Troy School District · Mathematics · Kindergarten
Form A · 120 minutes (with breaks) · 100 points

Kindergarten Mathematics — Testing-Out Examination

A student who passes this examination has demonstrated mastery of the Common Core Kindergarten standards (K.CC, K.OA, K.NBT, K.MD, K.G) and is eligible to advance directly to Grade 1 Mathematics.

Format and proctor instructions

Student Name
Proctor
Score

SESSION 1 · Tasks 1–3 (about 30 minutes)

1. Counting and cardinality 14 points
  1. Counting to 100 out loud. The proctor says: "Please count out loud starting from 1. I will tell you when to stop." The student counts to 100. (Proctor: stop the student at 100. Mark any number where the student gets stuck or skips. Award up to 3 points: 3 = counted to 100 with no mistakes; 2 = counted to 100 with at most 2 mistakes; 1 = counted to at least 50; 0 = otherwise.)

    Errors observed: ____________________________     Points: ___ / 3

  2. Counting forward from a given number. Proctor: "Start at 47 and count up to 60."

    Result: ____________________________     Points: ___ / 2

  3. Skip-counting by tens. Proctor: "Count by tens up to 100."

    Result: 10, 20, ___, ___, ___, ___, ___, ___, ___, ___     Points: ___ / 2

  4. Writing numerals. The student writes each numeral in the box: 0, 5, 9, 13, 17, 20.

    [student writes here]     Points: ___ / 2

  5. Count objects to answer "How many?" — line, array, scattered. The proctor presents three cards in turn:

    Card A: 14 stars in a single line. Student answer: ___     Card B: 18 dots in a 3-by-6 array. Student answer: ___     Card C: 9 fish scattered. Student answer: ___     Points: ___ / 3

  6. Compare two groups. The proctor places two piles of counters: pile X has 8 counters; pile Y has 11 counters. "Which pile has more? Which has fewer? How many more does Y have than X?"

    Student answers: more = ___    fewer = ___    difference = ___     Points: ___ / 2

2. Addition within 10 (objects, drawings, fingers) 12 points
  1. Find each answer using counters or fingers. The proctor lays out groups of counters and asks "How many in all?":

    (i) \(3 + 4\) → ___     (ii) \(5 + 2\) → ___     (iii) \(6 + 4\) → ___     (iv) \(0 + 7\) → ___     Points: ___ / 4

  2. Word problem (proctor reads): "There are 4 birds in a tree. 3 more birds fly into the tree. How many birds are in the tree now?"

    Student draws the situation here.     Answer: ___     Points: ___ / 2

  3. Break 7 into two groups in three different ways. "Show three ways to make 7 using two groups of counters."

    Student draws or describes:
    ___ + ___ = 7     ___ + ___ = 7     ___ + ___ = 7     Points: ___ / 3

  4. Make 10. The proctor says: "What number do I need to add to 6 to make 10?" Then: "To 4?" Then: "To 9?"

    Answers: ___, ___, ___     Points: ___ / 3

3. Subtraction within 10 10 points
  1. Find each answer (counters or fingers OK):

    (i) \(8 - 3\) → ___     (ii) \(10 - 6\) → ___     (iii) \(7 - 7\) → ___     (iv) \(9 - 4\) → ___     Points: ___ / 4

  2. Word problem (proctor reads): "Mia has 9 cookies. She gives 4 cookies to her brother. How many cookies does Mia have left?"

    Student draws the situation here.     Answer: ___     Points: ___ / 2

  3. Quick math facts to 5. Proctor reads each one quickly: "5 minus 2; 4 minus 1; 3 plus 2; 5 minus 5."

    Answers: ___, ___, ___, ___     Points: ___ / 4

— 10-minute break. —

SESSION 2 · Tasks 4–6 (about 30 minutes)

4. Make and break apart teen numbers 12 points
  1. Show 14 using one ten-rod and four ones (base-ten blocks). Then say: "14 is one 10 and 4 ones." Repeat for 11, 17, 19.

    Student demonstrations: 11 = ___ ten and ___ ones    17 = ___ ten and ___ ones    19 = ___ ten and ___ ones     Points: ___ / 6

  2. Break each teen number apart as \(10 + ?\):

    (i) \(13 = 10 + ?\)     (ii) \(15 = 10 + ?\)     (iii) \(18 = 10 + ?\)     Points: ___ / 3

  3. Build the number 16 in two different ways using counters and 10-frames. Sketch or describe each.

    Way 1: ____________________    Way 2: ____________________     Points: ___ / 3

5. Measurement attributes and comparison 12 points
  1. The proctor places three pencils of obviously different lengths on the table. The student orders them from shortest to longest.

    Order recorded by proctor: ____________________     Points: ___ / 2

  2. The proctor places two objects (e.g., a book and a stuffed animal) on the table. The student says which is heavier after lifting both.

    Student says: heavier = ____________________    lighter = ____________________     Points: ___ / 2

  3. The proctor sets out a mixed group of buttons: 4 red, 3 blue, 5 yellow. The student sorts them into groups by color and counts each.

    Counts: red ___, blue ___, yellow ___     Which group has the most? ___     Which has the fewest? ___     Points: ___ / 4

  4. The student arranges the three groups in order from fewest to most.

    Order: ____________________     Points: ___ / 2

  5. Describe one measurable attribute (length, weight, height) of a typical object, e.g., "This pencil is __________ (long / short / heavy / light)."

    Student response: ____________________     Points: ___ / 2

6. Name flat (2-D) shapes and position words 12 points
  1. The proctor shows the shape cards in turn: triangle, circle, square, rectangle, hexagon. The student names each and tells how many sides and corners (vertices).

    Triangle: ___ sides, ___ corners    Circle: ___ sides, ___ corners    Square: ___ sides, ___ corners    Rectangle: ___ sides, ___ corners    Hexagon: ___ sides, ___ corners     Points: ___ / 5

  2. The proctor places three objects on the table — a book, a cup, and a pencil. The proctor asks the student to describe positions:

    "Is the pencil above or below the book?" → ___
    "Is the cup beside or behind the book?" → ___
    "Is the pencil next to or far from the cup?" → ___     Points: ___ / 3

  3. Sketch each shape on the answer sheet:

    (i) a triangle     (ii) a square     (iii) a hexagon

  4. The proctor places two pattern-block triangles next to each other to form a larger shape. "What new shape did we make?" (Expected answer: a rhombus or "diamond" or larger triangle, depending on orientation.)

    Student response: ____________________     Points: ___ / 2

— 10-minute break. —

SESSION 3 · Tasks 7–8 (about 30 minutes)

7. Name solid (3-D) shapes & build simple shapes 14 points
  1. The proctor shows the four 3-D shape models in turn: cube, cone, cylinder, sphere. The student names each and points to one example of each in the room (e.g., a ball is a sphere; a soup can is a cylinder).

    Cube example: ____________________    Cone example: ____________________    Cylinder example: ____________________    Sphere example: ____________________     Points: ___ / 4

  2. How is a square (2-D) different from a cube (3-D)? Student explains in one phrase.

    Response: ____________________     Points: ___ / 2

  3. How is a circle different from a sphere?

    Response: ____________________     Points: ___ / 2

  4. Build a shape. The student uses pattern blocks to make a hexagon out of two trapezoids. Then out of six triangles. The proctor checks each.

    Built with two trapezoids? Yes / No    Built with six triangles? Yes / No     Points: ___ / 4

  5. Build with pattern blocks. The proctor says: "Use two triangles to build a square. Then use two squares to build a longer rectangle. Tell me what shape you made each time."

    Square from 2 triangles? Yes / No    Rectangle from 2 squares? Yes / No     Points: ___ / 2

8. Putting it all together — story problems 14 points

The proctor reads each story slowly, twice. The student may use counters, draw, or use fingers. The proctor records both the answer and the strategy used.

  1. "There are 5 frogs sitting on a log. 3 more frogs jump onto the log. Then 2 frogs hop off. How many frogs are on the log now?"

    Answer: ___    Strategy used: ____________________     Points: ___ / 3

  2. "A box has 10 crayons. 4 are red and the rest are blue. How many crayons are blue?"

    Answer: ___    Strategy used: ____________________     Points: ___ / 3

  3. "Sam counts 6 birds in his yard. He sees 4 more birds in the tree. How many birds in all?"

    Answer: ___    Strategy used: ____________________     Points: ___ / 3

  4. "Anna has 8 stickers. She gives some to her friend. Now she has 5 stickers. How many did she give away?"

    Answer: ___    Strategy used: ____________________     Points: ___ / 3

  5. "There are 12 cookies on a tray. The tray has two equal rows. How many cookies are in each row?"

    Answer: ___    Strategy used: ____________________     Points: ___ / 2