Seeds and sweets

Seeds and sweets

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about solving problems using addition or subtraction.
 
 
a)

 
Jane planted 28 carrot seeds and 14 cabbage seeds. 
Use the box below to work out how many seeds Jane planted altogether.
 
 
 
 

Total number of seeds planted __________
 
 
 
 

b)

 
 
During Diwali Ria got 74 sweets. She gave 46 to her brother. 
Use the box below to work out how many sweets Ria had left.
 
 
 
 

Number of stickers Mary had left __________
  
c)
 
Here is an equation 27 - 14 = 13.
Make up a story problem to go with this equation.
 
 
 
 
 
 
Task administration: 
This task is completed with pencil and paper only.
Level:
2
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Key Competencies: 
Using language, symbols, and texts
Keywords: 
addition, subtraction, story problems
Description of task: 
Students show how they perform an addition and a subtraction problem, and write their own subtraction story problem.
Curriculum Links: 
This resource can help to identify students' ability to use basic facts and knowledge of place value and partitioning whole numbers to solve addition and subtraction problems.
Key competencies
This resource involves recording the strategies students used to solve addition and subtraction problems. This relates to the Key Competency: Using language, symbols and text.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Additive thinking, set 5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
      Y4 (11/2003)
a)

 

 42

Working
Numerical strategies, any 1 of:

  • Horizontal equation (28 + 14 = ?);
  • Vertical algorithm;
  • Place value partitioning (e.g., 8 + 4 = 12, 20 + 10= 30);
  • Other part-whole strategies (e.g., 28 + 2 + 10 + 2).

Counting strategies using symbols or tally marks.

 1 mark


2 marks

or

1 mark

 easy


moderate

easy
b)

 

 28

Working
Numerical strategies, any 1 of:

  • Horizontal equation (74 – 46 = ?);
  • Vertical algorithm;
  • Place value partitioning (e.g., 74 – 40 = 34, 34 – 6 = 28);
  • Other part-whole strategies (e.g., 74 – 50 + 4).

Counting strategies using symbols or tally marks.

 1 mark


2 marks

or

1 mark

 difficult


moderate

easy
c)

 

 Any 1 of:

  • Writes a number story that involves subtraction of 14 from 27 and includes the answer of 13. (e.g., Joe had 27 books and he lost 14 of them and he only had 13 left.)
  • Writes a story problem that involves subtraction of 14 from 27 but does not include the answer of 13. (e.g., John had 27 seashells.  He gave 14 to his friend.  How many did he have left?)
 1 mark moderate
  Total 7 marks

Based on a representative sample of 155 Year 4 students in November 2003.

NOTE: Marks are given for the strategy used regardless of whether the answer is correct.

Diagnostic and formative information: 
  Common error Likely calculation Likely misconception
a) 32 20 + 10 = 30
8 + 4 = 12		 Does not do the equivalent of carrying the 10s digit in 12.
a) 14 28 – 14 Uses the wrong operator.
b) 32 70 – 40 = 30
6 – 4 = 2		 Equivalent of a "won't go" error because you can't do 4 – 6.
b) 120 74 + 46 Uses the wrong operator.

NOTE: The first and third errors can occur regardless of whether the vertical algorithm is used.

  Strategy used Percentage using strategy Percentage using strategy who got correct answer
a) Vertical algorithm1
Horizontal equation2 (28 + 14 = ?)
Place value partitioning3 (8 + 4 = 12, 20 + 10 = 30)
Other part whole strategies3 (e.g., 28 + 10 + 2 + 2)
Counting strategies using symbols or tallies4.		 27%
14%
8%
1%
23%		 91%
86%
69%
100%
69%
b) Vertical algorithm1
Horizontal equation2 (74 – 46 = ?);
Place value partitioning3 (e.g., 74 – 40 = 34, 34 – 6 = 28);
Other part whole strategies3 (e.g., 74 – 50 + 4).
Counting strategies using symbols or tallies4.		 32%
14%
8%
1%
16%		 62%
36%
31%
0%
32%
c) Writes a number story that involves taking 14 away from 27 and having 13 left5.
Writes a story problem involving taking 14 away from 27, and supplies the answer of 135.
Writes a story problem involving taking 14 away from 27, but does not give the answer6.		 27%
6%
19%		 -
-
-

Based on a representative sample of 155 Year 4 students in November 2003.

NOTES:
A number story is defined here as a story using the numbers provided, including the answer, e.g., Joe had 27 books and he lost 14 of them and he only had 13 left. A story problem is defined here as a story using the numbers provided and including a question or problem to solve, e.g., John had 27 seashells. He gave 14 to his friend, how many did he have left?

  1. This was the most common and the most successful strategy used, and was used by the more able students. However, the this can be performed without deeper understanding of the underlying place value and part-whole concepts involved. The students employing this method were typically of average ability.
  2. This strategy was relatively more successful in addition rather than in subtraction. Often the actual method that the student used to arrive at their answer was not evident.
  3. The students employing this method were typically of average ability. These methods may well become more common as the Numeracy project is implemented in more schools.
  4. The students employing this method were typically of lower ability.
  5. The students who did this were typically of  above average ability.
  6. The students who did this were typically of average ability.
Next steps: 
  1. Discuss the different strategies that students used to solve each problem. Try and begin the discussion with students who did not use the vertical algorithm. Affirm the value of alternative strategies.
  2. For students who did use the vertical algorithm, see if they understand why it works.
    This is easier for addition than it is for subtraction.
    For 28 + 14, the algorithm is very close to the following: 8 + 4 = 12; (2 + 10) + 20 + 10 = 42.
    For 74 – 46, the vertical algorithm is very close to the following: 74 – 6 = 68; 68 – 40 = 28.