Reasoning in the classroom
Year 4
Balls and
buckets
Support materials for teachers
Year 4 Reasoning in the classroom – Balls and buckets
These Year 4 activities require learners to solve problems within the context of throwing balls into buckets or
beanbags at targets. The first activity was included in the 2015 National Numeracy Tests (Reasoning). This is
followed by one further activity.
Balls and buckets
Learners work out combinations of addition facts
in order to obtain a target score within a games context.
Includes:
■■ Balls and buckets question
■■ Markscheme
Beanbag challenge
Learners throw beanbags at targets in order to reach a defined score and win the game.
Includes:
■■ Explain and question – instructions for teachers
■■ Resource sheet – Beanbag challenge 1
■■ Resource sheet – Beanbag challenge 2
Reasoning skills required
Identify
Communicate
Review
Learners identify the appropriate
steps needed to obtain a
target score.
They work together to agree
strategies; they explain their
results and procedures.
They review their work,
considering alternative
approaches and strategies.
Procedural skills
Numerical language
■■ Simple combinations
■■ Exactly
■■ Addition
■■ Add, subtract, multiply, divide
■■ Subtraction
■■ Multiplication
■■ Division
Year 4 Reasoning in the classroom: Balls and buckets
Introduction
Balls and buckets
Activity 1 – Balls and buckets
or
Outline
This Year 4 activity requires learners to work with simple combinations
of addition facts in order to obtain a target score when throwing balls
into buckets.
You will need
Q
Balls and buckets question
One page for each learner
M
Markscheme
Year 4 Reasoning in the classroom: Balls and buckets
Activity 1 – Balls and buckets – Outline
Q
Rhys throws balls into buckets.
He scores 16 with three balls like this.
Each ball
Each ball
Each ball
scores 2
scores 4
scores 6
Show how he can score exactly 16 with four balls.
Each ball
Each ball
Each ball
scores 2
scores 4
scores 6
Now show how he can score exactly 16 with five balls.
Balls and buckets
Each ball
Each ball
Each ball
scores 2
scores 4
scores 6
3m
Activity 1 – Balls and buckets – Question
M
Activity 1 – Balls and buckets – Markscheme
Marks
3m
Answer
Both question parts correct, i.e.
First question part, using four balls:
Or
Or
Second question part, using five balls:
Or
Or 2m
Just one question part correct
Year 4 Reasoning in the classroom: Balls and buckets
In this question it is not possible to
score just 1 mark
Activity 1 – Balls and buckets – Markscheme
M
Activity 1 – Balls and buckets – Exemplars
Question 2: Exemplars
4x4=16
Each ball
Each ball
Each ball
scores 2
scores 4
scores 6
Both question parts correct; 3 marks
●■
10+6=16
Each ball
Each ball
Each ball
scores 2
scores 4
scores 6
2
0
2
Each ball
Each ball
Each ball
scores 2
scores 4
scores 6
Both question parts correct; 3 marks
●■
2
3
Each ball
Each ball
Each ball
scores 2
scores 4
scores 6
Each ball
Each ball
Each ball
scores 2
scores 4
scores 6
Each ball
Each ball
scores 2
scores 4
scores 6
Year 4 Reasoning in the classroom: Balls and buckets
The use of numbers is unambiguous.
First question part correct; 2 marks
●■
Each ball
This learner checks their working which is to be encouraged.
The second response shows two different solutions, but the
calculation and smiley face identifies their chosen answer.
In the first part, some of the balls are clearly crossed out, leaving
1, 2, 1 balls which is correct. The second part must be incorrect
as more than five balls are used.
Activity 1 – Balls and buckets – Exemplars
Beanbag challenge
12
Activity 2 – Beanbag challenge
−
+
Outline
1 or
×
÷
This Year 4 activity entails learners throwing beanbags at targets. It is
a physical game, requiring a reasonably large area, so would fit well
within the playground, gym or hall.
19
Remember!
Beanbag challenge is played with two teams competing at any one
time. There are three games, each progressively more challenging.
Games could be played on a ‘round-robin’ basis with every team playing
every other team (which lends itself to further numerical reasoning
opportunities), or they could be undertaken on a knock-out basis.
Alternatively, just one of the games could be played, in teams or individually.
Learners can be provided with pen and paper for their working or this activity can be used to practise
mental numerical skills.
You will need
R
Resource sheet – Beanbag challenge 1
One sheet for each pair/small group
R
Resource sheet – Beanbag challenge 2
One sheet for each pair/small group
Beanbags
Each pair of teams needs five beanbags between them
Game board marked out
5
4
Score chart
Either in chalk on the ground, or on
flip chart or other large paper
3
Team
2
Scores are
written here
Team
1
Starting line
Year 4 Reasoning in the classroom: Balls and buckets
Activity 2 – Beanbag challenge – Outline
Activity 2 – Beanbag challenge
Explain
Mark out one or more game boards in the playground, gym or other large space, as
indicated in You will need. Also mark out (or write on a large sheet of paper) one or more
scoring charts. Split learners into small groups (teams) of around four, or into pairs. Each
team takes it in turns to throw five beanbags onto the ‘board’. Players within teams take it
in turns to throw, and score accordingly.
Game 1 – Add the scores from the beanbags
Teams start with a score of 100 (or other appropriate number). After the first player’s turn,
the team adds their scores from the five beanbags, then subtracts the total from the 100.
(Probably needs adult supervision!) They write this reduced target on the sheet and play
continues with total scores being subtracted from the running score. The first team to
reach zero is the winner. To finish, teams must use all five beanbags to score exactly the
number that is needed. Beanbags outside the playing board do not count.
Game 2 – Knock them out 1 – with three beanbags
Each team has a copy of Beanbag challenge 1. They have to obtain (and cross out) each
of the numbers on the sheet, using any operations they choose (addition, subtraction,
multiplication or division, or any mix. So one bag in the 4 area, one in the 2 area and one in the
1 area could be used to make 8 by multiplying, or 7 by adding, etc.)
All three beanbags must count (so they cannot obtain the number with two bags and ignore
the final one) and they must score exactly the target number. If a bag is on a line or goes
off the board, it is thrown again so all three bags score. Teams can target stars in any order.
The ‘wild’ star is any number they choose.
Game 3 – Knock them out 2 – with five beanbags (more challenging)
As above, but using all five beanbags and Beanbag challenge 2. Decide in advance
whether they must achieve exactly the target number in one turn to eliminate it (very
challenging), or whether they can work towards it across turns (e.g. with the target 23, they
might achieve 18 on one turn, and leave 5 to be achieved on another turn – but to eliminate
the target they must end by scoring exactly what is required, in this case 5).
Year 4 Reasoning in the classroom: Balls and buckets
Activity 2 – Beanbag challenge – Explain and question
Activity 2 – Beanbag challenge
■■ (Game 1) What is the highest score you can get in one turn? (25) If you got all five
beanbags in the 5 area every time, how many turns would you need before you got
from 100 to zero? (4)
Question
■■ (Game 1) If all five beanbags landed in the 1 area every time, how many turns would
you need to get from 100 to zero? (20)
■■ You have a score of X left. Can you score exactly X in your next turn? How?
■■ (Game 2/3) Have you remembered to think about using all the operations? Which
operation do you find easiest/hardest? Why?
■■ (Game 2/3) Was it easier at the start of this game to cross out numbers? Why/why not?
(It obviously gets harder as the choice of numbers is reduced.) What did you do to help
yourselves? (What strategy? How did they communicate with each other?)
Year 4 Reasoning in the classroom: Balls and buckets
Activity 2 – Beanbag challenge – Explain and question
R
Beanbag challenge 1
Use all 3 beanbags to score one of these numbers. All beanbags count.
24
20
18
0
25
WILD
12
1
+
7
Balls and buckets
×
−
÷
Remember!
19
Activity 2 – Beanbag challenge 1 – Resource sheet
R
Beanbag challenge 2
Use all 5 beanbags to score one of these numbers. All beanbags count.
23
30
18
0
45
WILD
50
1
+
27
Balls and buckets
×
−
÷
Remember!
19
Activity 2 – Beanbag challenge 2 – Resource sheet