Problems About Separating
Problems about separating follow the subtraction pattern: beginning amount minus amount removed equals what remains (b - a = r). In Grade 6 Saxon Math Course 1 (Chapter 2: Problem Solving with Number and Operations), students identify the three quantities in any separating situation and write the subtraction equation. If a bus started with 35 passengers and 12 got off, write 35 - 12 = 23. Given remainder and amount removed, add to find the original. Keywords like gave away, sold, ate, spent, or removed signal a separating problem structure.
Key Concepts
Property Problems about separating have a subtraction pattern: $$ \text{Beginning amount} \text{some went away} = \text{what remains} $$ $$ b a = r $$.
Examples A bus started with 35 passengers. At a stop, some got off, leaving 22. How many got off? $35 p = 22$, so $p = 35 22 = 13$ people. You had 40 dollars and bought a gift. You now have 18 dollars left. How much was the gift? $40 g = 18$, so $g = 40 18 = 22$ dollars. A jar contained 50 cookies. After a party, 15 cookies were left. How many cookies were eaten? $50 c = 15$, so $c = 50 15 = 35$ cookies.
Explanation Picture a pizza with 8 slices. After you and your friends eat, only 2 slices are left. The separating pattern is your detective tool to find how many slices vanished! By knowing the starting amount and what remains, you can always solve for the part that went away. It makes you a master of subtraction mysteries.
Common Questions
What is the separating pattern in math word problems?
Beginning amount minus amount removed equals what remains: b - a = r. Any of the three values can be the unknown.
A bus has 35 passengers; 12 get off. How many remain?
35 - 12 = 23 passengers remain.
How do you find the beginning amount if you know the amount removed and the remainder?
Add: b = a + r. If 8 were removed and 15 remain, beginning = 8 + 15 = 23.
What keywords signal a separating problem?
Words like gave away, sold, ate, used, left, spent, removed, or lost indicate the starting quantity is being reduced.
How does the separating pattern differ from a comparing pattern?
Separating involves removing part of a quantity over time. Comparing finds the difference between two static quantities.