nys common core mathematics curriculum mid … m1 assessments.pdf · nys common core mathematics...

Lesson New York State Common Core

Mid-Module Assessment Task NYS COMMON CORE MATHEMATICS CURRICULUM 5•1

Name Date

1. Compare using >, <, or =.

a. 0.4 0.127 b. 2 thousandths + 4 hundredths 0.036

c. 2 tens 3 tenths 1 thousandth 20.31 d. 24 tenths 2.5

e. 4 × 103 + 2 × 100 + 3 × 110

4 × 1000 + 2 × 102 + 3 × 110

f. 3 × 110

+ 4 × 11000

0.340

2. Model the number 8.88 on the place value chart.

a. Use words, numbers, and your model to explain why each of the digits has a different value. Be sure to use “ten times as large” and “one tenth as large” in your explanation.

Module 1: Place Value and Decimal Fractions 129

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b. Multiply 8.88 × 104. Explain the shift of the digits and the change in the value of each digit.

c. Divide the product from (b) by 102. Explain the shift of the digits and the change in the value of each digit.

3. Rainfall collected in a rain gauge was found to be 2.3 cm when rounded to the nearest tenth of a centimeter.

a. Circle all the measurements below that could be the actual measurement of the rainfall.

2.251 cm 2.349 cm 2.352 cm 2.295 cm

b. Convert the rounded measurement to meters. Write an equation to show your work.







4. Average annual rainfall totals for cities in New York are listed below.

Rochester 0.97 meters Ithaca 0.947 meters Saratoga Springs 1.5 meters New York City 1.268 meters

a. Put the rainfall measurements in order from least to greatest. Write the smallest total rainfall in

word form and expanded form. b. Round each of the rainfall totals to the nearest tenth. c. Imagine New York City’s rainfall is the same every year. How much rain would fall in 100 years? d. Write an equation using an exponent that would express the 100-year total rainfall. Explain how the

digits have shifted position and why.







Mid-Module Assessment Task Standards Addressed

Topics A–C

Generalize place value understanding for multi-digit whole numbers

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.

5.NBT.2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

5.NBT.3 Read, write, and compare decimals to thousandths.

a. 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).

b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

5.NBT.4 Use place value understanding to round decimals to any place.

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.

Evaluating Student Learning Outcomes

A Progression Toward Mastery is provided to describe steps that illuminate the gradually increasing understandings that students develop on their way to proficiency. In this chart, this progress is presented from left (Step 1) to right (Step 4). The learning goal for students is to achieve Step 4 mastery. These steps are meant to help teachers and students identify and celebrate what the students CAN do now and what they need to work on next.







A Progression Toward Mastery

Assessment Task Item and Standards Assessed

STEP 1 Little evidence of reasoning without a correct answer. (1 Point)

STEP 2 Evidence of some reasoning without a correct answer. (2 Points)

STEP 3 Evidence of some reasoning with a correct answer or evidence of solid reasoning with an incorrect answer. (3 Points)

STEP 4 Evidence of solid reasoning with a correct answer. (4 Points)

1

5.NBT.3a 5.NBT.3b

Student answers none or one part correctly.

Student answers two or three parts correctly.

Student answers four or five parts correctly.

Student correctly answers all six parts:

a. > d. <

b. > e. =

c. < f. <

2

5.NBT.1 5.NBT.2


Student answers two parts correctly.

Student is able to answers all parts correctly but is unable to explain his strategy in Part (a), (b), or (c) or answers three of the four parts correctly.

Student accurately models 8.88 on the place value chart and correctly:

Uses words, numbers, and a model to explain why each digit has a different value.

Finds the product of 88,800 and explains.

Finds the quotient of 888 and explains.

3

5.NBT.4 5.MD.1

Student is unable to identify any answers for Part (a) or answer Part (b) correctly.

Student identifies one or two answers correctly for Part (a) and makes an attempt to convert, but gets an incorrect solution for Part (b).

Student identifies two answers correctly for Part (a) and converts correctly for Part (b).

OR

Student identifies three answers correctly for Part (a) and converts with a small error for Part (b).

Student identifies all three answers correctly for Part (a) and answers Part (b) correctly:

a. 2.251 cm, 2.349 cm, 2.295 cm.

b. 2.3 ÷ 102 = 0.023








4

5.NBT.1 5.NBT.2 5.NBT.3 5.NBT.4


Student answers two problems correctly.

Student is able to answer all parts correctly but is unable to explain the strategy in Part (d).

OR

Student answers three of the four problems correctly.

Student correctly responds:

a. 0.947 m, 0.97 m, 1.268 m, 1.5 m.

Nine hundred forty-seven thousandths meters.

0.9 + 0.04 + 0.007 or (9 × 0.1) + (4 × 0.01) + (7 × 0.001).

b. Rochester ≈ 1.0 m, Ithaca ≈ 0.9 m, Saratoga Springs ≈ 1.5 m, NYC ≈ 1.3 m.

c. 126.8 m.

d. 1.268 × 102 = 126.8, with valid explanation.





Lesson

End-of-Module Assessment Task NYS COMMON CORE MATHEMATICS CURRICULUM 5•1

Name Date

1. The following equations involve different quantities and use different operations, yet produce the same result. Use a place value chart and words to explain why this is true.

4.13 × 103 = 4130 413,000 ÷ 102 = 4130

2. Use an area model to explain the product of 4.6 and 3. Write the product in standard form, word form, and expanded form.









3. Compare using >, <, or =.

a. 2 tenths + 11 hundredths 0.13

b. 13 tenths + 8 tenths + 32 hundredths 2.42

c. 342 hundredths + 7 tenths 3 + 49 hundredths

d. 2 + 31 × 110

+ 14 × 1100

2.324

e. 14 + 72 × 110

+ 4 × 11000

21.24

f. 0.3 × 102 + 0.007 × 103 0.3 × 10 + 0.7 × 102









4. Dr. Mann mixed 10.357 g of chemical A, 12.062 g of chemical B, and 7.506 g of chemical C to make 5 doses of medicine.

a. About how much medicine did he make in grams? Estimate the amount of each chemical by rounding to the nearest tenth of a gram before finding the sum. Show all your thinking.

b. Find the actual amount of medicine mixed by Dr. Mann. What is the difference between your estimate and the actual amount?

c. How many grams are in one dose of medicine? Explain your strategy for solving this problem.

d. Round the weight of one dose to the nearest gram.









End-of-Module Assessment Task Standards Addressed

Topics A–F

Generalize place value understanding for multi-digit whole numbers.

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.

5.NBT.2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

5.NBT.3 Read, write, and compare decimals to thousandths.

a. 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).

b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

5.NBT.4 Use place value understanding to round decimals to any place.

Perform operations with multi-digit whole numbers and with decimals to hundredths.

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.

Convert like measurement units within a given measurement system.

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.

Evaluating Student Learning Outcomes

A Progression Toward Mastery is provided to describe steps that illuminate the gradually increasing understandings that students develop on their way to proficiency. In this chart, this progress is presented from left (Step 1) to right (Step 4). The learning goal for students is to achieve Step 4 mastery. These steps are meant to help teachers and students identify and celebrate what the students CAN do now and what they need to work on next.










Assessment Task Item and Standards Assessed

STEP 1 Little evidence of reasoning without a correct answer. (1 Point)

STEP 2 Evidence of some reasoning without a correct answer. (2 Points)

STEP 3 Evidence of some reasoning with a correct answer or evidence of solid reasoning with an incorrect answer. (3 Points)

STEP 4 Evidence of solid reasoning with a correct answer. (4 Points)

1

5.NBT.1 5.NBT.2

Student is unable to provide a correct response.

Student attempts but is not able to accurately draw the place value chart or explain reasoning fully.

Student correctly draws the place value chart but does not show full reasoning or explains reasoning fully, but the place value chart does not match the reasoning.

Student correctly:

Draws the place value chart showing movement of digits.

Explains the movement of units to the left for multiplication and the movement of units to the right for division.

2

5.NBT.7

Student is unable to use the area model to find the product.

Student attempts to use an area model to multiply but does so inaccurately. Student attempts to write either the word or expanded form of an inaccurate product.

Student uses the area model to multiply but does not find the correct product. The student accurately produces a word and expanded form of an inaccurate product.

Student correctly:

Draws an area model.

Shows work to find the product of 13.8.

Accurately expresses the product in both word and expanded form.

3

5.NBT.3a 5.NBT.3b


Student answers two or three answers correctly.

Student answers four or five answers correctly.

Student correctly answers all six parts.

a. > d. >

b. = e. <

c. > f. <










4

5.NBT.1 5.NBT.2

5.NBT.3a 5.NBT.3b 5.NBT.4 5.NBT.7 5.MD.1

The student answers none or one part correctly.

The student answers two parts correctly.

The student is able to find all answers correctly but is unable to explain the strategy in Part (c) or answers three of the four parts correctly.

The student correctly:

a. Estimates 10.357 g to 10.4 g, 12.062 g to 12.1 g, and 7.506 g as 7.5 g; finds the sum 30 g; shows work or model.

b. Finds the sum 29.925 g and the difference 0.075 g.

c. Finds the quotient 5.985 g and explains accurately the strategy used.

d. Rounds 5.985 g to 6 g.







nys common core mathematics curriculum mid … m1 assessments.pdf · nys common core mathematics...

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