Grade 2 Mathematics — Testing-Out Examination
A student who passes this examination has demonstrated mastery of the Common Core Grade 2 standards (2.OA, 2.NBT, 2.MD, 2.G) and is eligible to advance directly to Grade 3 Mathematics.
Instructions for the proctor and student
- Time limit: 120 minutes total. The student should take a 5-minute break after problem 4 and again after problem 7. The proctor may read items aloud once on request.
- Tools allowed: a ruler (with cm and inches), pattern blocks, base-ten blocks, fraction bars, and a clock face. Calculators are not allowed.
- Show your work. Drawings, equations, and short written explanations all count as work.
- Find each (no fingers; use what you know):
(i) \(8 + 7\) (ii) \(9 + 6\) (iii) \(15 - 8\) (iv) \(13 - 4\) (v) \(7 + 9\) (vi) \(17 - 9\)
- Find the missing number:
(i) \(\square + 6 = 14\) (ii) \(8 + \square = 17\) (iii) \(\square - 5 = 9\) (iv) \(16 - \square = 7\)
- Use a "make ten" strategy to find \(8 + 6\). Show your work in two steps. (Hint: \(8 + 6 = 8 + 2 + 4\).)
- Three numbers are added: \(4 + 7 + 6\). Group them in two different ways to find the same total. State the property of addition you used (associative).
- Draw 3 equal groups of 4 stars. How many stars are there in all? Write a repeated-addition equation and an early multiplication equation that match your drawing.
- An array has 5 rows of 4 dots. Sketch it. How many dots in all? Write as a sum and as a multiplication.
- Is 18 an even or odd number? Explain by either pairing items or by writing 18 as a sum of two equal addends.
- Tell whether each is even or odd: 13, 24, 31, 50, 47.
- A box of crayons holds 8 crayons. Mr. Lee has 3 boxes. How many crayons in all? Show as repeated addition.
- Write 426 in expanded form (e.g., \(400 + 20 + 6\)). Then write the value of each digit ("the 4 in the hundreds place is 400," etc.).
- Read each number and write it in standard form:
(i) "five hundred eighty-three" (ii) "two hundred seven" (iii) "nine hundred forty"
- Compare each pair using \(<\), \(>\), or \(=\):
(i) 348 ___ 384 (ii) 600 ___ 599 (iii) 750 ___ \(700 + 50\)
- Skip-count by 5s starting from 105. Write the next eight numbers.
- Skip-count by 100s starting from 304. Write the next six numbers.
- Use the standard way (the algorithm) to find each answer. Show all regrouping (carrying or borrowing).
(i) \(247 + 158\) (ii) \(305 + 478\) (iii) \(623 - 246\) (iv) \(800 - 357\)
- Mental math (no algorithm — show your reasoning in words):
(i) \(540 + 60 = ?\) (ii) \(700 - 200 = ?\) (iii) \(390 + 110 = ?\)
- Word problem: 348 students attended a morning assembly and 256 students attended an afternoon assembly. How many students attended in total? Show your addition with regrouping.
— You may take a 5-minute break here. —
- Use a ruler to measure the length of a pencil (the proctor will provide one). Record the length in centimeters and in inches.
- Estimate, then measure, the length of your math notebook. Compare your estimate and your measurement; how close were you? Write the difference in centimeters.
- Add lengths: a piece of yarn is 14 cm long; another is 23 cm. What is the total length when laid end-to-end?
- Subtract lengths: a board is 65 inches long. A carpenter saws off 28 inches. How long is the remaining piece?
- Plot the lengths 14, 18, 22, 30 on a number line drawn from 0 to 40 in centimeters. Mark each clearly.
- Read each clock and write the time to the nearest 5 minutes. (The proctor will provide a clock face for the student to read or sketch.)
(i) hour hand near 3, minute hand on the 6 → ___ (ii) hour hand near 7, minute hand on the 4 → ___ (iii) hour hand near 11, minute hand on the 9 → ___
- It is 4:15 p.m. What time will it be in 30 minutes? In 1 hour 15 minutes?
- Count the value of each set of coins (use $ and ¢ symbols correctly):
(i) 3 quarters, 2 dimes, 1 nickel (ii) 1 dollar bill, 4 quarters, 3 pennies (iii) 2 dollar bills, 5 dimes, 6 nickels
- A student has $5. They buy a book for $2.75 and a pencil for $0.85. How much money do they have left? Show the subtraction with dollars and cents.
The 2nd grade collected data on favorite recess activity. The picture graph (key: each smiley = 2 students) shows:
Tag: 😊 😊 😊 😊 😊 (= 10 students)
Soccer: 😊 😊 😊 😊 (= 8 students)
Swings: 😊 😊 😊 (= 6 students)
Books: 😊 😊 (= 4 students)
- How many students were surveyed in all?
- How many more students chose Tag than chose Books?
- If two students changed their answer from Soccer to Books, how would the picture graph change? Sketch the new graph.
- Make a bar graph of the same data with the y-axis (number of students) marked in 2s, going from 0 to at least 10. Label both axes and give the graph a title.
- Write one true statement about the data. Write one prediction (e.g., "If we surveyed another class, I'd expect more students to choose ___ because ___.")
— You may take a 5-minute break here. —
- Name each shape and state how many sides and how many angles it has:
(i) triangle (ii) quadrilateral (iii) pentagon (iv) hexagon
- Partition a rectangle into 2 equal parts (halves) in two different ways. Sketch each.
- Partition a circle into 4 equal parts (fourths). Sketch and shade one fourth.
- Partition a rectangle into 3 equal parts (thirds). Sketch.
- Two students each draw a way to split a rectangle into halves. The first uses a horizontal line; the second uses a diagonal line. Are both halves equal? Explain in one sentence (think about whether the two parts have the same area).
- Name the 3-D shape: a solid with 6 square faces, 8 vertices, and 12 edges. Sketch it.
- Maya had 47 marbles. She gave 18 marbles to her sister. Then her grandmother gave her 25 more. How many marbles does Maya have now? Solve in two steps; write a number sentence for each.
- A library has 234 fiction books and 168 non-fiction books. How many books are there in all? If 75 books are checked out, how many books are on the shelves?
- A bag of apples weighs 4 pounds. Another bag of pears weighs 3 pounds. If the two bags are placed in a basket that itself weighs 1 pound, what is the total weight?