Standards PLUS Flexible Supplemental K-8 ELA & Math Online & Print Grade 5 SAMPLER Mathematics EL Strategies DOK 1-4 RTI Tiers 1-3 15-20 Minute Lessons Assessments Consistent with CA Testing Technology Standards PLUS Targeted Intervention Ready to Teach RTI Tier 1-2-3 Materials PRINT + DIGITAL Writing Program EL Strategies Performance Lessons Integrated Projects Written directly to the CA Standards by CA Educators
Standards PLUS is so much more Close the Achievement Gap with Seven Programs in One Embedded within Standards PLUS are: EL STRATEGIES All Standards Plus lessons explicitly teach communication skills, strategies, and conventions that meet the goal of EL Instruction. READY TO TEACH RTI / TIER 1-2-3 Standards Plus Lessons provide: Whole Class Instruction Targeted Intervention Intense Intervention Standards PLUS is Seven Programs in One: 15-20 MINUTE LESSONS DOK 1-2 / RTI Tiers 1-2 Research-based, Direct Instruction, K-8, ELA and Math lessons. Written to the state standards. PERFORMANCE LESSONS DOK 3 Students deepen and apply their knowledge into new applications. ASSESSMENTS DOK 1-2 Weekly formative assessments monitor student progress. Online assessments help students master digital item types. INTEGRATED PROJECTS DOK 4 Students apply knowledge to real-world situations. STANDARDS PLUS DIGITAL DOK 1-3 / RTI Tiers 1-3 Lessons and assessments match the the digital format of the state test. Students transfer their knowledge into a digital learning environment. TARGETED INTERVENTION LESSONS DOK 1-2 / RTI Tiers 2-3 Scaffolded lessons assigned based on assessment results. Digital program automates this process. WRITING PROGRAM (ELA Only) DOK 1-4 / RTI Tiers 1-2 Includes lessons on every writing genre. Writing performance lessons include skills trace, prompts, and rubrics. HOMEWORK/ PARENT CONNECTION (COMING SOON) 2
Sample Lessons Included in this Booklet Domain Lesson Focus Standard(s) Operations and Algebraic Thinking (Operations and Algebraic Thinking Standards 5.OA.1-5.OA.3) 5 Writing Numerical Expressions 6 Writing Numerical Expressions 7 Writing Numerical Expressions 8 Writing Numerical Expressions E2 Evaluation- Writing Numerical Expressions 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. 9 Interpret Numerical Expressions 5.OA.2: Write simple expressions that record calculations with numbers, and interpret 10 Interpret Numerical Expressions numerical expressions without evaluating them. For example, express the calculation add 8 and 7, 11 Interpret Numerical Expressions then multiply by 2 as 2 (8 + 7). Recognize that 3 (18932 + 921) is three times as large as 18932 + 12 Interpret Numerical Expressions 921, without having to calculate the indicated Evaluation- Interpret Numerical sum or product. E3 Expressions P10 Performance Lesson Operations and Algebraic Thinking: Expressions (5.OA.1, 5.OA.2) See the lesson index for the entire program on pages 28-35. 3
Domain: Operations & Algebraic Thinking Focus: Writing Numerical Expressions Lesson: #5 Standard: 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Sample Daily Lesson- Teacher Lesson Plan Lesson Objective: The students will write simple numerical expressions, which do not include parentheses, from written phrases. Introduction: Today we will review how to write a numerical expression from a word phrase. A numerical expression is a series of numbers and operation symbols that does not have an equal sign. Instruction: When you write a numerical expression, you are translating a word phrase into a series of numbers and operations. To translate a word phrase into a numerical expression, you need to know the key words that indicate each operation. Here are some words associated with each operation (You may want to brainstorm the list together with students. The list of key words will be used with all lessons for this standard.): Addition sum, add, more than, increased by, plus Subtraction difference, subtract, less than, decreased by, minus Multiplication multiply, product, multiplied by, times, double, triple Division divide, quotient, divided by, half, third, fourth, into Once you have identified the key word that indicates the operation, you have to decide on which side of the operation each number should be placed. Guided Practice: Direct students attention to Example A. Read the word phrase The product of 7 and 4. In this phrase the word product tells us we will multiply, so we can express this phrase as 7 x 4. Now look at Example B, 6 less than 15. The words less than tell us we will subtract, so we can express this phrase as 15 6. Independent Practice: Complete problems 1 through 8. Determine the correct operation based on the key words. Write each phrase as a numeric expression. Do not solve. For subtraction and division, pay careful attention to which side of the operation each number should be placed. Review: Review problems 1-8 with students. Discuss each answer, reviewing the key operation terms. Closure: Today we reviewed how to write numerical expressions from a word phrase. Turn to your partner and state at least two key terms for each of the four operations. Answers: 1. 3 + 12 or 12 + 3 2. 20 4 3. 5 x 3 or 3 x 5 4. 8 + 10 or 10 + 8 5. 9 x 7 or 7 x 9 6. 37 16 7. 15 3 8. 18 6 4
Domain: Operations & Algebraic Thinking Focus: Writing Numerical Expressions Lesson: #5 Standard: 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Key words: Addition: sum, add, more than, increased by, plus Subtraction: difference, subtract, less than, decreased by, minus Multiplication: multiply, product, multiplied by, times, double, triple Division: divide, quotient, divided by, half, third, fourth, into Examples: A. The product of 7 and 4 B. 6 less than 15 Directions: Write each phrase as a numerical expression. 1. The sum of 3 and 12 2. Subtract 4 from 20 3. Triple 5 4. 10 more than 8 5. 9 times 7 Sample Daily Lesson - Student Response Page 6. 37 decreased by 16 7. 15 divided by 3 8. The difference of 18 and 6 5
Domain: Operations & Algebraic Thinking Focus: Writing Numerical Expressions Lesson: #6 Standard: 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Sample Daily Lesson- Teacher Lesson Plan Lesson Objective: The students will write simple numerical expressions, which include parentheses and any combination of addition and subtraction, from written phrases. Introduction: Today we will review how to write numerical expressions that use parentheses and any combination of addition and subtraction. Instruction: When you write a numerical expression, you are translating a word phrase into a series of numbers and operations. Look for key words that indicate the operations to be used. Sometimes parentheses are used within an expression to show which operation should be solved first. Let s review some words associated with the operations of addition and subtraction: Addition sum, add, more than, increased by, plus Subtraction difference, subtract, less than, decreased by, minus Once you have identified the key words that indicate the operations, you have to decide on which side of the operations each number should be placed. When more than one operation is stated, include parentheses in the expression to indicate which operation should be completed first. Guided Practice: Direct the students attention to Example A. 16 decreased by the sum of 4 and 2. The key words decreased tell me I need to subtract. Sum tells me I need to add. Decreased by the sum tells me I need to determine the sum before I can decrease it. So I need to place parentheses around 4 + 2 to get the expression 16 (4 + 2). Look at Example B. Let s read the word phrase, 8 more than the difference of 7 and 3. In this phrase, the words more than tell us to add. The word difference indicates that we will subtract. I am going to reread the phrase: 8 more than the difference of 7 and 3 tells me that I need to determine the difference of 7 and 3 first before I can add 8 to it. Since 7 3 must be solved first, I will place parentheses around it. (7 3) Now complete the phrase 8 more than the difference of (7 3). 8 + (7 3). Repeat this thought process with Example C add 6 and 10, then decrease the sum by 5. (The answer for Example C is (6 + 10) - 5.) Independent Practice: Complete problems 1 through 8. Remember to use parentheses to show the grouping for a specific operation. Review: Review problems 1-8 with students. Discuss each answer, reviewing the key operation terms and use of parentheses. Closure: Today we reviewed how to write numerical expressions with parentheses from a word phrase. Turn to your partner and discuss how you know where to place the parentheses for problem 1. Answers: 1. (13 + 5) 2 2. (15 8) + 4 3. 25 (6 + 9) 4. (7 2) + 10 5. (14 + 7) 9 6. 12 (3 + 4) 7. (6 + 5) 4 8. 8 + (2 + 9) 6
Domain: Operations & Algebraic Thinking Focus: Writing Numerical Expressions Lesson: #6 Standard: 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Key Words: Addition: sum, add, more than, increased by, plus Subtraction: difference, subtract, less than, decreased by, minus Examples: A. 16 decreased by the sum of 4 and 2 B. 8 more than the difference of 7 and 3 C. Add 6 and 10, then decrease the sum by 5 Directions: Write each phrase as a numerical expression. 1. Subtract 2 from the sum of 13 and 5 2. 15 decreased by 8, then added to 4 3. The sum of 6 and 9 subtracted from 25 4. 2 less than 7, increased by 10 Sample Daily Lesson - Student Response Page 5. Add 14 and 7, then subtract 9 6. The difference of 12 and the sum of 3 and 4 7. 6 plus 5, decreased by 4 8. 8 more than the sum of 2 and 9 7
Domain: Operations & Algebraic Thinking Focus: Writing Numerical Expressions Lesson: #7 Standard: 5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Sample Daily Lesson- Teacher Lesson Plan Lesson Objective: The students will write simple numerical expressions, which include parentheses and any combination of addition, subtraction, or multiplication from written phrases. Introduction: Today we will review how to write numerical expressions that use parentheses and any combination of addition, subtraction, or multiplication. Instruction: When you write a numerical expression, you are translating a word phrase into a series of numbers and operations by looking for key words that indicate the operations to be used. Let s review some key words associated with addition, subtraction, and multiplication: Addition sum, add, more than, increased by, plus Subtraction difference, subtract, less than, decreased by, minus Multiplication multiply, product, multiplied by, times, double, triple Once you have identified the key words that indicate the operations, you have to decide on which side of the operations each number should be placed. When more than one operation is stated, you will need to include parentheses in the expression to indicate which operation to complete first. Look at the top of your page to see what happens when we move the parentheses. For the phrase 6 subtracted from the product of 3 and 8, the parentheses would go around 3 8 to give us (3 8) 6. In the next phrase, 3 times the difference of 8 and 6, the parentheses would go around the 8 and 6 so we would find the difference first. We would have 3 (8 6). Guided Practice: Direct students attention to Example A. Let s read the word phrase 4 times the difference of 9 and 2. In this phrase the word times tells us we will multiply. The word difference indicates that we will subtract. We know we want to subtract 2 from 9, so we can express that as (9 2). We want 4 times that difference, so the complete phrase can be written as 4 (9 2). Repeat this thought process with Example B, Triple the sum of 5 and 6. (The answer for Example B is (5 + 6) 3.) Independent Practice: Complete problems 1 8. Remember to use parentheses to show the grouping for a specific operation. Review: Review problems 1 8 with students. Discuss each answer, reviewing the key operation terms and use of parentheses. Closure: Today we reviewed how to write numerical expressions with parentheses from a word phrase. Turn to your partner and discuss how changing the expression in problem 4 from (4 8) 5 to 4 (8 5) would change the word phrase. Answers: 1. (2 8) 4 2. (10 + 5) 3 3. 2 (9 7) or (9 7) 2 4. (4 8) 5 5. (6 3) + 10 6. (13 + 7) 5 7. (8 2) 12 8. 4 (3 + 9) 8
Domain: Operations & Algebraic Thinking Focus: Writing Numerical Expressions Lesson: #7 Standard: 5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Key Words: Addition: sum, add, more than, increased by, plus Subtraction: difference, subtract, less than, decreased by, minus Multiplication: multiply, product, multiplied by, times, double, triple Examples: 6 subtracted from the product of 3 and 8: (3 8) 6 3 times the difference of 8 and 6: 3 (8 6) A. 4 times the difference of 9 and 2 B. Triple the sum of 5 and 6 Directions: Write each phrase as a numerical expression. 1. Subtract 4 from the product of 2 and 8 2. Add 10 and 5, then multiply by 3 3. Double the difference of 9 and 7 4. 5 less than the product of 4 and 8 Sample Daily Lesson - Student Response Page 5. 6 multiplied by 3, then increased by 10 6. 13 plus 7, then multiplied by 5 7. Decrease the product of 8 and 2 by 12 8. 4 times the sum of 3 and 9 9
Domain: Operations & Algebraic Thinking Focus: Writing Numerical Expressions Lesson: #8 Standard: 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Lesson Objective: The students will write simple numerical expressions, which include parentheses and any combination of all four operations, from written phrases. Introduction: Today we will review how to write numerical expressions that use parentheses and any combination of operations. Sample Daily Lesson- Teacher Lesson Plan Instruction: To translate a word phrase into a numerical expression, you need to know the key words that indicate each operation. Let s review some words associated with each operation: Addition sum, add, more than, increased by, plus Subtraction difference, subtract, less than, decreased by, minus Multiplication multiply, product, multiplied by, times, double, triple Division divide, quotient, divided by, half, third, fourth, into Once you have identified the key words that indicate the operations, you have to decide on which side of the operations each number should be placed. When more than one operation is stated, include parentheses in the expression to indicate which operation to complete first. Guided Practice: Direct students attention to Example A. Let s read the word phrase 5 times the sum of 8 and 12. In this phrase the word times tells us to multiply. The word sum indicates that we will add. 5 times the sum tells us we will multiply the sum by 5. Since we want to be sure to add 8 and 12 first to get the sum, we should put parentheses around that part of the expression, so we have (8 + 12). We want 5 times more than that sum, so the complete phrase can be written as 5 x (8 + 12). The parentheses are important because without them we would first multiply 5 x 8 and then add 12. Repeat this thought process with Example B, The difference of 25 and 10 divided by 3. (The answer for Example B is (25 10) 3.) Independent Practice: Complete problems 1-7. Remember to use parentheses to show a grouping for a specific operation if necessary. Review: Review problems 1-7 with students. Discuss each answer, reviewing the key operation terms and use of parentheses. Closure: Today we reviewed how to write numerical expressions with parentheses from a word phrase. Turn to your partner and discuss why the parentheses are important. How does it change an expression? Answers: 1. 2 x (4 + 9) or (4 + 9) x 2 2. (12 5) x 3 3. 7 + (8 2) 4. 10 + (6 x 15) 5. (20 6) 2 6. (5 + 14) 10 7. (8 x 2) 9 10
Domain: Operations & Algebraic Thinking Focus: Writing Numerical Expressions Lesson: #8 Standard: 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Key Words: Addition: sum, add, more than, increased by, plus Subtraction: difference, subtract, less than, decreased by, minus Multiplication: multiply, product, multiplied by, times, double, triple Division: divide, quotient, divided by, half, third, fourth, into Examples: 6 more than the product of 2 and 5: 6 + (2 x 5) The sum of 6 and 2, times 5: (6 + 2) x 5 A. 5 times the sum of 8 and 12 B. The difference of 25 and 10 divided by 3 Directions: Write each phrase as a numerical expression. 1. Multiply the sum of 4 and 9 by 2 2. Subtract 5 from 12, then multiply by 3 3. Add 7 to the quotient of 8 divided by 2 4. 10 more than the product of 6 and 15 Sample Daily Lesson - Student Response Page 5. Half the difference of 20 minus 6 6. 10 less than the sum of 5 and 14 7. Double 8, then subtract 9 11
Domain: Operations & Algebraic Thinking Focus: Writing Numerical Expressions Evaluation: #2 The weekly evaluation may be used in the following ways: As a formative assessment of the students progress. As an additional opportunity to reinforce the vocabulary, concepts, and knowledge presented during the week of instruction. Standard: 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. Sample Assessment - Teacher Lesson Plan Procedure: Read the directions aloud and ensure that students understand how to respond to each item. If you are using the weekly evaluation as a formative assessment, have the students complete the evaluation independently. If you are using it to reinforce the week s instruction, determine the items that will be completed as guided practice and those that will be completed as independent practice. Review: Review the correct answers with students as soon as they are finished. Answers: 1. (5.OA.2) 6 + 8 2. (5.OA.2) 3 x (9 + 2) 3. (5.OA.2) 15 (3 x 4) 4. (5.OA.2) (10 4) 2 5. (5.OA.2) C. (12 3) 2 12
Domain: Operations & Algebraic Thinking Focus: Writing Numerical Expressions Evaluation: #2 Key Words: Addition: sum, add, more than, increased by, plus Subtraction: difference, subtract, less than, decreased by, minus Multiplication: multiply, product, multiplied by, times, double, triple Division: divide, quotient, divided by, half, third, fourth, into Directions: For problems 1 4, write a numerical expression for each word phrase. For problem 5, choose the correct answer. 1. 8 more than 6 2. 3 times the sum of 9 and 2 3. The difference of 15 and the product of 3 and 4 4. Half the difference of 10 and 4 Sample Assessment - Student Response Page 5. 2 subtracted from the quotient of 12 and 3 A. 2 12 + 3 B. 2 (12 x 3) C. (12 3) 2 D. (12 + 3) 2 13
Domain: Operations & Algebraic Thinking Focus: Interpret Numerical Expressions Lesson: #9 Standard: 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Lesson Objective: The students will interpret simple numerical expressions, which do not include parentheses, into written phrases. Introduction: Today we will review how to interpret a numerical expression. When you interpret an expression, you are describing it with words. Sample Daily Lesson- Teacher Lesson Plan Instruction: To interpret a numerical expression, you need to know the key words that indicate each operation. Look at the words at the top of the student page. Addition sum, add, more than, increased by, plus Subtraction difference, subtract, less than, decreased by, minus Multiplication multiply, product, multiplied by, times, double, triple Division divide, quotient, divided by, half, third, fourth, into For very simple expressions that do not include parentheses, just reading the expression will give you a one-word phrase that would describe it. Guided Practice: Direct students attention to Example A. Read the expression 8 x 3. Reading this expression as 8 times 3 gives us one way to interpret or describe it. (Brainstorm other ways to interpret this expression with students: The product of 8 and 3, 8 multiplied by 3, triple 8, etc. and write those examples on the line.) Now look at Example B, 9 + 6. One way to interpret this expression is 9 plus 6. Brainstorm other ways to interpret this expression (the sum of 9 and 6, 6 more than 9, 9 increased by 6, etc.), and write the written phrase on the line. Independent Practice: Complete problems 1-4. Write two different word phrases to describe each numerical expression. Review: Review problems 1-4 with students. Discuss each answer, reviewing the key operation terms. Closure: Today we reviewed how to interpret numerical expressions into word phrases. Turn to your partner and discuss other ways to interpret problem 4 than the ways you described it. Answers: Answers will vary. Possible answers include: 1. 12 divided by 3, the quotient of 12 and 3, 3 into 12 2. 10 minus 4, the difference of 10 and 4, 4 less than 10, 10 decreased by 4, subtract 4 from 10 3. 7 times 5, 7 multiplied by 5, the product of 7 and 5 4. 8 divided by 2, the quotient of 8 and 2, 2 into 8, half of 8, divide 8 by 2 14
Domain: Operations & Algebraic Thinking Focus: Interpret Numerical Expressions Lesson: #9 Standard: 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Key words: Addition: sum, add, more than, increased by, plus Subtraction: difference, subtract, less than, decreased by, minus Multiplication: multiply, product, multiplied by, times, double, triple Division: divide, quotient, divided by, half, third, fourth, into Examples: A. 8 x 3 B. 9 + 6 Directions: Write two different word phrases to describe each numerical expression. 1. 12 3 2. 10 4 Sample Daily Lesson - Student Response Page 3. 7 x 5 4. 8 2 15
Domain: Operations & Algebraic Thinking Focus: Interpret Numerical Expressions Lesson: #10 Standard: 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Lesson Objective: The students will interpret simple numerical expressions, which include parentheses, into written phrases. Sample Daily Lesson- Teacher Lesson Plan Introduction: When you evaluate an expression, you are describing it with words. Today we will interpret expressions that include parentheses. Instruction: To evaluate numerical expressions with parentheses, you need to know the words that indicate the answer for each operation. Read the words that indicate the answer for each operation at the top of your page. (Review the chart with the students.) When the expression includes parentheses, there are two simple expressions within one numerical expression. Steps for writing an expression with parentheses into a written phrase are: 1. Read the operation in parentheses. 2. Identify the math term that indicates the answer. (sum, difference, product, quotient) 3. Describe how the second operation relates to the answer in the parentheses. Guided Practice: Look at Example A. Read the expression 3 (2 + 7). Step 1: Read the operation in parenthesis (2 + 7). Step 2: Identify the word that indicates the answer to an addition problem. In addition problems, the word for the answer is the sum. Write the sum of 2 and 7. Step 3: Describe how the second operation relates to the answer in the parenthesis: 3 times the sum of 2 and 7 or the sum of 2 and 7 multiplied by 3. Look at Example B, 2 (7 4). Describe the portion of the expression within the parentheses using the word sum, difference, product, or quotient. We can interpret 7 4 as the difference of 7 and 4. Next, describe how the second operation relates to the difference of 7 and 4. We want to multiply the expression within the parentheses by 2, so we can interpret the whole expression as 2 times the difference of 7 and 4, or as the difference of 7 and 4 multiplied by 2. Repeat this process for Example C, 6 + (12 3), if additional practice is needed. (The answer for Example C is The quotient of 12 and 3 added to six.) Independent Practice: Write a word phrase for each numerical expression for problems 1 through 4. Remember to interpret the operation within the parentheses first. Review: Review problems 1 4 with students. Discuss each answer, reviewing the key operation terms. Closure: Today we reviewed how to interpret numerical expressions into word phrases. Turn to your partner and share the words that indicate the answer to an addition, subtraction, multiplication or division problem. Answers: Answers will vary. Possible answers include: 1. The product of 6 and 9 added to 3 2. 2 more than the difference of 10 and 5 3. 15 divided by the sum of 2 and 3 4. 5 less than the product of 4 and 7 16
Domain: Operations & Algebraic Thinking Focus: Interpret Numerical Expressions Lesson: #10 Standard: 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Key words that indicate the answer to each operation: Sum: answer to an Addition problem Difference: answer to a Subtraction problem Product: answer to a Multiplication problem Quotient: answer to a Division problem Steps for writing an expression with parentheses: 1. Read the operation in parentheses 2. Identify the math term that indicates the answer. (sum, difference, product, quotient) 3. Describe how the second operation relates to the answer in the parentheses. Examples: A. 3 (2 + 7) B. 2 (7 4) C. 6 + (12 3) Directions: Write each numerical expression as a word phrase. 1. 3 + (6 9) 2. (10 5) + 2 Sample Daily Lesson - Student Response Page 3. 15 (2 + 3) 4. (4 7) 5 17
Domain: Operations & Algebraic Thinking Focus: Interpret Numerical Expressions Lesson: #11 Standard: 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Lesson Objective: The students will interpret simple numerical expressions, which include parentheses, into written phrases. Introduction: Today we will review how to interpret numerical expressions that include parentheses. When you interpret an expression, you are describing it with words. Sample Daily Lesson- Teacher Lesson Plan Instruction: To evaluate numerical expressions with parentheses, you need to know the words that indicate the answer for each operation. Read the words that indicate the answer for each operation at the top of your page. (Review the chart with the students.) When the expression includes parentheses, there are two simple expressions within one numerical expression. Steps for writing an expression with parentheses into a written phrase are: 1. Read the operation in parentheses 2. Identify the math term that indicates the answer. (sum, difference, product, quotient) 3. Describe how the second operation relates to the answer in the parentheses. Guided Practice: Direct students attention to Example A. Review the steps for writing an expression with parentheses into a written phrase. Read the expression (2 6) 3. Read the operation within the parentheses (2 6). Identify the word that indicates the answer for multiplication (product). Look at the expression again and describe how the second operation relates to the answer in the parentheses. The word phrase for this numerical expression is 3 less than the product of 2 and 6. Now read the expression in Example B, 12 (3 2). First, describe the portion of the expression within the parentheses using the word sum, difference, product, or quotient. We can interpret 3 2 as the product of 3 and 2. Next, describe how the second operation relates to the product of 3 and 2. We want to subtract the product within the parentheses from 12, so we can interpret the whole expression as 12 minus the product of 3 and 2, or as the product of 3 and 2 subtracted from 12. Repeat this process for Example C, (11 + 4) 5, if additional practice is needed. Independent Practice: Write a word phrase for each numerical expression for problems 1 through 4. Remember to interpret the operation within the parentheses first. Review: Review problems 1 4 with students. Discuss each answer, reviewing the key operation terms. Closure: Today we reviewed how to interpret numerical expressions into word phrases. Turn to your partner and state another way to describe problem 4 that is different than the way you interpreted it. Answers: Answers will vary. Possible answers include: 1. 2 more than the product of 6 and 2 2. The quotient of 8 and 4 multiplied by 7 3. 16 minus the quotient of 9 and 3 4. 6 less than the product of 3 and 5 18
Domain: Operations & Algebraic Thinking Focus: Interpret Numerical Expressions Lesson: #11 Standard: 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Key words that indicate the answer to each operation: Sum: answer to an Addition problem Difference: answer to a Subtraction problem Product: answer to a Multiplication problem Quotient: answer to a Division problem Steps for writing an expression into a written phrase: 1. Read the operation in parentheses. 2. Identify the word that indicates the answer for that operation. (sum, difference, product, or quotient) 3. Look at the expression again and describe how the second operation relates to the answer in the parentheses. Examples: A. (2 6) 3 B. 12 (3 2) C. (11 + 4) 5 Directions: Write each numerical expression as a word phrase. 1. 2 + (6 2) Sample Daily Lesson - Student Response Page 2. (8 4) 7 3. 16 (9 3) 4. (3 5) 6 19
Domain: Operations & Algebraic Thinking Focus: Interpret Numerical Expressions Lesson: #12 Standard: 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Lesson Objective: The students will interpret simple numerical expressions, which include parentheses, into written phrases. Introduction: Today we will review how to interpret numerical expressions that include parentheses. When you interpret an expression, you are describing it with words. Sample Daily Lesson- Teacher Lesson Plan Instruction: To evaluate numerical expressions with parentheses, you need to know the words that indicate the answer for each operation. Read the words that indicate the answer for each operation at the top of your page. (Review the chart with the students.) When the expression includes parentheses, there are two simple expressions within one numerical expression. Steps for writing an expression with parentheses into a written phrase are: 1. Read the operation in parentheses 2. Identify the math term that indicates the answer. (sum, difference, product, quotient) 3. Describe how the second operation relates to the answer in the parentheses. Guided Practice: Direct students attention to Example A. Read the expression 4 + (6 3). First, describe the portion of the expression within the parentheses using the word sum, difference, product, or quotient. We can interpret 6 3 as the product of 6 and 3. Next, describe how the second operation relates to the product of 6 and 3. We want to add the expression within the parentheses to 4, so we can interpret the whole expression as 4 plus the product of 6 and 3, or as the product of 6 and 3 added to 4. Repeat this process for Example B, (11 2) 3. (The answer for Example B is 3 into the difference of 11 and 2.) Independent Practice: Complete problems 1 4. Remember to interpret the operation within the parentheses first. Review: Write a word phrase for each numerical expression for problems 1 4. Discuss each answer, reviewing the key operation terms. Closure: Today we reviewed how to interpret numerical expressions into word phrases. Look at problem 4, (6 + 1) 8. Turn to your partner and discuss how you know that (6 + 1) 8 is eight times bigger than 6 + 1. Answers: Answers will vary. Possible answers include: 1. The product of 4 and 5 subtracted from 13 2. 9 more than the quotient of 4 and 2 3. 3 times the quotient of 10 and 5 4. The sum of 6 and 1 multiplied by 8 20
Domain: Operations & Algebraic Thinking Focus: Interpret Numerical Expressions Lesson: #12 Standard: 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Key words that indicate the answer to each operation: Sum: answer to an Addition problem Difference: answer to a Subtraction problem Product: answer to a Multiplication problem Quotient: answer to a Division problem Steps for writing an expression into a written phrase: 1. Read the operation in parentheses. 2. Identify the word that indicates the answer for that operation. (sum, difference, product, quotient) 3. Look at the expression again and describe how the second operation relates to the answer in the parentheses. Examples: A. 4 + (6 3) B. (11 2) 3 Directions: Write each numerical expression as a word phrase. 1. 13 (4 5) 2. (4 2) + 9 Sample Daily Lesson - Student Response Page 3. 3 (10 5) 4. (6 + 1) 8 21
Domain: Operations & Algebraic Thinking Focus: Interpret Numerical Expressions Evaluation: #3 The weekly evaluation may be used in the following ways: As a formative assessment of the students progress. As an additional opportunity to reinforce the vocabulary, concepts, and knowledge presented during the week of instruction. Standard: 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. Sample Assessment - Teacher Lesson Plan Procedure: Read the directions aloud and ensure that students understand how to respond to each item. If you are using the weekly evaluation as a formative assessment, have the students complete the evaluation independently. If you are using it to reinforce the week s instruction, determine the items that will be completed as guided practice and those that will be completed as independent practice. Review: Review the correct answers with students as soon as they are finished. Answers: 1. (5.OA.2) B, 9 divided by 3 Answers may vary. Possible answers include: 2. (5.OA.2) 5 added to the product of 2 and 7, or 5 more than the product of 2 and 7 3. (5.OA.2) The difference of 8 and 4 divided by 2, or 2 into the difference of 8 and 4 4. (5.OA.2) The product of 3 and 5 subtracted from 12, or 12 minus the product of 3 and 5 5. (5.OA.2) 2 times the sum of 3 and 7, or double the sum of 3 and 7 22
Domain: Operations & Algebraic Thinking Focus: Interpret Numerical Expressions Evaluation: #3 Key words that indicate the answer to each operation: Sum: answer to an Addition problem Difference: answer to a Subtraction problem Product: answer to a Multiplication problem Quotient: answer to a Division problem Directions: Circle the letter next to the phrase that describes the expression. 1. Which describes the expression 9 3? A. 3 divided by 9 B. 9 divided by 3 C. 3 less than 9 D. 9 into 3 Directions: Write the numerical expression as a word phrase. 2. 5 + (2 7) 3. (8 4) 2 Sample Assessment - Student Response Page 4. 12 (3 5) 5. (3 + 7) 2 23
Teacher Lesson Plan Page 1 of 2 Common Core Standards Plus Mathematics Grade 5 Performance Lesson #10 Domain: Operations and Algebraic Thinking Standard Reference: 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. Required Student Materials: Student Pages: BLM Pgs. 213-214 (Vocabulary & Student Worksheet) Scratch paper Lesson Objective: The students will use grouping symbols to write and evaluate expressions. They will interpret expressions without actually calculating the values of the expressions. Sample Performance Lesson - Teacher Lesson Plan Overview: Students will review the use of parentheses, brackets, and braces in numerical expressions. Students will also review how to write and interpret simple expressions as addressed in Common Core Standards Plus Operations and Algebraic Thinking Lessons 1-12, E1-E3. Students will: Use grouping symbols (parentheses, brackets, and braces) and evaluate expressions that include grouping symbols. Write simple expressions from a word phrase. Interpret expressions without finding the values of the expressions. Guided Practice: (Required Student Materials: BLM Pg. 213) Review the vocabulary terms: Expression, interpret, and evaluate. Review how and why to use grouping symbols to organize multiple groups in a numeric expression. Remind students to use the Order of Operations when evaluating expressions. Work from left to right. Parentheses (and other grouping symbols) Exponents Multiply and Divide (have the same priority) Add and Subtract (have the same priority) Review how to evaluate numeric expressions that have one or more groups. Review how to write simple expressions. With guidance, students will write and evaluate the numeric expressions for these word phrases: Seven times the sum of five + eight: 7(5+8) = 91 Two times sixty-two plus forty-eight: 2 x (62 + 48) = 220 Review how to interpret a numeric expression without finding the value. With guidance, students will interpret an expression and discuss the interpretation with a partner. Follow with a whole class discussion. 24
Teacher Lesson Plan Page 2 of 2 Common Core Standards Plus Mathematics Grade 5 Performance Lesson #10 Domain: Operations and Algebraic Thinking Independent Practice: (Required Student Materials: BLM Pg. 214) Have students: Use the information in the situation to write an expression that includes grouping symbols. Interpret two expressions and explain in writing how they interpreted the expressions without solving the expressions. Review & Evaluation: Option 1: Students trade papers with a partner and discuss if their answers are the same or different. Option 2: Teacher selects students answers to display and discuss possible answers with the class. Option 3: Teacher collects students papers and evaluates them for students ability to demonstrate conceptual understanding of the standard and ability to explain thinking. Sample Performance Lesoon - Teacher Lesson Plan 25
Student Page 1 of 2 Common Core Standards Plus Mathematics Grade 5 Performance Lesson #10 Domain: Operations and Algebraic Thinking Vocabulary: Expression: A string or list of mathematical symbols. 8 + 8 90 + 5 2 (77 + 3) 10 Interpret: Understanding a numerical expression without evaluating. Evaluate: Simplify, solve, or find the value of the expression. Grouping symbols: They are used to indicate/show when a group starts and ends; when there is more than one grouping in a problem, using different kinds of grouping symbols can help you separate the groups. Sample Performance Lesson - Student Response Page Parentheses (): Most common grouping symbol; parentheses surround the part of a math expression that must be solved first. 50 (10 5) Brackets []: Expressions cannot include brackets unless there are parentheses; brackets are used the second groupings. [5 + (25 5) 10] + 20 Braces {}: Expressions cannot include braces unless there are parentheses and brackets; braces are used for third groupings. {50 + [10 + (100 30) 10] + 9} Rules for translating a word phrase into a numerical expression. Step 1: Translate a word phrase into a series of numbers and operations. Step 2: Identify the key words that indicate the operation. Step 3: Decide on which side of the operation to place each number. Directions: Listen carefully to each word phrase and write it as a numeric expression. Evaluate the expression. 1. 2. Interpret the numeric expressions without finding the actual value. Discuss the interpretation with a partner. 3. 7 x (8900 + 5900) (8900 + 5900) 26
Student Page 2 of 2 Common Core Standards Plus Mathematics Grade 5 Performance Lesson #10 Domain: Operations and Algebraic Thinking Directions: Write a numeric expression for the following situation using appropriate grouping symbols. 4. Tyler needs money to pay for his baseball equipment. His mom gave him $50 and his dad gave him $60. A week later his grandma sent him $125. Tyler then spent $75 on a new mitt. Then his aunt sent him $50. Directions: Interpret the two expressions without finding their actual values. Explain how you interpreted the expressions. 5. [(4700 + 4500) + 989] x 2 [(4700 + 4500) + 989] x 8 Sample Performance Lesoon - Student Repsone Page 27
Common Core Standards Plus - Math Grade 5 Lesson Index Domain Lesson Focus Standard(s) Number and Operations in Base Ten (Number and Operations in Base Ten Standards 5.NBT.1-5.NBT.7) 5.NBT.1: Recognize that in a multi- digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. TE Page 1 Place Value Patterns 30 3 2 Place Value Patterns 32 4 3 Place Value Patterns 34 5 4 Place Value Patterns 36 6 E1 Evaluation - Place Value Patterns 38 7 5 Powers of Ten 5.NBT.2: Explain patterns in the number of zeros 40 9 of the product when multiplying a number by 6 Multiply by Powers of Ten 42 10 powers of 10, and explain patterns in the 7 Divide by Powers of Ten placement of the decimal point when a decimal is 44 11 8 E2 Multiply & Divide by Powers of Ten Evaluation - Powers of Ten multiplied or divided by a power of 10. Use whole- number exponents to denote powers of 10. 46 48 12 13 Performance Lesson Number and Operations in Base Ten: Power of Ten (5.NBT.1, 5.NBT.2) 9 Word Form of Decimals 5.NBT.3: Read, write, and compare decimals to thousandths. 5.NBT.3a: Read and write decimals to thousandths using base- ten numerals, number names, and expanded form, e.g., 347.392 = 3 100 + 4 10 + 7 1 + 3 (1/10) + 9 (1/100) + 2 (1/1000). P1 St. Ed. Page DOK Level 50 15-17 3 54 18 10 Expanded Form of Decimals 56 19 11 Standard Form of Decimals 58 20 12 Decimal Forms 60 21 E3 Evaluation - Decimal Forms 62 22 64 23 13 Compare Decimals 5.NBT.3b: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of 14 Compare Decimals 66 24 comparisons. 15 Round Decimals 5.NBT.4: Use place value understanding to round decimals to any place. 68 25 16 Round Decimals 70 26 E4 Evaluation Compare, Round Decimals 5.NBT.3b, 5.NBT.4 72 27 Performance Lesson Number and Operations in Base Ten: Working with Decimals P2 (5.NBT.3, 5.NBT.3a, 5.NBT.3b, 5.NBT.4) 17 Multiply Whole Numbers 5.NBT.5: Fluently multiply multi- digit whole numbers using the standard algorithm. 74 29-31 3 78 32 18 Multiply Whole Numbers 80 33 19 Multiply Whole Numbers 82 34 20 Multiply Whole Numbers 84 35 E5 Evaluation - Multiply Whole Numbers 86 36 21 Divide Whole Numbers 5.NBT.6: Find whole- number quotients of whole numbers with up to four- digit dividends and two- digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Performance Lesson Number and Operations in Base Ten: Multiplication and Division P3 (5.NBT.5, 5.NBT.6) 88 37 22 Divide Whole Numbers 90 38 23 Divide Whole Numbers 92 39 24 Divide Whole Numbers 94 40 E6 Evaluation- Divide Whole Numbers 96 41 98 43-44 3 28 2013 Learning Plus Associates
Common Core Standards Plus - Math Grade 5 Lesson Index Common Core Standards Plus Mathematics Grade 5 Domain Lesson Focus Standard(s) Number and Operations in Base Ten (Number and Operations in Base Ten Standards 5.NBT.1-5.NBT.7) 25 Add Decimals 5.NBT.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. TE Page St. Ed. Page 102 45 26 Add Decimals 104 46 27 Subtract Decimals 106 47 28 Subtract Decimals 108 48 E7 Evaluation - Add and Subtract Decimals 110 49 29 Multiply Decimals 5.NBT.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 112 51 30 Multiply Decimals 114 52 31 Multiply Decimals 116 53 32 Multiply Decimals 118 54 E8 Evaluation - Multiply Decimals 120 55 33 Multiply Decimals 5.NBT.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 122 57 34 Multiply Decimals 124 58 35 Divide Whole Numbers by 1/10 th 126 59 36 Divide Whole Numbers by 1/100 th 128 60 E9 Evaluation- Multiply and Divide Decimals 130 61 37 Divide a Decimal by a Whole Number 5.NBT.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 132 63 38 Divide a Decimal by a Whole Number 134 64 39 Divide a Whole Number by a Decimal 136 65 40 Divide Decimals to Hundredths 138 66 E10 Evaluation - Division with Decimals 140 67 P4 Performance Lesson Number and Operations in Base Ten: Operations with Decimals (5.NBT.7) Integrated Project #1: Now Serving Breakfast (5.NBT.1, 5.NBT.2, 5.NBT.3, 5.NBT.3a, 5.NBT.3b, 5.NBT.4, 5.NBT.5, 5.NBT.6, 5.NBT.7) Prerequisite Common Core Standards Plus Domain: Number and Operations in Base Ten Product: A breakfast menu with items and prices, and ten challenge problems based on the menu. DOK Level 142 69-71 3 149-152 72-74 4 Overview: In this project the students will work individually or in pairs to create a breakfast menu with multiple items and their individual prices. They will write ten challenge problems based on the menu that show an understanding of the standards taught in the Number and Operations in Base Ten Domain. They will present the menu and problems to another student or pair to solve the problems that have been written. Since this is a learning activity, all components will be completed in class. 2013 Learning Plus Associates 29
Common Core Standards Plus - Math Grade 5 Lesson Index Common Core Standards Plus Mathematics Grade 5 Domain Lesson Focus Standard(s) Number and Operations Fractions (Number and Operations Fractions Standards 5.NF.1-5.NF.7c) 1 Add Fractions 5.NF.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. TE Page St. Ed. Page 168 75 2 Add Fractions in Context 5.NF.2: see below 170 76 3 Add Mixed Numbers 5.NF.1 172 77 4 Add Mixed Numbers in Context 5.NF.2 174 78 E1 Evaluation Add Fractions and Mixed Numbers 5.NF.1, 5.NF.2 176 79 5 Subtract Fractions 5.NF.1 178 81 6 Subtract Fractions in Context 5.NF.2 180 82 7 Subtract Mixed Numbers 5.NF.1 182 83 8 Subtract Mixed Numbers in Context 5.NF.2 184 84 E2 Evaluation Subtract Fractions and Mixed Numbers 9 Add/Estimate Fraction Problems 5.NF.1, 5.NF.2 186 85 5.NF.2: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. 188 87 10 Add/Estimate Fraction Problems 190 88 11 Subtract/Estimate Fraction Problems 192 89 12 Subtract/Estimate Fraction Problems 194 90 E3 Evaluation Solving Fraction Problems 196 91 13 Interpret Fractions as Division 5.NF.3: Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. 198 93 14 Interpret Fractions as Division 200 94 15 Solve Problems with Fractions 202 95 16 Solve Problems with Mixed Numbers 204 96 E4 Evaluation Solving Fraction Problems 206 97 Performance Lesson Number and Operations Fractions: Add & Subtract P5 Fractions and Mixed Numbers (5.NF.1, 5.NF.2, 5.NF.3) 17 Multiply Fractions 5.NF.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 5.NF.4a: Interpret the product (a/b) q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a q b. DOK Level 208 99-101 3 212 102 18 Multiply Fractions 214 103 19 Multiply Fractions 216 104 20 Multiply Fractions 218 105 E5 Evaluation - Multiply Fractions 220 106 30 2013 Learning Plus Associates
Common Core Standards Plus - Math Grade 5 Lesson Index Domain Lesson Focus Standard(s) Number and Operations Fractions (Number and Operations Fractions Standards 5.NF.1-5.NF.7c) TE Page St. Ed. Page 21 Multiply Fractions 5.NF.4, 5.NF.4b: Find the area of a rectangle with 222 107 fractional side lengths by tiling it with unit squares of 22 Multiply Fractions to Find Area 224 108 the appropriate unit fraction side lengths, and show 23 Multiply Fractions to Find Area that the area is the same as would be found by 226 109 24 E6 Multiply Fractions to Find Area Evaluation- Multiply Fractions to Find Area multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. 228 230 110 111 232 113 25 Interpret Multiplication as Scaling 5.NF.5: Interpret multiplication as scaling (resizing), by: 5.NF.5a: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, 26 Interpret Multiplication as Scaling 234 114 27 Interpret Multiplication as Scaling without performing the indicated multiplication. 5.NF.5, 5.NF.5b: Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number; explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relate the principle of fraction equivalence a/b = (n a)/(n b) to the effect of multiplying a/b by 1. 236 115 28 Interpret Multiplication as Scaling 238 116 Evaluation- Interpret Multiplication as E7 Scaling 29 Fraction Multiplication Problems 5.NF.5, 5.NF.5a, 5.NF.5b 240 117 242 119 30 Fraction Multiplication Problems 244 120 31 Fraction Multiplication Problems 246 121 32 Fraction Multiplication Problems 248 122 E8 Evaluation- Fraction Multiplication 5.NF.6: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Problems 250 123 Performance Lesson Number and Operations Fractions: Multiplying Fractions P6 (5.NF.4, 5.NF.4a, 5.NF.5, 5.NF.5b,, 5.NF.6) 33 Divide a Fraction by a Whole Number 5.NF.7: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 5.NF.7a: Interpret division of a unit fraction by a non- zero whole number, and Evaluation- Divide a Fraction by a Whole compute such quotients. DOK Level 252-253 125-128 3 258 129 34 Divide a Fraction by a Whole Number 260 130 35 Divide a Fraction by a Whole Number 262 131 36 Divide a Fraction by a Whole Number 264 132 E9 Number 266 133 37 Divide a Whole Number by a Fraction 268 135 38 Divide a Whole Number by a Fraction 270 136 39 Divide a Whole Number by a Fraction 5.NF.7b: Interpret division of a whole number by 272 137 a unit fraction, and compute such quotients. 40 Divide a Whole Number by a Fraction 274 138 Evaluation- Divide a Whole Number by a E10 276 139 Fraction 41 Solve Real World Fraction Problems 278 141 5.NF.7c: Solve real world problems involving 42 Solve Real World Fraction Problems division of unit fractions by non- zero whole 280 142 43 Solve Real World Fraction Problems numbers and division of whole numbers by unit 282 143 fractions, e.g., by using visual fraction models and 44 Solve Real World Fraction Problems equations to represent the problem. 284 144 E11 Evaluation- Real World Fraction Problems 286 145 P7 Performance Lesson Number and Operations Fractions: Real World Fraction Problems (5.NF.7, 5.NF.7a, 5.NF.7b, 5.NF.7c) 288 147-149 3 2013 Learning Plus Associates 31
Common Core Standards Plus - Math Grade 5 Lesson Index Common Core Standards Plus Mathematics Grade 5 Domain Lesson Focus Standard(s) Measurement and Data (Measurement and Data Standards 5.MD.1-5.MD.5c) 1 Converting Metric Units 5.MD.1: Convert among different- sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi- step, real world problems. TE Page St. Ed. Page 302 150 2 Converting Metric Units 304 151 3 Converting Customary Units 306 152 4 Converting Customary Units 308 153 Evaluation - Converting Measures within the Same System 5 Fractional Data Sets E1 310 154 312 155 6 Fractional Data Sets 314 156 5.MD.2: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Evaluation - Solving Problems with Fractional Data Sets Performance Lesson Measurement and Data: Measurement Units & Line Plots (5.MD.1, 5.MD.2) 9 Measure with Cubic Units 5.MD.3: Recognize volume as an attribute of solid figures and understand concepts of volume measurement. 7 Fractional Data Sets 316 157 8 Fractional Data Sets 318 158 E2 P8 320 159 DOK Level 322 161-163 3 326 164 10 Measure with Cubic Units 328 165 11 Measure with Cubic Units 5.MD.4: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 330 166 12 Measure with Cubic Units 332 167 E3 Evaluation - Measure with Cubic Units 5.MD.3, 5.MD.4 334 168 13 14 15 16 E4 Find Volume by Multiplying Edge Lengths Find Volume by Multiplying Edge Lengths Find Volume by Multiplying Edge Lengths Find Volume by Multiplying Edge Lengths Evaluation- Find Volume by Multiplying Edge Lengths 17 Apply the Formulas for Volume 5.MD.5: Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. 5.MD.5a: Find the volume of a right rectangular prism with whole- number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole- number products as volumes, e.g., to represent the associative property of multiplication. 336 169 338 170 340 171 342 172 344 173 346 175 18 Apply the Formulas for Volume 348 176 19 20 E5 Apply Volume Formulas to Solve Problems Apply Volume Formulas to Solve Problems Evaluation- Apply Volume Formulas to Solve Problems 5.MD.5b: Apply the formulas V = l w h and V = b h for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real world and mathematical problems. 350 177 352 178 354 179 32 2013 Learning Plus Associates
Common Core Standards Plus - Math Grade 5 Lesson Index Common Core Standards Plus Mathematics Grade 5 Domain Lesson Focus Standard(s) Measurement and Data (Measurement and Data Standards 5.MD.1-5.MD.5c) 21 22 23 24 Volume of Non- overlapping Right Rectangular Prisms Volume of Non- overlapping Right Rectangular Prisms Solving Volume Problems by Decomposing Prisms Solving Volume Problems by Decomposing Prisms 5.MD.5c: Recognize volume as additive. Find volumes of solid figures composed of two non- overlapping right rectangular prisms by adding the volumes of the non- overlapping parts, applying this technique to solve real world problems. TE Page St. Ed. Page 356 181 358 182 360 183 362 184 E6 Evaluation - Solving Volume Problems 364 185 P9 Performance Lesson Measurement and Data: All About Volume (5.MD.3, 5.MD.4, 5.MD.5, 5.MD.5a, 5.MD.5b, 5.MD.5c) Integrated Project #2: Recycled Home Design (5.NF.1, 5.NF.2, 5.NF.3, 5.NF.4, 5.NF.4a, 5.NF.4b, 5.NF.5, 5.NF.5a, 5.NF.5b, 5.NF.6, 5.NF.7, 5.NF.7a, 5.NF.7b, 5.NF.7c, 5.MD.1, 5.MD.3, 5.MD.4, 5.MD.5, 5.MD.5a, 5.MD.5b, 5.MD.5c) Prerequisite Common Core Standards Plus Domains: Number and Operations Fractions and Measurement and Data DOK Level 366 187-189 3 373-378 191-194 4 Project Objective: The students will apply what they have learned in the Number and Operations Fractions and Measurement and Data Domains to design a home made from recycled cargo containers and determine the size of air conditioner needed based on the cubic capacity of the home they design. Overview: In this project, the students will design a house made exclusively of recycled cargo containers. They will draw the house design, provide the square footage of the home, and use the cubic capacity of the home to determine the air conditioner size needed to cool the home. They will write a description of the home, including rooms and amenities found in the home. They will present their designs to the class. Since this is a learning activity, all components will be completed in class. 2013 Learning Plus Associates 33
Common Core Standards Plus - Math Grade 5 Lesson Index Common Core Standards Plus Mathematics Grade 5 Domain Lesson Focus Standard(s) Operations and Algebraic Thinking (Operations and Algebraic Thinking Standards 5.OA.1-5.OA.3) 1 Evaluating Expressions 5.OA.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. TE Page St. Ed. Page 392 195 2 Evaluating Expressions 394 196 3 Evaluating Expressions 396 197 4 Evaluating Expressions 398 198 E1 Evaluation- Evaluating Expressions 400 199 5 Writing Numerical Expressions 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. 402 201 6 Writing Numerical Expressions 404 202 7 Writing Numerical Expressions 406 203 8 Writing Numerical Expressions 408 204 E2 Evaluation- Writing Numerical Expressions 410 205 9 Interpret Numerical Expressions 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. 412 207 10 Interpret Numerical Expressions 414 208 11 Interpret Numerical Expressions 416 209 12 Interpret Numerical Expressions 418 210 E3 Evaluation- Interpret Numerical Expressions 420 211 P10 Performance Lesson Operations and Algebraic Thinking: Expressions (5.OA.1, 5.OA.2) 422-423 213-214 3 13 Generating Arithmetic Patterns 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. 426 215 14 Pattern Relationships 428 216 15 Pattern Relationships 430 217 16 Pattern Relationships 432 218 E4 Evaluation- Pattern Relationships 434 219 17 Pattern Relationships 436 221 DOK Level 18 Pattern Relationships 438 222 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. 19 Graphing Patterns 440 223 20 Graphing Patterns 442 224 E5 Evaluation- Pattern Relationships 444 225 P11 Performance Lesson Operations and Algebraic Thinking: Patterns (5.OA.3) 446 227-228 3 34 2013 Learning Plus Associates
Common Core Standards Plus - Math Grade 5 Lesson Index Common Core Standards Plus Mathematics Grade 5 Domain Lesson Focus Standard(s) Geometry (Geometry Standards 5.G.1-5.G.4) 1 Plotting Points on a Coordinate Grid 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. TE Page St. Ed. Page 456 229 2 Plotting Points on a Coordinate Grid 458 230 3 Graphing and Interpreting Points 460 231 4 Graphing and Interpreting Points 462 232 E1 Evaluation- Understanding and Interpreting Coordinate Systems 5.G.1, 5.G.2 464 233 P12 Performance Lesson Geometry: Graph It! (5.G.1, 5.G.2) 466 235-236 3 5 Understanding Attributes of Triangles 6 Creating a Hierarchy of Triangles 7 Understanding Attributes of Quadrilaterals 5.G.3: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. 470 237 5.G4: Classify two- dimensional figures in a hierarchy based on properties. 472 238 5.G.3 474 239 8 Creating a Hierarchy of Quadrilaterals 5.G.4 476 240 E2 Evaluation- Two Dimensional Shapes Classifying and Hierarchy 5.G.3, 5.G.4 478 241 P13 Performance Lesson Geometry: Just Plane Hierarchy (5.G.3, 5.G.4) 480 243-244 3 Integrated Project #3: What s in a Building? (5.OA.1, 5.OA.2, 5.OA.3, 5.G.1, 5.G.2, 5.G.3, 485-489 245-247 4 5.G.4) Prerequisite Common Core Standards Plus Domains: Operations and Algebraic Thinking and Geometry Product: A mathematical analysis of the types of figures, their attributes, and relative numbers and patterns of the figures within an assigned building. Overview: In this project the students will learn about a famous building. They will study the geometric composition of the building, including windows, doors, towers, columns, base, overall shape, and/or unique features to provide a mathematical description of the building. They will explain the shapes, patterns, and attributes of the features unique to the building. They will include numerical expressions, numerical patterns, and graphs to represent the geometrical figures included in the building. They will orally present what they have learned. You may choose to have students work individually or in pairs. Since this is a learning activity, all components will be completed in class. DOK Level 2013 Learning Plus Associates 35
Standards Plus is Proven Effective in California Schools CALIFORNIA SBAC GROWTH RATE STANDARDS PLUS SCHOOLS SBAC GROWTH RATE* more than doubled OVER 83% of Schools that implemented Standards Plus in 2015-2016 more than doubled the California SBAC growth rate in one or more grade level. Standards Plus Closes the Achievement Gap with 7 Different Programs in One Standards Plus includes: Today s Lesson Performance Lessons Integrated Projects 15-20 Minute Direct Instruction Lessons in Print and Online Increase EL Performance with Equity ELA & Math in Grades K-8 Transfer of Knowledge to a Digital Learning Environment Intervention Materials Built-In Students Experience Technology Consistent with the CA Test Fits into Every Budget starting at $10.00 www.standardsplus.org 1 877 505 9152 a Student