Some problems cannot be answered in one move. You have to work something out first.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Find the hidden question
Ask yourself: what do I need to know before I can answer what was asked?
Hold on to the middle answer
The first answer is not the answer. Write it down, then use it in the second step.
A tape diagram helps. Draw what you know, then see what is missing.
Step 2: Try It Yourself
The bars hold the first answer. Then find the second.
First amount and Second amount
6
5
So far
11
6 and 5 make 11.
How many
11 and 9 make 20. There are 9 empty spaces.
6 and 5 make 11.
Step 3: In Real Life
Lunch money
You have 20 dollars. Lunch is 8 and a drink is 3. First: 8 + 3 = 11. Then: 20 − 11 = 9 left. The first answer was hiding.
Step 4: Watch an Example
One step at a time.
Watch Ana Take Two Steps
Ana had 6 shells. She found 5 more. Then she gave 3 to Leo. How many does she have now?
- Step 1
She sees the question is about the end.
Watch Ben Take Two Steps
Ben had 14 stickers. He gave 6 to Mia. Then he got 7 more. Ben starts. You finish.
- Step 1
He asks the hidden question. How many after giving 6?
Step 5: Your Turn
Practice makes it stick.
The Bakery
Problem 1 of 12
A tray held 8 buns. 6 more were baked. Then 5 were sold. How many buns are left?
buns
The Library
Problem 2 of 12
Leo borrowed 9 books. He returned 4. Then he borrowed 3 more. How many does he have?
books
Two Steps Each
Find the middle answer first. Then finish.
Problem 3 of 12
7 apples. 6 more come. 4 are eaten. How many now?
Problem 4 of 12
15 birds. 7 fly away. 2 come back. How many now?
Problem 5 of 12
5 red pens and 6 blue pens. 3 are lost. How many are left?
Find the Mistake
A friend wrote two steps. Find the slip, then fix it.
Problem 6 of 12
12 cars. 4 drive away. 5 more come. Mia says 8. What did Mia do?
Mia's work for the cars
- 112 − 4 = 8
- Answer8 cars
Problem 7 of 12
What should Mia get? How many cars now?
cars
Problem 8 of 12
Sam had 9 stickers. He got 6. He gave 5 away. Which line is the slip?
Sam's work for the stickers
- 19 + 6 = 15
- 29 − 5 = 4
- Answer4 stickers
Problem 9 of 12
What should Sam get? How many stickers now?
stickers
Which Way?
Pick the quicker way for this story.
Problem 10 of 12
10 apples. 4 are eaten. 4 more come. Which way is quicker?
Problem 11 of 12
8 fish. 2 more come. Then 5 more. Which way is quicker?
Show the Missing Part
Build it, then check.
Problem 12 of 12
11 is 6 and how many? Show that part.
How many
Step 6: Quick Check
Show what you know.
Question 1 of 2
9 pieces of candy. 5 more given. 6 eaten. How many are left?
Question 2 of 2
In a two-step problem, what is the first answer you find?
Ready for more?Optional. Past the lesson, for anyone who wants it.
Stretch 1 of 1
10 grapes. Kim eats 3. She gets 5 more. She eats 4. How many now?
grapes
What You Learned
- Some problems hide a first question inside them.
- Work out the middle answer, then use it.
- The middle answer is never the answer.
For the grown-up
This lesson is where the child solves two-step word problems within 20, identifying the hidden first question. Fluency within twenty is not speed for its own sake. Facts that come without thinking free up the working memory that the next four years of mathematics need, and a child recomputing 8 + 6 every time has nothing left over for the problem it sits inside.
Watch for finger counting that has gone underground — a pause, a glance away, lips moving. The strategy has not gone; it has just got quieter.
Short and often beats long and rare. Two minutes of the facts they nearly know is worth more than twenty minutes of the ones they already do.
The hidden first question — A two-step problem asks you something the numbers cannot answer directly. Somewhere in the story there is a smaller question you must answer first. Finding that hidden question is the actual skill; the arithmetic afterwards is easy.
A worked case — Maya had 12 stickers. She gave 5 to her brother, then her aunt gave her 7. How many now? The hidden first question is how many she had after giving some away: 12 - 5 = 7. Now the real question can be answered: 7 + 7 = 14. Two steps, two number sentences.
Write both sentences down — Do not try to hold the middle number in your head. Write 12 - 5 = 7 on one line and 7 + 7 = 14 on the next. When a teacher or a friend reads your work they can follow it, and when you make a mistake you can see exactly which step went wrong instead of starting over.
Find the hidden middle answer — There were 12 birds. 5 flew away, then 4 more came. First step: 12 − 5 = 7. That seven is the hidden number. Second step: 7 + 4 = 11. Eleven birds. The question never mentions the seven. You have to work it out and hold it.