Grade Span Differentiation ~

Computation Assessments for K-2, 3-5, 6-8 and High School

Clare Harrington

University of Maine Farmington

March 9, 2013

K-2:

Use place value understanding and properties of operations to add and subtract:

CCSS.Math.Content.2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

CCSS.Math.Content.2.NBT.B.7 Add and subtract within 1000, 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. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Represent and solve problems involving addition and subtraction.

CCSS.Math.Content.2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1

CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them.

CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.

CCSS.Math.Practice.MP4 Model with mathematics.

CCSS.Math.Practice.MP6 Attend to precision.

Scoring chart: 8 possible points

Part A: 1 pt for correct Ballpark number sentence.

1 pt for correct number model.

` 1 pt for clearly showing how the solution was reached and 1 point for correct answer.

1 pt for correct answer with correct label.

Part B: 1 pt for using the correct numbers.

1 pt for using words that clearly indicate addition is needed.

1 pt for clearly showing how the solution was reached and 1 point for correct answer.

1 pt for correct answer with correct label.

Rubric:

Exceeds 8 points; plus student uses correct grammar and accurate mathematical terms.

Meets 7- 8 points; Student completes all parts of the assessment with no errors.Partially Meets 5-6 points; Student shows understanding but has made some calculation

errors.Does not meet 0-4 points; Student may or may not attempt work but work is incomplete or

contains many errors.

Student Rubric:

I got it! I got it all right!

I’m working on this.

I did at least half of this right.

I need some help, please.

I can’t do this or I tried to do this but still don’t get it.

Grade 2 assessment:

Write a number model to show your ballpark estimate. Write a number sentence to solve the problem. Show ALL work.

A. There are two second grade classes at Park School. One class has 34 children. The other has 29 children. How many children are in second grade at Park School?

Ballpark estimate: _________________________

Number model: __________________________

Show work:

Answer: _____________________________

B. Write a number story for 18 + 57. Solve your number story.

__________________________________________________ Show Work:

__________________________________________________

__________________________________________________

__________________________________________________

__________________________________________________

Answer: ____________________________

Grades 3-5:

Grade 4 CCSS.Math.Content.4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.

CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them.

CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.

CCSS.Math.Practice.MP4 Model with mathematics.

CCSS.Math.Practice.MP6 Attend to precision.

Scoring chart:

Part A: 1 pt for correct number model.

` 1 pt for clearly showing how the solution was reached

1 point for correct answer.

1 pt for correct answer with correct label.

Part B: .5 point for each correct box. (4 points total)

Rubric:

Meets 7- 8 points; Student completes all parts of the assessment with only 1 minor error.Partially meets

5-6 points; Student shows understanding but has made some calculation errors.

Does Not meet

0-4 points; Student does not attempt work or attempts work but work is incomplete or contains many errors.

Student Rubric:

Meets I have shown all my work and it is all correct.

Partially meets

I did all the work but made some minor mistakes.

Does Not meet

I did not try to answer the problems or I did not answer the questions correctly.

Grade 4 Assessment

Use the U.S. traditional algorithm to solve each problem.

A. Hiroshi had $356 in his bank account this morning. This afternoon he deposited $85 into the account. How much is in Hiroshi’s account now?

Show all work.

Answer: _____________________________________

B: Fill in the missing digits in the addition problems.

Grades 6-8:

Compute fluently with multi-digit numbers and find common factors and multiples. CCSS.Math.Content.6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them.

CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.

CCSS.Math.Practice.MP4 Model with mathematics.

CCSS.Math.Practice.MP6 Attend to precision.

Scoring: possible

1 pt for each correct answer.

1 point for each correct work example.

.5 point given for correct set up but incorrect calculations.

.25 points given for each correct number in box.

.25 points for decimal point placed accurately in the answer.

Rubric for student and assessor: (thanks to Amanda Pullen for sharing her rubric and allowing me to adapt it.)

MEETS

3

PARTIALLY MEETS2

DOES NOT MEET1

I can add decimals. Shows understanding and work is correct.Scored 3.25 pts.

Shows understanding but has made a calculation error. Scored 2-3 pts.

Shows little or no understanding of how to add decimals. Scored less than 2 pts.

I can subtract decimals. Shows understanding and work is correct. Scored 4 pts.

Shows understanding but has made a calculation error. Scored 2.5 – 3.75

Shows little or no understanding of how to subtract decimals.Scored less than 2.5 pts.

I can multiply decimals.

Shows understanding and work is correct.Scored 3.25 pts

Shows understanding but has made a calculation error.Scored 2-3 pts.

Shows little or no understanding of how to multiply decimals. Scored less than 2 pts.

I can divide decimals. Shows understanding and work is correct.Scored 3.25 pts

Shows understanding but has made a calculation error.Scored 2-3 pts.

Shows little or no understanding of how to divide decimals. Scored less than 2 pts.

Grade 6 Assessment:

Solve using US standard algorithm.

A. 5.201 + 2.49 = ______________________

Show all work.

B. 7.1 – 2.855 = ______________________

Show all work.

C. 4.13 x 2.1 = ______________________

Show all work.

D. 6.9/ 2.1 = ______________________

Show all work. (Carry answer out 2 decimal points.)

E.

F. Solve 32.52 / .6 using the US Traditional algorithm. Insert decimal point(s) where necessary.

Answer: ________________________

High School

CCSS.Math.Content.HSN-CN.A.2 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them.

CCSS.Math.Practice.MP6 Attend to precision.

Scoring:

1 pt for each correct answer.

Rubric for both student and assessor:

Meets 6 points; student work is correct.Partially Meets

3-5 points; Student shows understanding but there are some incorrect incorrect answers.

Does Not Meet

0-3 points; student does not show clear understanding of complex numbers.

HS Assessment:

1. (3 - 5i) + (3 + 5i) =

2. (3 - i) (2 - 2i) =

3. (3 – 4i) – (1 – 4i) =

4. (4 + 2i) + (-2 + 3i) =

5. (3 + 4i) (3 – 4i) =

6. (-3 + 2i) – (4 – i) =

Answers:

1. (3 - 5i) + (3 + 5i) = 6

2. (3 - i) (2 - 2i) = -8 + 4i

3. (3 – 4i) – (1 – 4i) = 2

4. (4 + 2i) + (-2 + 3i) = 2 + 5i

5. (3 + 4i) (3 – 4i) = 25

6. (-3 + 2i) – (4 – i) = -7 + 3i