Mid-Year Cumulative Review - First Grade Mathematics

Congratulations on reaching the midpoint of your first grade mathematical journey! Take a moment to look back at the immense mountain of math skills you have already conquered: you have mastered counting forward and backward to 20, explored place value up to 50, learned the core strategies of addition and subtraction within 10 and 20, and solved challenging word problems! This mid-year review is designed to give your math muscles a comprehensive workout, ensuring that all your foundational skills are sharp and ready for the second half of the year.

Part 1: Number Sense, Counting, and Place Value

Let us review the structure of numbers from zero up to fifty and the principles of place value.

Place-Value Review:
Number: 38
Tens Digit: 3  -> Value = 30 (3 Rods of Ten)
Ones Digit: 8  -> Value =  8 (8 Loose Units)
Expanded Form: 30 + 8 = 38
10 More than 38 is 48 (+10)
10 Less than 38 is 28 (-10)

Comparing and Ordering

When comparing two numbers, always examine the tens place first! If the tens are tied, compare the ones place. For 42 vs. 39: 4 tens is greater than 3 tens, so 42 > 39, even though 9 is bigger than 2!

Part 2: Addition and Subtraction Fluency to 20

Fluency means solving math facts quickly, accurately, and flexibly using smart mental strategies.

The Key Mental Strategies:
- COUNT ON: Start with the bigger number and count forward (e.g., 8 + 3: "8... 9, 10, 11").
- DOUBLES & NEAR DOUBLES: Use twins to add (e.g., 6 + 6 = 12, so 6 + 7 = 13).
- MAKE A TEN: Borrow from one addend to complete a 10 (e.g., 8 + 5 = 10 + 3 = 13).
- THINK ADDITION: Solve subtraction by finding the missing part (e.g., 14 - 9 = ?: 9 + 5 = 14, so 14 - 9 = 5).

Fact Families

Remember that three numbers form a fact family of four equations: For 5, 8, 13: 5 + 8 = 13, 8 + 5 = 13, 13 - 5 = 8, 13 - 8 = 5!

Part 3: Word Problem Detective Work

Review the three types of word problem mysteries: Result Unknown: 8 + 6 = ? (Answer: 14) Change Unknown: 8 + ? = 14 (Answer: 6) Start Unknown: ? + 6 = 14 (Answer: 8)

Practice Exercises

Exercise 1: Decompose the number 47 into tens and ones. Write 47 in expanded form, and state what number is 10 more and what number is 10 less.

Exercise 2: Solve each addition equation using a mental strategy: 7 + 7 = __ 7 + 8 = __ 9 + 6 = __ 8 + 4 = __

Exercise 3: Solve each subtraction equation: 10 - 4 = __ 15 - 8 = __ 12 - 9 = __ 16 - 7 = __

Exercise 4: Read and solve: "Lucas had 9 stickers. His sister gave him some more stickers. Now Lucas has 16 stickers in all. How many stickers did his sister give him?" Identify the problem type and write the equation.

Solutions and Explanations

Solution to Exercise 1: 47 has 4 tens and 7 ones. Expanded form: 40 + 7 = 47. 10 more than 47 is 57. 10 less than 47 is 37.

Solution to Exercise 2: 7 + 7 = 14 (Doubles fact) 7 + 8 = 15 (Doubles plus one: 14 + 1 = 15) 9 + 6 = 15 (Make a ten: 10 + 5 = 15) 8 + 4 = 12 (Make a ten: 10 + 2 = 12)

Solution to Exercise 3: 10 - 4 = 6 (Friends of 10) 15 - 8 = 7 (Think addition: 8 + 7 = 15) 12 - 9 = 3 (Count up: 9 to 12 is 3 hops) 16 - 7 = 9 (Think addition: 7 + 9 = 16)

Solution to Exercise 4: This is a Change Unknown problem because the amount given by the sister is missing. Equation: 9 + ? = 16 (or 16 - 9 = 7). Lucas's sister gave him 7 stickers.