Number sentences and story problems

Number sentences and story problems

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about writing number sentences and creating story problems.
illustration: selection of number sentences
A number sentence uses numbers and symbols instead of words.
For example the story problem:
Three friends have 59 marbles. If Tamatea has 12 and Sarah has 28, how many does Bob have? 
could be written as 59 – 12 – 28 = ? (a number sentence).

Question 1Change answer

a)  Sione was working out how much money he had.
     He started with $482 in the bank, spent $152 on a tablet, $50 on t-shirts, and $25 on food.
     Write a number sentence to show how much money Sione has left.
    

Question 1Change answer

b) Max has been working out how many runs in total he has got for his team.
    So far he has scored 18, 24, 60, 103, and 25 runs. 
   Write a number sentence to show how many runs he has scored so far.
   

Question 1Change answer

c)  Awhina had 640 marbles.  She decided to give them away to her family. 
     She gave 90 to her younger sister, 80 to her brother, 30 to her mother and 50 to her father.
    Write a number sentence to show how many marbles Awhina had left.
    

Question 1Change answer

d)  Write a story problem for the number sentence:
     70 + 15 + 25 = ?

Question 1Change answer

 e)  Write a story problem for the number sentence:
      365 – 160 – 50 – 123 = ?
Task administration: 
This task can be completed online or with pencil and paper.
Level:
3
Curriculum info: 
Maths, Number and Algebra, Equations and expressions
Key Competencies: 
Using language, symbols, and texts
Keywords: 
number sentences, story problems, addition, subtraction
Description of task: 
Students write number sentences for story problems, and create story problems from number sentences.
Curriculum Links: 
Key competencies
This resource involves writing word problems that corresponds to  given number sentences. This relates to the Key Competency: Using language, symbols and text.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Using symbols and expressions to think mathematically, set 4
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
    Y6 (11/2006)
a) Any 1 of:

  • writes an equation with the correct answer, e.g., 482 – 152 – 50 – 25 = 255
  • writes an equation with an incorrect answer, e.g., 482 – 152 – 50 – 25 = 256
  • writes an equation with no answer, e.g., 482 – 152 – 50 – 25
 easy
b) Any 1 of:

  • writes an equation with the correct answer, e.g., 18+24+60+103+25 = 230
  • writes an equation with an incorrect answer, e.g., 18+24+60+103 +25 =232
  • writes an equation with no answer, e.g., 18+24+60+103+25
 easy
c) Any 1 of:

  • writes an equation with the correct answer, e.g., 640 – 90 – 80 – 30 – 50 = 390
  • writes an equation with an incorrect answer, e.g., 640 – 90 – 80 – 30 – 50 = 390
  • writes an equation with no answer, e.g., 640 – 90 – 80 – 30 – 50
 easy
d) Accept any question or statement that incorporates 70 + 15 + 25 with or without the answer. moderate
e) Accept any question or statement that incorporates 365 – 160 – 50 – 123 with or without the answer. moderate

Based on a representative sample of 152 students.

Teaching and learning: 
  1. The focus of this resource is on the ability of students to translate between number sentences and story problems rather than correct calculation.  Accordingly, the importance is placed on the creation of the equation rather than the answer.  However students that provided the correct answer tended to also indicate a higher mathematical ability across the sample.  Many students wrote a suitable equation but with the answer incorrect.
  2. Ultimately, students should be aiming to write a story problem as a question with an answer. For questions d) and e) the correct student responses were either:
  • a question involving the appropriate operation, e.g., "I had $70 and I found $15 on the ground, then Dad gave me $25.  How much money do I have now?"; or
  • a statement with the correct operation and answer (optional), e.g., "There's 365 sheep on the farm.  If 160 get sent to the works, 50 get sent off to get shorn, and 123 sold to another farm.  How many left in the field?  (32)"
Diagnostic and formative information: 
  Common error Likely misconception
a)
b)
c)		 255
230
390		 Solution only
Students write the solution only (this could be correct or incorrect), not the number sentence to describe the problem.  This could indicate an understanding that maths is only about finding answers.
a)
b)
c)		 482–152 = 330–50 = 280–25 = 255
18+24 = 42+60 = 102+103 = 205+25 = 230
640–90 = 550–80 = 470–30 = 440–50 = 390		 Students incorrectly use the equals sign in a string.
Next steps: 
Solution only
Students who solved the problem without writing a number sentence may have developed an understanding that maths is only about "getting the answer".  Discuss the importance of being able to "formulate" the story problem into a suitable number sentence and encourage students to write down their thinking.

Equality
Students who exhibited an incorrect use of the equals sign could be encouraged to use a symbol or sign to show their processes, e.g.,
     3 x 2  = 6
     3 x 5 =  15
→ 6 + 15 =  21
A misuse of the equals sign could indicate a misunderstanding of the meaning of the equals sign.  Students need to understand that the expression on the left-hand side of the equals sign should represent the same quantity as the expression on the right-hand side of the equals sign, or that "=" means "the same as".  To explore this concept further, click on the link or use the keyword equality.

Statements or questions?
For students who wrote the story problem as a statement, encourage them to turn that into a question (the common form for story problems), and to work towards incorporating the answer.