Give And Take

What is Give and Take?

"Give and Take" is about giving away (sharing/losing) or getting more of something (receiving/adding). When we give, the number becomes less — we subtract. When we take (or get), the number becomes more — we add.

How to solve a Give and Take problem

• Read the question and find the initial amount (how many at first).
• Find whether someone gives (subtract) or takes/gets (add) and how many are given or taken.
• Write a simple number sentence (equation) and solve.
• Check your answer by doing the opposite operation: addition checks subtraction and vice versa.

Important ideas for Class 3

• Give = subtract (−). Example: 8 apples, give 3 → 8 − 3 = 5 apples left.
• Take/Get = add (+). Example: 6 marbles, get 2 more → 6 + 2 = 8 marbles.
• You cannot give more than you have — if a question asks that, point out it is not possible or ask how many more are needed.

What is Addition (Giving)?

Addition means putting two or more groups together or giving objects to a group. When we add, we find the total or how many there are altogether. We write addition with a plus sign (+) and an equals sign (=). Example: 3 + 2 = 5 means when we give 2 more to 3, we get 5.

Key words and symbols

• Plus sign (+): shows we are joining groups.
• Equals sign (=): shows the total or answer.
• Addends: the numbers being added (in 4 + 3, both 4 and 3 are addends).

Ways to do addition

1. Using objects or pictures: Count real items (blocks, pencils) or draw pictures and count all.
2. On a number line: Start at the first number and make jumps equal to the second number to find the total.
3. By counting on fingers: Start at the bigger number and count on the smaller number.
4. Using place value (tens and ones): Make groups of tens and ones and then add ones and tens separately; carry to tens if needed.
5. Column (vertical) addition: Write numbers one under the other by place value, add ones column first, then tens, carrying if required.

Properties that help

• Commutative property: a + b = b + a (e.g., 2 + 5 = 5 + 2).
• Associative property: (a + b) + c = a + (b + c) (useful when adding more than two numbers).
• Additive identity: a + 0 = a (adding zero does not change the number).

Tips for children

• Use real objects first (toys, stones, fruits).
• Draw pictures or use number lines for visual help.
• Practice small sums (facts up to 10) to build speed and confidence.

What is subtraction (taking away)?
Subtraction means taking away one number from another to find how many are left. We write it as minuend − subtrahend = difference. For example, 8 − 3 = 5: 8 is the minuend (start), 3 is the subtrahend (taken away) and 5 is the difference (left).

Words we use:

• Minuend: the number you start with (e.g. 8)
• Subtrahend: the number taken away (e.g. 3)
• Difference: what remains (e.g. 5)

Ways to do subtraction (age 7–9 methods):

• Using objects (concrete): Put out the minuend number of objects, take away the subtrahend objects, count what remains.
• Number line (jump back): Put your finger on the minuend and make jumps of 1 (or larger jumps) backwards equal to the subtrahend to land on the difference.
• Column method (vertical subtraction): Write numbers one under the other by place value (units under units, tens under tens). Subtract units, then tens. If the top digit is smaller than the bottom digit, borrow 1 from the next left place (regrouping).

Steps for subtraction with borrowing (example 42 − 17):

1. Write: 42
   −17
2. Start with units: 2 − 7 is not possible, so borrow 1 ten from 4 tens. The 4 tens becomes 3 tens and the 2 units become 12 units.
3. Do units: 12 − 7 = 5.
4. Do tens: 3 − 1 = 2. So result is 25.

Checking your answer: Addition is the reverse: difference + subtrahend should equal the minuend (e.g. 25 + 17 = 42).

Solving word problems: Read carefully, find the numbers to subtract, decide which number is being taken away, use objects/number line/column method, and check by adding the result back.

What is a number sentence?
A number sentence is a short sentence made with numbers and symbols that tells us a mathematical fact. It has numbers, operation symbols (like + or −), and usually an equals sign (=). Example: 5 + 3 = 8.

Common symbols

• + means add (put together)
• − means take away (subtract)
• = means equals (shows two sides are the same)
• < means less than
• > means greater than
• □ or ? is used for a missing number

How to read and make number sentences
Read from left to right: 7 − 2 = 5 is read “seven minus two equals five.” We can make number sentences from pictures or real objects: if you have 6 apples and give 2 to a friend, the sentence is 6 − 2 = 4.

Solving number sentences
Use counting, objects, or a number line. For a missing number in addition (a + b = ?), count forward. For a missing addend (a + ? = c), use subtraction: ? = c − a. For subtraction with a missing minuend (? − b = c), use addition: ? = b + c.

Tips
Use drawings (dots, sticks, counters), a number line to show jumps, or a bar model to compare amounts. Check answers by doing the opposite operation (inverse): if you think 4 + 3 = 7, check 7 − 3 = 4.

A number line is a straight line with numbers placed at equal intervals. For Class 3, we usually draw a number line from 0 up to 10 or 20. The numbers increase as you move to the right and decrease as you move to the left. A number line helps children see addition as jumps to the right and subtraction as jumps to the left.

How to use it:

• Addition: Start at the first number, then make jumps to the right equal to the second number. The point you land on is the sum.
• Subtraction: Start at the first number, then make jumps to the left equal to the number you take away. The point you land on is the result.
• Missing number: Use jumps forward or backward to find the number that makes the statement true (for example, ? + 4 = 9).
• Compare and difference: Count how many jumps are needed from one number to another to find the difference or to see which is larger.

Benefits: number lines make abstract operations visual, build number sense, and help check answers by counting jumps.

What are Number Bonds?
A number bond is a simple way to show how a whole number is made from two parts. It helps children see the 'part–part–whole' relationship. For example, the number 8 can be split into 3 and 5. We draw a big circle for the whole (8) and two smaller circles connected to it for the parts (3 and 5).

What are Fact Families?
A fact family is a group of related addition and subtraction facts that use the same three numbers. Using the parts and whole from a number bond we can write four facts: two additions and two subtractions. For the numbers 3, 5 and 8 the fact family is: 3 + 5 = 8, 5 + 3 = 8, 8 - 3 = 5, 8 - 5 = 3.

Why they are useful:

• Number bonds build number sense by showing how numbers combine and split.
• Fact families link addition with subtraction so students learn that subtraction is the inverse (opposite) of addition.
• They make mental calculation faster and help with learning tables and missing-number problems.

How to teach/use them: Start with objects (counters, beads, fruit). Make a whole group, split into two parts, draw the number bond, and then write the four related facts (the fact family). Use number lines, ten-frames, and bar models to support understanding.

Word problems (story sums) are maths questions written in sentences. They describe a real-life situation and ask you to find a number. In Class 3, most story sums use addition and subtraction. Solving them needs reading carefully, finding the important numbers, deciding which operation to use, drawing a picture or model, doing the calculation and checking the answer.

Steps to solve a word problem:

1. Read the whole story to understand what is happening.
2. Underline the numbers and the question (what you must find).
3. Decide the operation — add if things are joined together, subtract if some are taken away or we compare.
4. Draw a simple picture, bar model or number line to show the story.
5. Write the number sentence (e.g., 7 + 5 = ? or 12 − 4 = ?).
6. Calculate carefully and check by reversing the operation (for subtraction, add to check; for addition, check by subtraction).

Tips: Look for words that show adding (together, in all, more, total) or subtracting (left, left over, less, remains). For missing numbers use the inverse operation: if ? + 8 = 13 then ? = 13 − 8.

What is Comparison of Quantities?

Comparison of quantities means finding which amount is more, which is less, or whether two amounts are equal. We use words like "more", "less", "equal" and symbols > (greater than), < (less than) and = (equals) to show the result.

How to compare numbers (simple steps)

• Look at the number of digits. The number with more digits is greater. Example: 456 > 89.
• If both have the same number of digits, compare digits from left to right. The first larger digit makes that number greater. Example: compare 372 and 365 → at tens place 7 > 6, so 372 > 365.
• You can also place numbers on a number line: the one to the right is greater.
• To find how much one quantity is more or less than another, subtract: Difference = Bigger number − Smaller number.

Comparing measured quantities

• Always use the same unit before comparing (e.g., both in kg, both in m or both in litres). If units differ, convert one so both use the same unit.
• Examples of measured items: lengths, weights, volumes, time. Compare their numerical values after units match.

Using symbols

• Use > when the left quantity is greater, e.g., 12 > 7.
• Use < when the left quantity is smaller, e.g., 5 < 9.
• Use = when two quantities are the same, e.g., 8 = 8.

Tips for Class 3 students

• Draw pictures (dots, stars, candies) to compare small numbers.
• Use real objects like pencils or apples to count and compare.
• Use a number line or bar pictures to see which is bigger.

Checking Work and Simple Strategies helps children make fewer mistakes when adding or subtracting. It shows easy ways to solve a problem and then check the answer to be sure it is correct.

How to check your work

• Use the reverse operation: If you added two numbers, check by subtracting one addend from the result. If you subtracted, check by adding the answer and the subtracted number to see if you get the original number.
• Estimate: Round numbers to the nearest ten and do a quick estimate to see if the answer is close.
• Draw a picture or use objects: Use counters, fingers, or a drawing to model the problem and confirm the answer.
• Use number bonds or tens frames: Break numbers into parts (tens and ones) to add or subtract easily, then check by recombining the parts.
• Counting on or back: For small additions, count forward from the larger number; for subtraction, count backward to check.

Simple strategies explained

• Make ten: Change a pair of numbers so one becomes 10, then add the rest. Example: 8 + 7 = 8 + 2 + 5 = 10 + 5 = 15.
• Break-apart (tens and ones): Split numbers into tens and ones, add tens first, then ones. Example: 46 + 29 = (40 + 20) + (6 + 9) = 60 + 15 = 75.
• Use doubles and near-doubles: If you know 7 + 7 = 14, then 7 + 8 = 14 + 1 = 15.
• Use the commutative idea for addition: Change order to make adding easier (5 + 27 = 27 + 5).

These methods build confidence and make checking quick and fun for Class 3 students.

What this topic means: In the chapter "Give and Take", "give" usually means taking away (subtraction) and "take" often means adding (addition). Classroom Activities and Practice helps children use objects, pictures and number lines to understand giving away, taking more, and checking answers by doing the opposite operation.

How to teach and practice:

• Use real objects (buttons, pencils, counters). Let one child give some objects to another and count what remains.
• Show number sentences next to the activity (e.g. 8 − 3 = 5 or 6 + 4 = 10).
• Use a number line: for addition jump forward, for subtraction jump backward. This builds a visual link between the action and the number sentence.
• Teach fact families: if 4 + 3 = 7 then 7 − 3 = 4 and 7 − 4 = 3.
• Follow a 4-step problem solving routine: read the problem, model with objects or drawings, write the number sentence, solve and check (use inverse operation).

Classroom activities examples: role-play (children swap cards), pair work (one gives, one records), flashcard races (solve give/take quickly), writing missing-number sentences, and creating pictorial stories (draw and write).