Collecting beads

Collecting beads

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about finding the missing amount in maths word problems.

glass beads

Some students were collecting beads to make necklaces with.

Question 1Change answer

a)  Lana had 236 beads. She bought 78 more beads.

     How many beads does she now have? 

Question 1Change answer

b)  Talia had 254 beads. She needs to have 328 beads.

     How many more beads does she need? 

Question 1Change answer

c)  Lee had some beads. He bought 65 more beads.
     This gave him a total of 424 beads.

     How many beads did he start off with? 

Question

d) i)  Which problem did you find easiest?

    • Lana had 236 beads and got 78 more. How many does she now have?

    • Talia started with 253 beads and finished with 328. How many more did she get?

    • Lee got 65 more beads which gave him a total of 424. How many did he start with?

    • They were all as easy as each other.

ii) Why was this easiest?

Question

e) i) Which question did you find hardest?

    • Lana had 236 beads and got 78 more. How many does she now have?

    • Talia started with 253 beads and finished with 328. How many more did she get?

    • Lee got 65 more beads which gave him a total of 424. How many did he start with?

    • They were all just as hard as each other.

ii) Why was this hardest?
Task administration: 
This task can be completed with pen and paper or online (with SOME auto marking).
Levels:
3, 4
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Key Competencies: 
Managing self, Using language, symbols, and texts
Keywords: 
addition, subtraction, key competencies
Description of task: 
Student solve addition problems where the missing value is located in different positions. This may mean that students transform the problem into a subtraction one. Students reflect on the easiest and hardest problems, and explain their choice.
Curriculum Links: 

Key competencies

This resource involves students reflecting on which arithmetic computations they found the easiest, and explaining the  reasons for this. This relates to the Key Competency: Managing self and Using language, symbols and text.

For more information see https://nzcurriculum.tki.org.nz/Key-competencies

Learning Progression Frameworks
This resource can provide evidence of learning associated with
Additive thinking, sets 6-7
Additive thinking, sets 7-8
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
    Y6 (11/2013) 
a) 314 very easy
b) 74 moderate
c) 359 moderate

Results based on an online sample of 56 Y6 students.

Student responses

Questions d) and e): Which calculations were easiest / hardest?

  Question d):   
Which was easiest?		 Question e):
Which was hardest?
236 + 78 = ?  About 50% About 10%
253 + ? = 328  About 10% About 15%
? + 65 = 424  About 10% About 60%
All / none  About 30% About 20%

The most common responses are bolded,i.e., half of the students replied that 236 + 78 was the easiest, and over half said ? + 65 as the hardest.

Question d) and e): Typical reasons for items being easy or hard include:

Reasons for being easy (d) Reasons for being hard (e) Student examples
Addition is easier than subtraction. Subtraction is harder than addition.

I like adding numbers together rather than subtracting.
Because I had to subtract numbers which is hard for me.
The numbers are small. The numbers are big.

Because its smaller numbers.
Because it had large numbers so it was easier to lose count.
The difference between the numbers is small
(for 253 + ? = 328 or 236 + 78 = ?)		 The difference between the numbers is big (for ? + 65 = 424).

Because you only had to add a little bit more.
Becase it was just like adding little numbers.
Because 65 is far away from 424.
  Comments on the location of the missing number (for ? + 65 = 424). [Hard] because you had to find out how many beads he had before (for ? + 65 = 424).
Descibes the strategy  

Add 230 and 70  = 300 then add the 14.
Because adding 70 onto 236 is 306 + 8 is 314.

Many students either gave a non-specific answer, or did not give any reasons.

Results based on an online sample of 56 Y6 students.

Diagnostic and formative information: 
Student strategies
Student results in the trial utilised the following addition and subtraction strategies:
  • Using partitioning strategies when adding and multiplying using hundreds, tens and ones consistently using correct compensation (Year 7, Number Framework Stage 7 – Advanced multiplicative).
  • Partitioning using rounding and compensation to jump through tidy numbers or partitioning by rounding one number to a tidy number then compensation or
    Using the vertical algorithm with understanding.  (Year 6, Number Framework Stage 6).
  • Place value partitioning one number into hundreds, tens and ones then adding it on to the other in parts (Year 5, Number Framework Stage 6).
  • Place value partitioning both numbers using hundreds, tens and ones with correct compensation (Year 4, Number Framework Stage 5).
  • Counting strategies (Year 2, Number Framework Stage 1-4).
  Common error Likely reasons Next steps

b)

c)

582

489

 Student adds given numbers rather than subtracting them. The student may have misread the question. They could re-read the question carefully.

b)

c)

134 or 34

341 or 441
Student uses subtraction and takes away the bigger number from the smaller.
This happens with both place value partitioning and the vertical algorithm.

Students could do simpler subtractions where the strategy does not work (e.g., 65 - 57, which should be single digit).

Get students to show their working on the number line.
a) 214 or 304 The student does not " carry" tens to hundreds or ones to tens in addition. Students could explore alternative strategies such place value partitioning [e.g., 200 + (30 + 70) + (6 + 8) = 200 + 100 + 14]

b)

c)

174 or 274

369

 Student does not "rename" or "renames" incorrectly. Students could explore renaming using money ($100, $10 and $1 notes) or grouping the beads.

  • Firstly take off 3 $10s.
  • Then substituting 10 $1 for $10.
  • Then take 8 lots $1 away from 14 lots of $1.
  • This demonstrates a correct "renaming" of $10 as 10 lots of $1.