length (Conversion)

Grade 4 Math Unit 4

4th Math Unit 4 Updated December 2, 2015 Page 14 of 19

Conversion Rule and Visual: http://www.studyzone.org/mtestprep/math8/g/convertunitmeasless.cfm

BIGUNIT

SMALLUNIT

X÷ Conversion Wheel

Grade 4 Math Unit 4

4th Math Unit 4 Updated December 2, 2015 Page 15 of 19

(C) Solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate.

4.08C

Students will use the four operations to solve word problems involving distance, volume, mass and money.

4.8C Study Jams - Measurement Motivation Math – Unit 34

Grade 4 Math Unit 4

4th Math Unit 4 Updated December 2, 2015 Page 16 of 19

Grade 4 Math Unit 4

4th Math Unit 4 Updated December 2, 2015 Page 17 of 19

DATA ANALYSIS – 5 days MAT.4.09 Data analysis. The student applies mathematical process standards to solve problems by collecting, organizing, displaying, and interpreting data. The student is expected to: (A) represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions

4.09A Students need to be able to identify different types of graphs. Students need to be able to collect data to put into charts and graphs. Students need to be able to create each of the following types of graphs: • Frequency Table • Dot plots/Line graphs • Stem & Lear Plot

Dot plots are simple plots on a number line where each dot (X) represents a piece of data in the data set. Dot plots are suitable for small to moderate size data sets and are useful for highlighting the distribution of the data including clusters, gaps, and outliers.

A histogram shows the distribution of continuous data using intervals on the number line. The height of each bar represents the number of data values in that interval. In most real data sets, there is a large amount of data and many numbers will be unique. A graph (such as a dot plot) that shows how many ones, how many twos, etc. would not

• categories • data • dot plot • frequency table • whole numbers • graph tiles • labels • scaled intervals • stem-and-leaf

plot • fractions • categorical data • decimal

HMH GoMath Module 17 Create a graph Region 11 Livebinder http://illuminations.nctm.org/ 4.9A Study Jam – Stem and Leaf Plots

Grade 4 Math Unit 4

4th Math Unit 4 Updated December 2, 2015 Page 18 of 19

be meaningful. Students group the data into convenient ranges and use these intervals to generate a frequency table and histogram.

On the other hand, you could make a stem-and-leaf plot for the same data:

Grade 4 Math Unit 4

4th Math Unit 4 Updated December 2, 2015 Page 19 of 19

(B) solve one- and two-step problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot

The “stem” is the left-handed column which contains the tens digit. The “leaves’ are the lists in the right-handed column, showing all the ones digits for each of the tens, twenties, thirties, and forties. As you can see the original values can still be determined; you can tell where 40, 40, and 41 are in the stem-and-leaf plot.

4.09B Students need to be able to read graphs and analyze the data. Students need to be able to make predictions from analyzing graphs.