Grade 1 Math

Building strong foundations in numbers and operations

1
Counting & Cardinality (Counting to 120)

Key Vocabulary

Counting:Saying numbers in order
Number Order:Numbers arranged from smallest to largest
Before/After:The number that comes right before or after another number
Between:A number that comes after one number and before another

Understanding the Concept

When we count, we say numbers in order: 1, 2, 3, 4, 5... and so on! In first grade, we learn to count all the way to 120. That's a lot of numbers! Here are some important ideas: • Every number has a number that comes BEFORE it (the number is 1 less) • Every number has a number that comes AFTER it (the number is 1 more) • We can find numbers that come BETWEEN two other numbers For example: • The number BEFORE 10 is 9 • The number AFTER 10 is 11 • The number BETWEEN 10 and 12 is 11 When we count by 10s, we say: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120!

Worked Examples

Example 1: What number comes right after 47?

Example 2: What number comes between 29 and 31?

Example 3: Count by 10s from 50 to 90. What numbers do you say?

Practice Questions

Question 1: What number comes right before 56?

Question 2: Which number is between 78 and 80?

Question 3: If you count by 10s starting at 30, what is the next number?

Question 4: What number comes after 99?

Teacher's Tip from Mr. Augustine

Practice counting every day! Count toys, count steps, count snacks. The more you practice, the easier it gets. When counting past 100, remember the pattern: 101, 102, 103... it's just like counting to 20, but with 100 in front!

2
Addition within 20 (Counting On & Make-a-Ten)

Key Vocabulary

Addition:Putting two or more numbers together to find the total
Sum:The answer when you add numbers together
Counting On:Starting with one number and counting up to add
Make-a-Ten:A strategy where we make 10 first, then add the rest

Understanding the Concept

Addition means putting numbers together to find how many in all. There are two great strategies for adding: **Counting On Strategy:** Start with the bigger number and count up! Example: 8 + 3 Start at 8, then count: 9, 10, 11 Answer: 11 **Make-a-Ten Strategy:** Make 10 first, then add what's left! Example: 8 + 5 • 8 needs 2 more to make 10 • Break 5 into 2 and 3 • 8 + 2 = 10, then 10 + 3 = 13 Answer: 13 The Make-a-Ten strategy is super helpful because adding to 10 is easy!

Worked Examples

Example 1: Solve 7 + 4 using the Counting On strategy

Example 2: Solve 9 + 6 using the Make-a-Ten strategy

Example 3: Emma has 8 crayons. Her friend gives her 7 more. How many crayons does Emma have now?

Practice Questions

Question 1: What is 6 + 5?

Question 2: If you count on from 9 to add 9 + 3, what is the sum?

Question 3: What is 7 + 8?

Question 4: Tom has 5 toy cars. He gets 9 more for his birthday. How many toy cars does he have now?

Teacher's Tip from Mr. Augustine

The Make-a-Ten strategy is like a superpower for addition! Once you can quickly make 10, adding becomes so much easier. Practice your combinations that make 10: 1+9, 2+8, 3+7, 4+6, 5+5. Know these by heart!

3
Subtraction within 20 (Counting Back & Fact Families)

Key Vocabulary

Subtraction:Taking away or finding the difference between numbers
Difference:The answer when you subtract
Counting Back:Starting with a number and counting down to subtract
Fact Family:A group of related addition and subtraction facts using the same numbers

Understanding the Concept

Subtraction means taking away or finding how many are left. **Counting Back Strategy:** Start with the bigger number and count backwards! Example: 11 - 3 Start at 11, count back 3: 10, 9, 8 Answer: 8 **Fact Families:** Fact families show how addition and subtraction are related! Example with numbers 5, 3, and 8: • 5 + 3 = 8 • 3 + 5 = 8 • 8 - 3 = 5 • 8 - 5 = 3 All four facts use the same three numbers! If you know one fact, you can figure out the others. Subtraction is the opposite of addition. If 7 + 5 = 12, then 12 - 5 = 7!

Worked Examples

Example 1: Solve 14 - 5 using the Counting Back strategy

Example 2: Complete the fact family for 6, 7, and 13

Example 3: Maya had 15 stickers. She gave 8 to her sister. How many stickers does Maya have left?

Practice Questions

Question 1: What is 12 - 4?

Question 2: If 9 + 5 = 14, what is 14 - 5?

Question 3: What is 16 - 9?

Question 4: There were 13 birds on a tree. 6 birds flew away. How many birds are still on the tree?

Teacher's Tip from Mr. Augustine

Fact families are your friends! When you learn an addition fact, you're actually learning four facts at once. Practice saying them out loud: 'If 8 plus 6 equals 14, then 14 minus 6 equals 8!' This helps your brain make connections.

4
Place Value (Tens and Ones)

Key Vocabulary

Place Value:The value of a digit based on its position in a number
Tens:Groups of 10 ones
Ones:Single units
Greater Than/Less Than:Comparing which number is bigger or smaller

Understanding the Concept

Every digit in a number has a special place and value! In a two-digit number like 47: • The 4 is in the TENS place. It means 4 tens, or 40. • The 7 is in the ONES place. It means 7 ones, or 7. • Together: 40 + 7 = 47 **Understanding Tens:** 1 ten = 10 ones 2 tens = 20 ones 3 tens = 30 ones ...and so on! **Comparing Numbers:** To compare two numbers, look at the tens place first! • 56 vs 48: 5 tens is more than 4 tens, so 56 > 48 • If the tens are the same, look at the ones place • 34 vs 37: Both have 3 tens, but 7 ones is more than 4 ones, so 37 > 34 We use these symbols: > means "greater than" (bigger) < means "less than" (smaller) = means "equal to" (the same)

Worked Examples

Example 1: What is the value of the digit 6 in the number 63?

Example 2: Compare 52 and 58. Which is greater?

Example 3: Show 45 as tens and ones

Practice Questions

Question 1: How many tens are in the number 72?

Question 2: Which number is less than 64?

Question 3: What number is the same as 3 tens and 8 ones?

Question 4: Which symbol makes this true? 45 ___ 54

Teacher's Tip from Mr. Augustine

Use base-ten blocks or draw pictures to see tens and ones! Draw a long stick for each ten and a dot for each one. This helps you really understand that 47 is 4 long sticks (tens) and 7 dots (ones). The more you visualize it, the easier place value becomes!

5
Measurement & Time

Key Vocabulary

Length:How long something is from one end to the other
Measure:To find out how long, tall, or wide something is
Hour:60 minutes; the short hand on a clock shows hours
Half Hour:30 minutes; halfway between two hours

Understanding the Concept

**Measuring Length:** We can measure how long things are using different units! • We can use paper clips, blocks, or other objects to measure • Line up the objects end-to-end with no gaps • Count how many objects fit along the length Example: A pencil might be 5 paper clips long! **Telling Time:** A clock has two hands: • The SHORT hand points to the HOUR • The LONG hand points to the MINUTES **Hour (o'clock):** When the long hand points to 12, it's exactly on the hour! • If the short hand points to 3 and long hand points to 12, it's 3:00 (3 o'clock) **Half Hour:** When the long hand points to 6, it's half past the hour (30 minutes after) • If the short hand is between 3 and 4, and the long hand points to 6, it's 3:30 (half past 3) Remember: The short hand moves slowly and shows the hour. The long hand moves faster and shows the minutes!

Worked Examples

Example 1: A crayon is 4 paper clips long. A marker is 6 paper clips long. How much longer is the marker?

Example 2: What time is shown when the short hand points to 7 and the long hand points to 12?

Example 3: The short hand is between 2 and 3, and the long hand points to 6. What time is it?

Practice Questions

Question 1: A book is 8 blocks long. A notebook is 5 blocks long. How much longer is the book?

Question 2: What time is it when the short hand points to 5 and the long hand points to 12?

Question 3: If the long hand points to 6, how many minutes past the hour is it?

Question 4: School starts at 8:00. Lunch is at 12:00. How many hours is that?

Teacher's Tip from Mr. Augustine

Practice telling time throughout the day! Every time you look at a clock, say the time out loud. For measuring, use fun objects like toy cars, crayons, or your own hand spans. The more you practice with real objects, the better you'll understand measurement!

6
Geometry & Fractions (Shapes & Equal Parts)

Key Vocabulary

2D Shape:A flat shape like a circle, square, or triangle
3D Shape:A solid shape like a cube, sphere, or cone
Half:One of two equal parts
Fourth (Quarter):One of four equal parts

Understanding the Concept

**2D Shapes (Flat Shapes):** • Circle: Round, no corners • Square: 4 equal sides, 4 corners • Rectangle: 4 sides (opposite sides equal), 4 corners • Triangle: 3 sides, 3 corners **3D Shapes (Solid Shapes):** • Sphere: Like a ball, round all around • Cube: Like a box, 6 square faces • Cylinder: Like a can, 2 circular ends • Cone: Like an ice cream cone, 1 circular base and 1 point **Equal Parts (Fractions):** When we divide a shape into equal parts, each part is the same size! **Halves:** • 2 equal parts • Each part is called one half (1/2) • Example: Cut a pizza into 2 equal pieces **Fourths (Quarters):** • 4 equal parts • Each part is called one fourth (1/4) or one quarter • Example: Cut a sandwich into 4 equal pieces Important: The parts must be EQUAL (the same size) to be halves or fourths!

Worked Examples

Example 1: Name this shape: It has 4 equal sides and 4 corners.

Example 2: A circle is divided into 2 equal parts. What fraction is each part?

Example 3: A rectangle is divided into 4 equal parts. Sarah colors 1 part blue. What fraction did she color?

Practice Questions

Question 1: Which shape is like a ball?

Question 2: A square is divided into 2 equal parts. What is each part called?

Question 3: How many equal parts are in one whole divided into fourths?

Question 4: A pizza is cut into 4 equal slices. You eat 1 slice. What fraction of the pizza did you eat?

Teacher's Tip from Mr. Augustine

Look for shapes everywhere! Find circles (plates, clocks), rectangles (doors, books), and 3D shapes (balls, boxes, cans) around your house. For fractions, practice with real food like sandwiches or pizza. When you cut something into equal parts and eat one piece, you're learning fractions in a delicious way!

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