Grade



Grade 5

Quarter One

Content Strand:

NUMBER SENSE AND BASE TEN

Standard:  5.NSBT.1

Understand that, in a multi-digit whole number, a digit in one place represents 10 times what the same digit represents in the place to its right, and represents 1/10 times what the same digit represents in the place to its left.

Related Standards: 4.NSBT.1

Vocabulary: tenths, hundredths, thousandths, decimal, whole number, fraction

Example:

Two rods are 2 tenths of the whole.

Two tens are 2 tenths of one hundred.

  [pic][pic]

[pic]

Show decimals and their relationship to a whole on the number line.

|Strategies/Activities: |Inquiry Skills |

| |(If Applicable) |

|Review whole number place value. | |

|Using base ten blocks or grid paper, name the hundreds flat as one whole.  Have students work or teacher demonstrate that a tens rod is | |

|one-tenth of the hundreds flat.  Repeat with unit block and tens rod to show that the unit block is one-tenth of the tens rod.  Repeat | |

|activity with unit blocks and hundreds flat to show that a unit block is one-one hundredth of a flat. | |

|Use decimal cards to reinforce the concept. | |

|Give students index cards with numbers 0-9 and a decimal card.  Call out a number and have the students create that number.  Walk around to | |

|check that the students have the digits in the correct places.  This activity could be done in teams giving each student one card and having | |

|them organize themselves to create the number. | |

Resources:

Text: Envision Textbook Topic 1-1

Exemplar Lessons:



- fndtn-lesson

Web Sites:

AAA Math: Decimals

Better Lesson:

Khan Academy:

Sample Assessment-like Questions:

Multiple Choice: Constructed Response:

Which of the following sets of cubes represents [pic]

0.24 of the whole?

[pic]

[pic]

Content Strand: Number Sense and Base Ten

Standard:  5.NSBT.2

Related Standards: 5.NSBT.5 , 5.NSBT.6

Vocabulary:  powers of ten, patterns, product, quotient, exponent

Example:  5 x 10^2 = 500

       5 10^2 = 0.05

|Strategies/Activities: |Inquiry Skills |

|Review Mental Math |(If Applicable) |

|Have students converse about the pattern they see when a number is multiplied by ten, one hundred, or one thousand. Then, have them explore | |

|what would happen when a number is divided. (The use of manipulatives could be a start) | |

|Discuss exponents and have students brainstorm reasons why exponents might be used. (to abbreviate large numbers) | |

Resources:

Text:

Exemplar Lessons:



Web Sites:









Sample Assessment-like Questions:

Multiple Choice:                                         

[pic]

Open Ended:

In class Veronica told her teacher that when you multiply a number by 10, you just always add 0 to the end of the number.  Think about her statement, then answer the following questions.

When does Veronica’s statement work?

When doesn’t Veronica’s statement work?

Is the opposite true?  When you divide a number by 10, can you just remove a 0 from the end of the number?  When does that work? When doesn’t that work?

Number Sense and Base Ten

Standard:  5.NSBT.3

Read and write decimals in standard and expanded form.

Related Standards:

Vocabulary: decimal, whole number, tenths, hundredths, thousandths, standard form, word form

Example:

21.269 and 21 269/1000 are read as twenty-one and two hundred sixty-nine thousandths

|Strategies/Activities: |Inquiry Skills |

| |(If Applicable) |

1. Use grid paper to show decimals and write the amount.

2. Use base ten blocks to model tenths, hundredths, and thousandths.

[pic]

|___ | |___ |___ |___ |___ |

|1’s | |10ths |100ths |1,000ths |10,000ths |

3. Use sentence strips and make a number line of decimal place value.   Then have students make the decimal with the number cards.  They are to read the numbers after the teacher tells which place value to put a digit in.

3. Play “I Have, Who Has?”  Write a number in word form on one side of an index card and a different number in numeric form on the reverse side.  Give each student a card.  The teacher begins the game by saying, “Who has four and 38 hundredths?”  The student with that number on the card says, “I have 4.38, who has twenty-three and one tenth?” and so on.

[pic]

Resources:

Text: Envision Lesson 1-1 and 1-2

Exemplar Lessons:

Lesson/ http/:::lesson:443339:reading-and-writing-with-decimals

- fndtn-lesson

Web Sites:

AAA Math:

Better Lesson:

Khan Academy:

Learn Zillion:

Sample Assessment-like Questions:

Multiple Choice:

What is fifty-four and six hundred seventeen [pic]

thousandths expressed in standard form?

A. 0.54617 B.  546.17

C.  5.4617 D.  54.617

Constructed Response

Read the following decimals and explain how they are different.

0.2 0.02 0.002

Content Strand: Number Sense and Base Ten

Standard: Round decimals to any given place within thousandths. (5.NSBT.4)

Related Standards: 4.NSBT.3

Vocabulary: tenths, hundredths, thousandths, rounding

Example:

[pic]

|Strategies/Activities: |Inquiry Skills |

| |(If Applicable) |

|Have students shop at their favorite store (on iPAD) or use an ad from the newspaper to allow them to apply rounding in the real| |

|world. | |

|Review Place Value of Decimals. | |

|Use a rounding wheel. | |

|Use a song to help students remember the steps for rounding. | |

Resources:

Text:

EnVision Lesson 2-2

Exemplar Lessons:

BetterLesson:

Learn Zillion:

Web Sites:

Khan Academy:

Learn Zillion:

YouTube:

Sample Assessment-like Questions:

Multiple Choice: Open Ended:

Joan estimated the answer to

these four math problems by first

rounding the numbers to the

nearest tenth and then multiplying.

For which problem did she

multiply 3.0 × 5.0?

A 2.72 × 4.45

B 2.44 × 5.37

C 2.95 × 5.03

D 3.28 × 5.84

Grade 5

Content Strand: Number Sense & Base Ten

Standard: Fluently multiply multi-digit whole numbers using strategies to include a standard algorithm.

Related Standards: 4.NSBT.4, 4.NSBT.5

Vocabulary: standard algorithm, multi-digit whole number, factors, product

Example:

A book company printed 452 books. Each book had 45 pages. How many pages did the book company print?

452 x 45 = 20,340

AREA Model:

400 50 2

40

5

|Strategies/Activities: |Inquiry Skills |

| |(If Applicable) |

Review Area Model from 4th Grade.

Relate Area Model to Standard Algorithm or have students determine how the two relate based on their knowledge.

Review Place Value and how it relates to the Standard Algorithm and Area Model.

Use the newspaper or store ads to create real world problems.

Have students create their own multiplication problems.

Resources:

Text:

Everyday Mathematics: Student Reference Book pp. 19-20, 24C, 24D

EnVision Lesson 3-6, 3-7, 3-8



Exemplar Lessons:

Better Lesson:

Web Sites:









Sample Assessment-like Questions:

Multiple Choice: Open Ended:

Justine can type 43 words per minute.

At that rate, how many words can she type

in 45 minutes?

a. 1,725 words

b. 1,735 words

c. 1,935 words

d. 1,965 words

Content Strand: Number Sense and Base Ten

Standard:  Divide up to a four-digit dividend by a two-digit divisor, using strategies based on place value, the properties of operations, and the relationship between multiplication and division. (5.NSBT.6)

Related Standards: 4.NSBT.4 – 6, 5.NSBT.5

Vocabulary: dividend, divisor, quotient, share, divide, evenly

Example: Area Model

[pic]2124 divided by 9 = 236

|Strategies/Activities: |Inquiry Skills |

| |(If Applicable) |

Review place value.

Review Array Model for Multiplication and relate the two.

Have students complete an activity that requires them to “share” to help students understand

the concept of division.

Relate division to the real world: Your class won the cash prize for a contest and need to share it evenly among all the students, determine how much money each student will receive.

Resources:

Text:

Go Math

Exemplar Lessons:



Web Sites:













Sample Assessment-like Questions:

Open Ended:

At a school carnival there is an egg toss station. There are 314 students. Twelve eggs are in one carton. How many cartons are needed so that all students receive an egg? Explain why your answer is correct.

Multiple Choice:

[pic]

Content Strand: Number Sense and Base Ten

Standard:  Add, subtract, multiply, and divide decimal numbers to hundredths using concrete area models and drawings. (5.NSBT.7)

Related Standards: 4.NSF.7 , 5.NSBT.6, 5.NSBT.7

Vocabulary: tenths, hundredths

Example: [pic]

[pic]

[pic][pic]

|Strategies/Activities: |Inquiry Skills |

|Review decimal place value. |(If Applicable) |

|Use base-ten blocks as a tool for students to build their own models for addition, subtraction, | |

|multiplication, and division. | |

|Discuss how base-ten blocks are used and why they can be used to represent certain amounts. | |

|Have students create their own problems using the base-ten blocks for a partner to solve. | |

|Extend. Give students one factor/addend and the product/sum and have them determine the operation using the base-ten blocks. | |

Resources:

Text:

Exemplar Lessons:



Web Sites:









!

Sample Assessment-like Questions:

**SEE EXAMPLES ABOVE ALSO

Multiple Choice:

[pic]

Open Ended:

Use the model below to answer the following.

[pic]

[pic]        +   [pic] =  

John used the model above to show 3.7 + 0.26. Is John’s model correct? Why or Why Not?

Grade 5

Quarter Two

Content Strand: Algebraic Thinking and Operations

Standard: Evaluate numerical expressions involving grouping symbols (i.e. parentheses, brackets, braces). (5.ATO.1)

Related Standards: 4.NSBT.4,4.NSBT.5, 4.NSBT.6, 5.NBT.6, 5.NBT.7

Vocabulary: evaluate, expressions, equations, numerical expressions, parentheses, brackets, braces

Example:

 4{4[3 + (4 + 3) + 60] }

4{4{3 + 7 + 60]}

4{4[10 + 60]}

4{4[70]}

4{280}

1120

|Strategies/Activities: |Inquiry Skills |

| |(If Applicable) |

1. Have students talk about something that they do in their everyday life that requires them to follow a set of steps (i.e. making a peanut butter and jelly sandwich, washing their hair, typing their shoes).

2. Have a class discussion: Why do you think it is important to have steps that should be followed when doing certain things? What might happen if you didn’t have steps in place?

3. Show students a YouTube video explaining the Order of Operations.

Resources:

Text:

Exemplar Lessons:



Web Sites:

✓&query=order%20of%20operations&page=1&sort=Relevance&models%5B%5D=LessonPlan&models%5B%5D=LessonSet&models%5B%5D=Resource

Sample Assessment-like Questions:

Multiple Choice:

When solving the following problem, which operation will be performed first?

5 + ({3 x 8} + 4)

a. 8 + 4

b. 5 + 3

c. 5 + 24

d. 3 x 8

Open Ended:

Two students worked together to evaluate the following numerical expression. Their work is shown below.

Ashley Mike

5 + ({3 x 8} + 4) 5 + ({3 x 8} + 4)

5 + (3 x 12) 5 + (24 + 4)

5 + 36 5 + 28

41 33

Which student evaluated the problem correctly? Where did the student who did not evaluate correctly make the mistake? Explain.

Grade ______

Content Strand: Algebraic Thinking and Operations

Standard: Translate verbal phrases into numerical expressions and interpret numerical expressions as verbal phrases. (5.ATO.2)

Related Standards: 4.NSBT.4, 4.NSBT.5, 4.NSBT.6, 5.NSBT.5, 5.NSBT.6

Vocabulary: translate, numerical expressions, verbal phrases, sum, difference, more than, less than

Example:

Three more than four = 4 + 3

Seven less than the sum of two and eight = (2+ 8) – 7 or 2 + 8 – 7

Twenty-five divided by the product of five and one = 25 ÷ (5 x 1) or 25 ÷ 5 x 1 or 25 ÷ 5 ? 1

|Strategies/Activities: |Inquiry Skills |

| |(If Applicable) |

1. Have students match verbal phrases to numerical expressions and explain how they know the answer is correct.

2. Move from single operation verbal phrases and have students match them.

3. Have students write their own verbal phrases and have a partner match the numerical expression.

Resources:

Text:

Exemplar Lessons:



Web Sites:



✓&query=numerical%20expressions&page=1&sort=Relevance&models%5B%5D=LessonPlan&models%5B%5D=LessonSet&models%5B%5D=Resource

Sample Assessment-like Questions:

Multiple Choice:

Which of the following is the correct numerical expression for the following verbal phrase.

The sum of five and four divided by three

a. 5 + 4 ÷ 3

b. 5 + ( 4 ÷ 3 )

c. (5 + 4 ) ÷ 3

d. 5 – 4 ÷ 3

Open Ended:

Jason says that the correct numerical expression for “divide the sum of four and eight by three” is 3 ÷ 4 + 8. Is Jason correct? If not, explain why and include the correct numerical expression.

Grade 5

Content Strand: Algebraic Thinking and Operations

Standard: Investigate the relationship between two numerical patterns.

a. Generate two numerical patterns given two rules and organize in tables; b. Translate the two numerical patterns into two sets of ordered pairs;

c. Graph the two sets of ordered pairs on the same coordinate plane;

d. Identify the relationship between the two numerical patterns. (5.OA.3)

Related Standards: 4.ATO.5, 5.G.1

Vocabulary: pattern, rule, table, ordered pairs, coordinate plane, numerical pattern

Example:

[pic]

[pic]

|Strategies/Activities: |Inquiry Skills |

| |(If Applicable) |

1. Start with tasks that require students to complete patterns, and then move to discussing how this data may be show in different ways.

2. Have students collect their own data on a topic of their choice, and then have them display it in the coordinate grid.

Resources:

Text:

Exemplar Lessons:



Web Sites:







Sample Assessment-like Questions:

Multiple Choice:

|Michael and John each created a numeric pattern. Both patterns start with 0. | | |

|The terms in Michael’s pattern are always two times the same terms in John’s pattern. | | |

|What could be the rules for the two patterns? | | |

|A. Michael: Add 2 John: Add 0 | | |

|B. Michael: Add 6 | | |

|John: Add 3 | | |

|C. Michael: Multiply by 2 | | |

|John: Multiply by 0 | | |

|D. Michael: Multiply by 6 John: Multiply by 3 | | |

Open Ended

[pic]

**For the assessment item above, you may want to have students graph the points themselves, based off of a given rule, and then answer Part A and B.

Content Strand: Geometry

Standard:  5.G.1

Define a coordinate system.

  A. The x- and y- axis are perpendicular number lines that intersect at 0 (the origin).

  B. Any point on the coordinate plane can be represented by its coordinates (ordered pair)

  C. The first number in an ordered pair is the x-coordinate and represents the horizontal distance     from the origin.

  D. The second number in an ordered pair is the y-coordinate and represents the vertical distance from the origin.

Related Standards: Standard 5.G.1 can be taught concurrently with standards 5.G.2 and 5.ATO.3

Vocabulary:

Intersect, ordered pair, horizontal, vertical, point, plot, x-axis, y-axis, coordinate, perpendicular

Example:

|Strategies/Activities: |Inquiry Skills |

| |(If Applicable) |

1. Read The Fly on the Ceiling by Julie Glass

2. The teacher will demonstrate on a grid how to move horizontally, then vertically to locate the ordered pairs.

3. Show how coordinates are used on a map and how they help us find things on a map.

3. In an open area, such as outside or in a gym, have students form several lines.   Give students a coordinate, such as (5, 2).  Students must then move five steps to the right, then two up.  Continue giving two numbers as coordinates.

4. Use painter’s tape or masking tape on floor tiles in classroom to create a large grid.

5. Allow students to create maps of the school grounds or nearby areas on grid paper.

Resources:

Text: Envision Lesson 16-1

Exemplar Lessons:



Web Sites:

Khan Academy:

Better Lesson:

AAAKnow:

AAAKnow for ESOL students:

Sample Assessment-like Questions:

Multiple Choice:

Which of the following is the correct x-coordinate for the school?

              [pic]

Open Ended:

Pretend a new student just enrolled at your school. Explain the difference between the x axis and y axis on a coordinate grid so that the new student will understand so that he or she will be ready for tomorrow’s lesson.

Content Strand: Geometry

Standard:  5.G.2

Plot and interpret points in the first quadrant of the coordinate plane to represent real world and mathematical situations.

Related Standards: This standard can be taught concurrently with 5.G.1

Vocabulary: coordinate, ordered pair, point, plot, x-axis, y-axis

Example:

[pic][pic]

|Strategies/Activities: |Inquiry Skills |

| |(If Applicable) |

1. The teacher will demonstrate on a grid how to move horizontally, then vertically to locate the ordered pairs.

2. Show how coordinates are used on a map and how they help us find things on a map.

3. In an open area, such as outside or in a gym, have students form several lines.  Give students a coordinate, such as (5, 2).  Students must then move five steps to the right, then two up.  Continue giving two numbers as coordinates.

4. Pair students and give them a 5x5 grid.  Also give each student number cards (1-5).  The teacher shows a coordinate that can be plotted on the 5x5 grid.  Partner one shows a number card for the number of spaces the point is to the right of D; partner two shows number card for the number of spaces the point is from D.  Then plot the point.

5. Read The Fly on the Ceiling by Julie Glass and Richard Walz and locate the objects Descartes places in his room.

6. Play a game of Battleship to practice plotting points.

Battleship

Resources:

Text: Envision Lesson 16-1

Book: The Fly on the Ceiling by Julie Glass

Exemplar Lessons:





Web Sites:

Khan Academy:

Better Lesson:

AAAKnow:

AAAKnow for ESOL students:

Kaylee’s Krazy Math:

Sample Assessment-like Questions:

Multiple Choice: Constructed Response:

Name the ordered pair for point A.    Name three coordinates that make up            the triangle.                                        

A. (2,3)   [pic]       [pic]

B. (2,2)

C. (3,2)[pic]

D. (3,3)

Content Strand: Geometry

Standard:  5.G.3

Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

Related Standards:

Vocabulary: polygon, octagon, pentagon, quadrilateral, parallelogram, square, rhombus, triangle, rectangle, trapezoid

Example: What is the definition of a parallelogram? Does a square fit into that category?

|Strategies/Activities: |Inquiry Skills |

| |(If Applicable) |

Polygon Memory Game

The Great Trapezoid Debate

Resources:

Text: Envision Topic 15

Exemplar Lessons:





Web Sites:

Khan Academy:

LearnZillion:

Better Lesson:

EngageNY:

AAAKnow:

AAAKnow for ESOL students:

Kaylee’s Krazy Math:

Sample Assessment-like Questions:

Multiple Choice:

This quadrilateral has one pair of parallel sides. Which is it?

A. square

B. rectangle

C. triangle

D. trapezoid

Constructed Response:

Which quadrilaterals must have all four sides of equal length?

Content Strand: Geometry

Standard:  5.G.4

Classify two-dimensional figures in a hierarchy based on their attributes.

Related Standards:

Vocabulary: triangle, rectangle, square, quadrilateral, parallelogram, trapezoid, rhombus, congruent, parallel

Example:

1. How are a rhombus, trapezoid, rectangle, and square similar?  (They are all 4-sided quadrilaterals.)

2. How is a trapezoid different from a rhombus, a rectangle, and a square? (It is not a parallelogram.)

3. Define a quadrilateral and a parallelogram.

|Strategies/Activities: |Inquiry Skills |

| |(If Applicable) |

1. Give groups of students sets of cut-out polygons.  Ask students to sort polygons into similar shapes and describe similarities and differences.  Use questions in example. Quadrant A

2. Review prefixes from GI.B.1.  Discuss how polygon names were derived. Quadrant A

3. Students design and build their own three dimensional prism or pyramid using toothpicks and marshmallows, gumdrops, or clay. Quadrant C

4. Have geometric solids, such as pyramids, triangular prisms, and rectangular prisms available for students to contrast and compare three-dimensional shapes they have and have not built. Quadrant B

5. Put pairs of three-dimensional shapes together.  Ask students to explain why they are or are not in the same classification (e.g., pyramids, prisms, etc.). Quadrant C

Resources:

Text: Envision Topic 15

Exemplar Lessons:







Web Sites:

Khan Academy:

LearnZillion:

Better Lesson:

AAAKnow:

AAAKnow for ESOL students:

Kaylee’s Krazy Math:

Sample Assessment-like Questions:

[pic]

-----------------------

Explain what a decimal number represents. Use a number line or another visual to illustrate your example.

Round 12.756 to the nearest tenth.

Look at the place value to the right (hundredths).

12.756 rounds to 12.8.

Joan went to the grocery store to purchase cupcakes for her class party. The cupcakes she wanted to purchase cost $3.95. Joan used rounding to determine how much she would pay for the cupcakes and told her mother she needs $4.00. Is Joan correct? Why or why not?

16,000

2,000

2,000

250

80

+ 10

20,340

16,000 2,000 80

2,000 250 10

Solve the following by inserting the correct digit.

1 _ 8

x 4 2

_ 5 6

_ 1 _ 0

_ 3 _ 6

Order of Operations

P – Parenthesis ( Braces, Brackets)

E – Exponents

M – Mulitplication

D – Division

A – Addtion

S – Subtraction

After students have completed the task, have them create ordered pairs

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