Grade 1 Mathematics — Testing-Out Examination
A student who passes this examination has demonstrated mastery of the Common Core Grade 1 standards (1.OA, 1.NBT, 1.MD, 1.G) and is eligible to advance directly to Grade 2 Mathematics.
Instructions for the proctor and student
- Time limit: 120 minutes total, in three sessions of about 35 minutes each, separated by 5-minute breaks. Sessions are: Problems 1–3, Problems 4–6, Problems 7–8.
- Tools allowed: ruler (in inches and centimeters), pattern blocks, base-ten blocks (units and rods), counters, fraction strips, and a clock face. Calculators are not allowed.
- The proctor reads each problem aloud once. The proctor may re-read a single sentence on request, but should not paraphrase or simplify the wording.
- Students show work with drawings, equations, or short sentences. A correct answer with no shown work earns half credit.
SESSION 1 · Problems 1–3
- Find each (no fingers — use what you know):
(i) \(5 + 8\) (ii) \(7 + 9\) (iii) \(13 - 6\) (iv) \(15 - 7\) (v) \(6 + 6\) (vi) \(11 - 4\)
- Find the missing number. Use a related fact or counting strategy.
(i) \(\square + 7 = 13\) (ii) \(9 + \square = 15\) (iii) \(\square - 4 = 8\) (iv) \(14 - \square = 6\)
- Use the "make ten" strategy to find \(8 + 5\). Show your work in two steps. (Hint: \(8 + 5 = 8 + 2 + 3\).)
- True or false? Explain each in one sentence.
(i) \(7 + 5 = 5 + 7\) (ii) \(8 - 3 = 3 - 8\) (iii) \( 4 + 6 + 2 = 4 + (6 + 2) \)
- Word problem: There were 9 birds on a tree. Then 5 more birds flew in. How many birds are on the tree now? Write a number sentence.
- Word problem: Tara has 12 stickers. She gives 4 stickers to her brother. How many stickers does Tara have left?
- Count aloud (the proctor will listen) from 87 to 105. The student should say each number clearly. (Proctor: mark any errors.)
- Write the number that comes:
(i) just after 79: ___ (ii) just after 99: ___ (iii) just before 60: ___ (iv) just after 119: ___
- Skip-count by 10s starting at 30: 30, 40, ___, ___, ___, ___, ___.
- Write each number using base-ten blocks (tens and ones). For example, 47 = 4 tens and 7 ones. Do this for 36, 80, 104, 92.
- Compare each pair using \(<\), \(>\), or \(=\):
(i) 47 ___ 74 (ii) 60 ___ 6 tens (iii) 89 ___ 98
- Add a 2-digit and a 1-digit number (you may use base-ten blocks):
(i) \(34 + 5\) (ii) \(78 + 6\) (iii) \(59 + 8\)
- Add a 2-digit and a multiple of ten:
(i) \(35 + 20\) (ii) \(48 + 40\) (iii) \(72 + 30\)
- Add two 2-digit numbers (regroup if needed):
(i) \(26 + 47\) (ii) \(58 + 35\)
- Subtract a multiple of 10:
(i) \(80 - 30\) (ii) \(60 - 40\) (iii) \(95 - 50\)
— 5-minute break. —
SESSION 2 · Problems 4–6
- Use a ruler to measure the length of a pencil (the proctor will provide one). Record in inches and in centimeters, to the nearest whole unit.
- The proctor will lay three objects on the table: a pencil, a marker, and a ribbon. Order them from shortest to longest by their measured lengths. Record the order.
- Measure length using a small unit. The proctor will provide 1-inch tiles. The student lines up tiles end-to-end along an object and records the length in tiles.
Object 1 length = ___ tiles Object 2 length = ___ tiles
- If two pencils are 6 inches and 4 inches, how much longer is the first pencil than the second? Show the subtraction.
- The proctor will display (or sketch) each clock face. Read the time on each (to the nearest half hour) and write it as ___:00 or ___:30.
(i) hour hand on 4, minute hand on 12 → ___:___ (ii) hour hand between 7 and 8, minute hand on 6 → ___:___ (iii) hour hand on 11, minute hand on 12 → ___:___
- Sketch a clock face that shows 9:30. Be sure both hands are drawn correctly.
- It is 3:00. What time will it be in 30 minutes? In 1 hour? In 1 hour 30 minutes?
- True or false: At 6:30, the minute hand points directly at the 6 on the clock face. Explain in one sentence.
The class collected data on favorite weather. The tally chart shows:
Sunny: |||| |||| || (= 12 students)
Rainy: |||| | (= 6 students)
Snowy: |||| |||| (= 9 students)
Cloudy: ||| (= 3 students)
- How many students were surveyed altogether?
- How many more students chose Sunny than chose Cloudy?
- How many fewer students chose Rainy than chose Snowy?
- Make a bar graph of the data, labeling both axes and giving the graph a title. Use a vertical scale of 1 (each unit on the y-axis represents 1 student).
- Write one true sentence about the data (e.g., "More students chose Sunny than any other weather.").
— 5-minute break. —
SESSION 3 · Problems 7–8
- Name each shape and state how many sides and how many corners (vertices) it has:
(i) triangle (ii) square (iii) rectangle (non-square) (iv) trapezoid (v) hexagon
- Compose new shapes from pattern blocks: how many green triangles fit inside one yellow hexagon? Explain in one sentence with a sketch.
- Cut a square into halves (two equal parts) in two different ways. Sketch each.
- Cut a square into fourths (four equal parts) in two different ways. Sketch each.
- Two students share one pizza equally. What fraction of the pizza does each student get? Write the fraction word ("one-half") and the symbol \(\dfrac{1}{2}\).
- Four students share one pizza equally. What fraction does each student get? Write the word and the symbol.
- Which gives each child a larger piece — sharing a pizza among 2 people or among 4 people? Explain in one sentence.
- A box has 18 crayons. The teacher takes out 6 and gives them to one student. Then the teacher takes out 4 more and gives them to another student. How many crayons are left in the box? Write number sentences for each step.
- Marco has 7 red marbles and 8 blue marbles. He puts them all in a bag. Then he gives 5 marbles to his friend. How many marbles are left in Marco's bag?
- A baker made 24 cookies. She put them on plates of 6 cookies each. How many plates does she fill? Show how you grouped them (think of 24 as 6 + 6 + 6 + 6 — repeated subtraction or repeated addition).
- An apple weighs 5 ounces. A banana weighs 4 ounces. A pear weighs 6 ounces. If you put one of each in a bag, what is the total weight?
- Lila has 30 cents. She wants to buy a pencil that costs 25 cents. Does she have enough? How much extra money will she have after buying the pencil? Show your subtraction.