Elementary Mathematics

5th Grade Unit 8: Growth Patterns


Unit at a Glance

Suggested Dates:

April 23- May 6

Estimated Duration:
10 days/10 lessons

Investigation 1: 3 lessons (combine 1.1 & 1.2 and
1.4 & 1.5)

Investigation 2: 4 lessons
(2.1-2.4 only)

1 day Geometry within the coordinate plane lesson

2 days Coordinate Graphing- Complete the Robots and Coordinates Performance Task from Smarter Balanced


*Note- The Common Core adaptation for Ten-Minute Math (Practicing Place Value) includes expanded form.



Tools for Teachers

Coordinate Graphing Game  Catch the Fly

Practice evaluating mathematical expression

5.OA.3  Coordinate Plane Activity

Algebraic Expression Match Activity

Real World 5G2 Activities

IXL Common Core Skill Activities

Coordinate Grid Examples 5G

Brackets, braces and parentheses EXPLANATION

End of Unit Assessment  rubric for Unit 8

5th Grade Vocabulary

Investigations Vocabulary

Investigations Unit Vocabulary

Extension Projects
                       
3-5 Literature List

STANDARDS FOR MATHEMATICAL PRACTICE

MP4.  Are your students thinking about the relationships between the data to see if it makes sense?  In what ways could they model using these mathematical representations in real life?  What equations do students use as they model the pattern?

MP7.  Can your students understand how numbers and spaces are organized and put together?  Are they able to understand the location on grids and make use of this structure?  Where and when might a grid be used in real life? In what ways do students discover patterns in the data?  How can you encourage them to find the rule and continue the graph while making sense of the pattern?



TEAM TIME!
DISCUSS THE FOLLOWING WITH YOUR GRADE LEVEL TEAM:

Can placing a line graph’s data on a table help students find a pattern?  What is a constant rate of change? How does a line graph show values and changes in values? 

 

Read p. 116-119 and discuss any “AHA” moments you might have.  Do any of these ideas relate to your students?  How?


 Read p.125 in the Teacher’s Manual, “Assessment: Comparing Animals’ Growth.” Next, create an activity that your students can practice these skills using realistic data.  How will this be helpful?  Will you require your students to show evidence of their findings?  Will the students be able to draw conclusions based on the data?  How?

What's the difference between linear and nonlinear change?  Read "Understanding Linear and Nonlinear Change" on pages 13-14 with your team in Unit 8 and discuss.   

When students find a 'rule' and record it as an expression, they are Modeling with Mathematics.  Is it possible to write a 'rule' when the rate of change is not constant?   Pages 130-132 in Unit 8 address this and other issues regarding rates of change.

OPPORTUNITIES FOR DIFFERENTIATION...

Suggestions for students who are struggling…

Have them work in a small group to create their own table and graph. Allow these children to measure their own heights, write them in a table and plot them on a graph.  This experience can make it more “real” to the students because they will be using personal data. 

Suggestions for students who fully understand…

Students might enjoy creating their own set of data related to a make believe animal or researching data of a real animal.  The students can use the data to place in a table and then graph to find the rate of change.  Can they come up with an equation for this animal? 

While doing “The Doubling Penny Jar” the students could increase the number of rounds to calculate the number of pennies and a matching equation.


*Remember to upload files to share with others, or locate files to use, on the wiki. Be sure to join discussion posts with other colleagues to ask questions, answer questions, and discuss math.
Common Core Standards in the Unit


Link to CCSS Unpacking Document- Updated Sept. '14



Graph points on the coordinate plane to solve real-world and mathematical problems.

5.G.1. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

5.G.2. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Write and interpret numerical expressions.

5.OA.1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

5.OA.2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

Analyze patterns and relationships.

5.OA.3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.



Words you should hear students use in Mathematical Conversations...

rate of change, steady rate,  area, perimeter, parentheses, brackets, braces, numerical expressions, coordinate grid, coordinate plane, x-axis, y-axis, first quadrant, point, lines, coordinate plane, ordered pairs, horizontal, vertical, pattern, rules

Ask students to think, pair, share; “How can you compare data with a table?”  Look for students to use the following words: x-axis, pattern, y-axis

Have a student choose 3 words from the list below.  Ask students to whisper something to their partner using at least 2 of the words.  Then have several students share what they heard someone else say.





TAKE NOTE FORE EACH INVESTIGATION
Investigation 1 focuses on 5.OA.3 and 5.NBT.3, 5.G.1 and 5.G.2.  The students use tables and graphs to represent constant rates of change.  They must also take in account a situation that has a beginning amount. 

They will also focus on rates that are nonlinear or do not have a constant rate of change but can be determined.

Be sure to read the unpacking section for 5.OA.3. and add more opportunities for students to work with the concepts in 5.OA.3.



Investigation 2 focuses on 5.OA.1, 5.OA.2, 5.OA.3, 5.G.1 and 2.  The students will continue to use tables and graphs but will also evaluate the steepness of the graph.  They will also write and use mathematical expressions based on the data. Students will also calculate the perimeter and area of a rectangle.





TEN MINUTE MATH! 
Practicing Place Value

Students will read and write numbers up to 100,000, add and subtract multiples
of 10 from 3-5 digit numbers, read and write decimal and fraction numbers,
add and subtract tenths and hundredths from decimal fractions and numbers.

*Note- The Common Core adaptation for Ten-Minute Math (Practicing Place Value) includes expanded form.
Estimation and Number Sense

The students will estimate solutions for 3-5 digit addition and subtraction problems and practice breaking apart and reordering numbers mentally.