5th Grade Elementary Math Planning Guide 2012-2013 DRAFT
5th Year at a Glance DRAFT = Holiday/Workday/Annual Leave = Flex Day
1st Quarter: 44 daysM / T / W / Th / F
Aug / 28 / 29 / 30 / 31
Sep / 4 / 5 / 6 / 7
10 / 11 / 12 / 13 / 14
17 / 18 / 19 / 20 / 21
24 / 25 / 26 / 27 / 28
Oct / 2 / 3 / 4 / 5
8 / 9 / 10 / 11 / 12
15 / 16 / 17 / 18 / 19
22 / 23 / 24 / 25 / 26
2nd Quarter: 46 days
M / T / W / Th / F
Oct / 30 / 31 / Nov / 2
5 / 6 / 7 / 8 / 9
12 / 13 / 14 / 15 / 16
18 / 20 / 21 / 22 / 23
26 / 27 / 28 / 29 / 30
Dec / 4 / 5 / 6 / 7
10 / 11 / 12 / 13 / 14
17 / 18 / 19 / 20 / 21
24 / 25 / 26 / 27 / 28
31 / Jan / 2 / 3 / 4
7 / 8 / 9 / 10 / 11
14 / 15 / 16 / 17 / 18
3rd Quarter: 46 days
M / T / W / Th / F
Jan / 22 / 23 / 24 / 25
28 / 29 / 30 / 31 / Feb
4 / 5 / 6 / 7 / 8
11 / 12 / 13 / 14 / 15
18 / 19 / 20 / 21 / 22
25 / 26 / 27 / 28 / Mar
4 / 5 / 6 / 7 / 8
11 / 12 / 13 / 14 / 15
18 / 19 / 20 / 21 / 22
25 / 26 / 27 / 28 / 29
4th Quarter: 44 days
M / T / W / Th / F
Apr / 2 / 3 / 4 / 5
8 / 9 / 10 / 11 / 12
15 / 16 / 17 / 18 / 19
22 / 23 / 24 / 25 / 26
29 / 30 / May / 2 / 3
6 / 7 / 8 / 9 / 10
13 Eog? / 14
Eog? / 15 Eog? / 16 Eog? / 17 Eog?
20 / 21 / 22 / 23 / 24
27 / 28 / 29 / 30 / 31
Jun / 4 / 5 / 6 / 7
UNIT 1: NUMBER PUZZLES & MULTIPLE TOWERS Grade:5
Begin With The End In Mind / Unit at a Glance – 19 LessonsJournal Task: While multiplying 365 x 27, Monica multiplied 365 x 9 and then multiplied the product by 3. Sebastian multiplied 365 x 20 and 365 x 7 and added the two products. Which one is correct? Explain how you know. / Investigation 1: Finding Factors and Prime Factors
-4 Lessons (1.1-1.4 only)
Investigation 2: Multiplication Strategies
-7 Lessons 2.4a (combine 2.4-2.5)
Investigation 3: Division Strategies -8 Lessons
Common Core Clusters and Standards addressed in this unit / Standards for Mathematical Practice
Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.5 and 5.NBT.6
Write and interpret numerical expressions. 5.OA.1 and 5.OA.2
Understand the place value system. 5.NBT.2 / What opportunities can you give students to model with mathematics in this unit?
How can looking for and making use of place value structures lead students to understand strategies?
Take Note!
Notes about each Investigation / 1 / During this Investigation, students work with standard 5.NBT.5 and 5.NBT.6. Make sure to read this portion of the DPI Unpacking document before teaching this unit for detailed examples of solving problems using strategies based on place value, properties of operations, and/or the relationship between multiplication and division. Spend the first few lessons making sure that students are successful with the numbers in Investigations before moving students to larger numbers.
2 / During this Investigation, students work with standard 5.NBT.5 in their work halving and doubling factors.
Many students use the open array with little understanding about the connection to the distributive property. Record representations for 18x14 as (18x10)+(18x4). Explicitly remind students about the term “distributive property” and model it throughout this unit.
Session 2.4a includes work on the order of operations. After this session, integrate brackets, braces and parenthesis into quick images work *See Quick Images note below.
3 / Creating multiple towers will help students reason about the magnitude of number (5.NBT.1)
The doubling and halving work directly relates to standard 5.NBT.5
5.NBT.6- Find whole number quotients using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain using equations, arrays, and area models.
Unit 1- Continued
Ten-Minute Math / The Language of MathematicsActivity / Product
Quotient
Operations
Multiples
Factors
Reasonableness
Distributive Property
parentheses, brackets, braces, numerical expressions
Quick Images / As students solve quick images, record their solutions using parenthesis, brackets, and braces (5.OA.1) where applicable. For example, if a student says, “I saw 3 groups of 8 dots which is 24, then 6 more dots” record as (8x3)+6. Ask students if the solution would be the same if you solved it like this: 8 x (3+6) The goal is to introduce parenthesis, brackets, and braces so that students realize why they are used. See DPI Unpacking document pages 5-6.
Today’s Number / Teacher will assign a number of the day and students will write as many numerical expressions as possible with that solution. Encourage students to use parentheses and brackets in these.
What to use when students are struggling with the work in this unit / I have students who clearly understand, what other learning opportunities can I provide?
2-digit by 1-digit
Array cards (gr 3)
Big array/small array (gr 4)
Open array- breaking numbers apart by place value / Avoid moving to working with larger numbers during this unit. Students should have extensive experiences with 2-digity by 2-digit multiplication before working with multiplying by a 3-digit number. If students are proficient with 1 strategy, ask them to respond to questions like, “How is your strategy similar to, or different from, ___’s?”
Technology Connections
Standard(s) / Link/Resource
5.NBT.6 / http://www.teachertube.com/viewVideo.php?video_id=265802&title=Division_and_Multiplication_Models_and_Related_Number_Sentences_2 This is a great video that uses base-10 blocks to model numbers and them shows how to divide them into groups. Great for visual learners.
5.NBT.7 / http://player.discoveryeducation.com/index.cfm?guidAssetId=0af38e35-fc74-4119-ba0e-34c3296993ee This video shows real life examples of using multiplication and division in the sports world.
Professional Learning Opportunities
Read the information on Standards 5.NBT.2, .5 and 6 as well as 5.OA.1 and 5.OA.2 in the DPI Unpacking document before teaching this unit.
Unit 1 page 161 in teacher’s edition- Multiplication Strategies. This will explain the different strategies available to students while learning the multiply or divide.
Unit 1 page 171 in teacher’s edition- Developing Computations Strategies that Make Sense. This reading helps to make sense of why we are teaching the students the methods and strategies in this unit.
Read pages the information on standards 5.NBT.2, .5 and 6 as well as 5.OA.1 and 5.OA.2 in the DPI Unpacking document before teaching this unit.
UNIT 2 Grade:5
Begin With The End In Mind / Unit at a Glance – 12 LessonsExplain the relationship between the volume and the area of the base of a rectangular prism.
If we had a cube that was 2 units wide, 2 units long, and 2 units tall and then doubled each of the dimensions what would happen to the area of the base and the volume? How do you know? / Investigation 1: Finding the Volume of Boxes –
8 Lessons (incl. 1.5A)
Investigation 2: Using Standard Cubic Units-
4 Lessons (incl. 2.4A)
Investigation 3: SKIP this Investigation
Common Core Clusters and Standards / Standards for Mathematical Practice
5.MD3 a & b: Recognize and understand concepts of volume measurement using a unit cube; a solid figure is said to have “n” cubic units
5.MD4 a, b &c : find the volume by filling a figure with centimeter cubes and by using the formula, understand the volume will be the same / How can students use tools to find the volume of a solid figure?
How can students model volume with an equation?
Have the students extend their understanding by applying mathematical formulas.
Take Note!
Notes about each Investigation / 1 / Introduce volume by building boxes and filling with centimeter cubes. After experiences filling a rectangular prism with cubes, allow students to come up with a formula. Make explicit connections between the number of cubes and the formula.
2 / Introduce volume units by cubic measures. The students will build models of cubic units of measure and determine the best unit of cubic measure to measure a large area. Make sure to provide experiences in which students are given two dimensions and the volume, but must find the third dimension (e.g., A rectangular prism is 5 cm long, 3 cm wide and has a volume of 90 cubic centimeters. How tall is the prism?”
Ten-Minute Math / The Language of Mathematics
Activity / Attribute
Volume
Cubic units
Area
dimentions
Quick Images: 3D / 5.MD.5c briefly view a 3D structure, build it from a mental image using cubes
Estimation and number sense / 5.NBT.6given a multiplication or division equation, use strategies to get the best estimate
What to use when students are struggling with the work in this unit / I have students who clearly understand, what other learning opportunities can I provide?
http://www.uen.org/Lessonplan/preview?LPid=28403
in this lesson the students will make a solid shape using play dough, for an extension to further their understanding, have the students build the same shape using centimeter cubes and compare the volume found from the formula with the play dough and the volume found by counting the centimeter cubes. / http://illuminations.nctm.org/LessonDetail.aspx?id=L783
here is an activity that uses volume of a hay bale and find which hay bale is a better price by volume
Technology Connections
Standard(s) / Link/Resource
5.MD.5b / www.youtube.com/watch?v=JijhDDJvExo
this is a volume song
5.MD.5c / library.thinkquest.org/20991/geo/solids.html
how to find the volume of many types of solid figures
5.MD.3
5.MD.4
5.MD.5 / www.onlinemathlearning.com/solid-geometry.html
games, worksheets and extra practice
Professional Learning Opportunities
http://www.articlesbase.com/homeschooling-articles/how-to-find-the-volume-of-a-cuberectangular-solid-or-cylinder-70610.html#.T8bC8Tc5k_8.email
http://www.mhpdonline.com/video_library/index.php?PROGRAM=46&VIDEO=-1&MODE=NG5&CHAPTER=9
Teacher note, p. 115- strategies for finding how many packages- suggest trying the activity before presenting it to your class
DPI Unpacking Doucment
Unit 3: Thousands of Miles, Thousands of Seats
Begin With The End In Mind / Unit at a Glance – 13 LessonsExplore the inverse relationship between addition and subtraction and multiplication and division. How can you use the inverse relationship to solve equations with the US standard algorithm? / Investigation 1: Using Place Value
– 5 Lessons
Investigation 2: Studying Subtraction
-2 Lessons (Omit 2.4 and 2.5)
Investigation 3: Adding and Subtracting Large Numbers
-5 Lessons
Common Core Clusters and Standards / Standards for Mathematical Practice
5.NBT.1- given a multi-digit number, the number in the ones place represents 10 times as much as the number to its right and 1/10 the number to its right
5.NBT.5- fluently multiply whole numbers using the US algorithm
5.NBT.6- find whole number quotients of 4 digit by 2 digits using a variety of strategies / What kinds of patterns can the students find when solving equations with powers of 10? (MP 8)
What tasks can you pose to students to provide opportunities for them justify and prove their understanding? (MP 2, MP 3)
What questions can you pose to assess students’ understanding of place value? (MP 8).
Take Note!
Notes about each Investigation / 1 / Using Place Values- The students use place-value relationships and multiples of 10, 100, and 1000 to add and subtract large numbers. Make sure to emphasize how numbers can be decomposed by place (1,682 = 1,000 + 600 + 80 +2) to support their addition and subtraction work.
2 / Studying Subtraction- The students investigate various strategies for subtracting large numbers. Remember to encourage students to be more efficient using larger chunks as they break numbers apart, use the open number line, and solve subtraction tasks.
3 / Adding and Subtracting Large Numbers- Students refine various strategies and use what they know about place value to solve addition and subtraction problems involving large numbers. In this investigation, Close to 7,500 can be modified to be an easier game (Close to 1,000 is a 4th grade game), or a more difficult game, such as Close to 6,111 or a number that requires students to use addends that will require students to have more than 10 in a given place and have to trade (10 ones for a 10, 10 tens for a 100, etc.)
Unit 3- Continued
What to use when students are struggling with the work in this unit / I have students who clearly understand, what other learning opportunities can I provide?Use 2-digit and 3-digit numbers when working with situations that involve crossing over a decade.
Fluency with addition and subtraction facts can be further developed through activities such as Tens Go Fish (Grade 2) and Roll and Record Subtraction (Grade 1 and 2). / Students that have a clear understanding of addition and subtraction should explore other strategies. Investigation 2.4 involves exploring why the subtraction algorithm works. Having students compare similarities and differences between the U.S. standard algorithm and alternative algorithms is appropriate for all students.
Pose multi-step tasks that involve both addition and subtraction that require students to determine which operation to use.
Ten-Minute Math / The Language of Mathematics
Activity / Tenths
Hundredths
Powers
Properties
Quotient
Product
Sum
Difference
Practicing Place value / Students practice reading, writing and saying numbers up to 100,000. Add and Subtract multiples of 10 examining the changes in place value.
Estimation and Number Sense: Closest Estimate / The students choose the closest estimate of a given multiplication or division problem solving the equation mentally
Technology Connections
Standard(s) / Link/Resource
5.NBT.5 / http://www.youtube.com/watch?v=n1VHRxOU9-s&feature=related
Video about subtracting with regrouping without actually regrouping.
5.NBT.5 / www.youtube.com/watch?v=0fKBhvDjuy0
This is a science connection to powers on 10, Every ten seconds we
view the starting point from ten times farther out until our own galaxy is barely visible
5.NBT.1 / cdsearch.britannica.com/lm/games/GM_3_9/GM_3_9.htm
computer game that adds and subtracts powers of 10
Professional Learning Opportunities
Dialogue Boxes, Unit 3, p. 142-147
Teacher note, unit 3, page 113- Place Value, exploring the base-ten system
Unpacking DPI
Unit 4: What’s That Portion? Fractions and Percents