End-of-Year Cumulative Review - First Grade Mathematics

Welcome to the grand finale of First Grade Mathematics! Over the course of this school year, you have transformed into a brilliant, capable mathematician. You can count all the way to 120, decompose two-digit numbers, add and subtract within 100 with regrouping, measure lengths accurately, tell time on analog and digital clocks, count mixed coins, classify 2D and 3D shapes, partition fractions into halves and fourths, and interpret data graphs! This end-of-year review celebrates all your hard work and prepares you to step proudly into second grade.

The Big Domains of First Grade Math

Let us take a grand tour across all the major mathematical domains you have mastered this year:

The First Grade Math Mastery Wheel:
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| 1. Numbers to 120: Place value, tens and ones, comparison.  |
| 2. Operations to 100: Regrouping, mental math, word problems.|
| 3. Measurement: Length without gaps/overlaps, non-standard. |
| 4. Time: Hours and half-hours (:00 and :30), A.M. and P.M.  |
| 5. Money: Pennies, Nickels, Dimes, Quarters to 25¢.         |
| 6. Geometry: Defining attributes, 2D polygons, 3D solids.   |
| 7. Fractions: Equal shares, halves, fourths, the whole.     |
| 8. Data: Tally marks, frequency tables, bar graphs.         |
+-------------------------------------------------------------+

Two-Digit Operations Review

Let us review vertical addition with composing a ten (regrouping):

Adding 48 + 27:
    [1]  <- Regrouped Ten (8 + 7 = 15 ones = 1 ten and 5 ones!)
     4  8
 +   2  7
 --------
     7  5   (1 + 4 + 2 = 7 tens!)
Sum: 75!

Subtracting Tens and Ones

When subtracting 86 - 30: subtract 3 tens from 8 tens to get 5 tens; the 6 ones stay unchanged: 56! When subtracting 59 - 4: subtract 4 ones from 9 ones to get 5 ones; the 5 tens stay unchanged: 55!

Time, Money, and Geometry Highlights

Key facts to remember for second grade: Clock: Minute hand on 12 means :00 (o'clock). Minute hand on 6 means :30 (half-past). Coins: Penny = 1¢, Nickel = 5¢, Dime = 10¢, Quarter = 25¢. Fractions: 2 halves = 1 whole. 4 fourths = 1 whole. All shares must be equal! Shapes: A triangle has 3 sides and 3 vertices. A rectangle has 4 straight sides and 4 square corners. A cube has 6 square faces and 8 vertices.

Practice Exercises

Exercise 1: Solve this vertical addition problem showing regrouping: 37 + 28.

Exercise 2: You have 1 dime, 2 nickels, and 4 pennies. Sort the coins from greatest to least value and find the total amount of money in cents.

Exercise 3: Look at an analog clock. The long minute hand is on 6, and the short hour hand is halfway between 10 and 11. Write the time in digital format and as a word phrase.

Exercise 4: A teacher has a ribbon that is 14 inches long and cuts off 6 inches for an art project. How many inches of ribbon are left? Write the equation.

Solutions and Explanations

Solution to Exercise 1: In 37 + 28: Add ones: 7 + 8 = 15 ones. Trade 10 ones for 1 ten and write 5 in the ones column; carry the 1 ten. Add tens: 1 + 3 + 2 = 6 tens. The sum is 65.

Solution to Exercise 2: Arranging from greatest to least: Dime (10¢), Nickel (5¢), Nickel (5¢), Penny (1¢), Penny (1¢), Penny (1¢), Penny (1¢). Count: 10¢ -> 15¢ -> 20¢ -> 21¢, 22¢, 23¢, 24¢. Total value is 24¢.

Solution to Exercise 3: The digital time is 10:30. In words, it is "ten-thirty" or "half past ten."

Solution to Exercise 4: 14 - 6 = 8 inches. There are 8 inches of ribbon left.