ORIGINAL RESEARCH ARTICLE
published: 17 July 2014
doi: 10.3389/fpsyg.2014.00782
The relation between children’s constructive play activities,
spatial ability, and mathematical word problem-solving
performance: a mediation analysis in sixth-grade students
Meike Oostermeijer, Anton J. H. Boonen* and Jelle Jolles
Faculty of Psychology and Education, Department of Educational Neuroscience, VU University, Amsterdam, Netherlands
Edited by:
Layne Kalbfleisch, George Mason
University, USA
Reviewed by:
Li-Jen Kuo, Northern Illinois
University, USA
Jason Steffener, Columbia University,
USA
*Correspondence:
Anton J. H. Boonen, Faculty of
Psychology and Education,
Department of Educational
Neuroscience, VU University, Van der
Boechorststraat 1, 1081 BT
Amsterdam, Netherlands
e-mail: a.j.h.boonen@vu.nl
The scientific literature shows that constructive play activities are positively related to
children’s spatial ability. Likewise, a close positive relation is found between spatial ability
and mathematical word problem-solving performances. The relation between children’s
constructive play and their performance on mathematical word problems is, however , not
reported yet. The aim of the present study was to investigate whether spatial ability acted
as a mediator in the relation between constructive play and mathematical word problem-
solving performance in 128 sixth-grade elementary school children. This mediating role
of spatial ability was tested by utilizing the current mediation approaches suggested by
Preacher and Hayes (2008). Results showed that 38.16% of the variance in mathematical
word problem-solving performance is explained by children’s constructive play activities
and spatial ability. More specifically, spatial ability acted as a partial mediator, explaining
31.58% of the relation between constructive play and mathematical word problem-solving
performance.
Keywords: constructive play, spatial ability, mental rotation, mathematical word problem-solving performance,
elementary school
INTRODUCTION
In its home and school environment, almost every child is involved
in playing with Legos, blocks, and jigsaw puzzles. The term con-
structive play, which has a central role in this study, is often used to
categorize these play activities. Constr uctive play generally involves
the manipulation, construction, and motion of objects in space
(i.e., rotating, Mitchell, 1973; Pomerleau et al., 1990; Caldera et al.,
1999). The aim of the present study is to examine the link between
children’s constructive play a ctivities and two interrelated factors,
namely spatial ability and mathematical word problem-solving
performance. Although a positive relation between constructive
play and spatial ability is reported by several authors (e.g., Bjork-
lund and Douglas-Brown, 2008; Levine et al., 2012)aswellasa
positive relation between spatial ability and mathematical word
problem-solving performance (Blatto-Vallee et al., 2007; Beentjes,
2008; Casey et al., 2008), a relation between constructive play and
mathematical word problem-solving perfor mance is barely inves-
tigated. A possible reason for this absence is that spatial ability acts
as a mediator in the relation between children’s constructive play
activities and their performances on mathematical word problems.
The present study is primarily focused on testing this mediating
role of spatial ability.
THE RELATION BETWEEN CONSTRUCTIVE PLAY AND SPATIAL ABILITY
The majority of the studies that examined constructive play has
focused on its relation with (the development of) spatial abil-
ity (e.g., Grimshaw et al., 2002; Bjorklund and Douglas-Brown,
2008; Levine et al., 2012). Spatial ability involves the ability to
represent, modify, gener ate, and recall symbolic, non-linguistic
information (Linn and Petersen, 1985; Tracy, 1987; Hegarty
and Waller, 2005). Generally, three categories of spatial abil-
ity are distinguished in the literature, namely spatial perception,
spatial visualization, and mental rotation (Linn and Petersen,
1985; Hegarty and Waller, 2005). Spatial perception involves
determining spatial relationships with respect to the orientation
of one’s own body, in spite of distracting information. Spa-
tial visualization is commonly associated with tasks that involve
complicated, multistep manipulations of spatially presented infor-
mation. Mental rotation includes the ability to mentally remem-
ber and subsequently rotate an object in the space (Linn and
Petersen, 1985; Hegarty and Waller, 2005 ). Numerous studies
have demonstrated that constructive play activities contribute
to the development of spatial ability, in specific mental rota-
tion (Tracy, 1987; Brosnan, 1998; Caldera et al., 1999; Wolfgang
et al., 2001; Grimshaw et al., 2002; Bjorklund and Douglas-Brow n,
2008; Levine et al., 2012). In the present study, spatial ability
is, therefore, referred to as the performance on mental rotation
tasks.
According to the scientific literature, constructive play activi-
ties like Legos, blocks, and jigsaw puzzles exert the most influence
on spatial ability (Mitchell, 1973; Pomerleau et al., 1990; Caldera
et al., 1999; Levine et al., 2012). For example, evidence shows that
the more children play with Legos, the more they improve in their
spatial skills (Brosnan, 1998; Wolfgang et al., 2003). Besides play-
ing with Legos, also block play has shown a positive relation with
children’s spatial ability (Sprafkin et al., 1983; Tracy, 1987; Caldera
et al., 1999). Preschool children that are more interested in block
play and reproducing complex block models perform better on
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spatial ability tasks. Also jigsaw puzzles are examined in rela-
tion with spatial ability. Recent research of Levine et al. (2012)
has revealed that the frequency of playing with jigsaw puzzles
contributed to the development of spatial ability. Jigsaw puzzles
appear to appeal to both the mental and physical rotation of the
pieces to fit them into different places.
THE RELATION BETWEEN SPATIAL ABILITY AND MATHEMATICAL
WORD PROBLEM SOLVING
Besides the positive relation between constructive play and chil-
dren’s spatial ability, a positive relation between spatial ability and
mathematical ability, particularly mathematical word problem
solving, is also reported in several studies (Guay and McDaniel,
1977; Lean and Clements, 1981; Tracy, 1987; Casey et al., 1992;
Hegarty and Kozhevnikov, 1999; Kozhevnikov et al., 2002; Blatto-
Vallee et al., 2007; Beentjes, 2008). Blatto-Vallee et al. (2007)
showed, for example, that spatial ability explained almost 20%
of unique variance in mathematical word problem-solving per-
formance. Casey et al. (1997, 2001, 2008) reported that the
direct role of spatial ability in mathematical word problem solv-
ing lies in performing the actual mathematical operations and
numerical reasoning. Other studies have shown the importance
of spatial ability in the production of visual-schematic repre-
sentations (e.g., Hegarty and Kozhevnikov, 1999; Van Garderen,
2006; Krawec, 2010). In order to facilitate the understanding
of the text base of a mathematical word problem, one has to
make a coherent visual representation of the essential infor-
mation of the problem. These visual representations include
the spatial relations between solution-relevant elements of the
word problem text (e.g., Hegarty and Kozhevnikov, 1999; Van
Garderen and Montague, 2003; Thevenot and Oakhill, 2006;
Van Garderen, 2006; Thevenot, 2010). To be able to make
these types of representations, spatial ability is needed. So,
children with good spatial skills are better able to make visual-
schematic representations than children with poor spatial skills
(e.g., Hegarty and Kozhevnikov, 1999; Van Garderen and Mon-
tague, 2003; Van Garderen, 2006; Krawec, 2010). The production
of visual-schematic representations is found to be positively
related to the performance on mathematical word problems (Van
Garderen and Montague, 2003; Van Garderen, 2006; Krawec,
2010).
THE PRESENT STUDY
In summary, the scientific literature reports a positive relation
between children’s constructive play activities and spatial ability.
Spatial ability increases as children engage more in playing with
Legos, blocks, and jigsaw puzzles (Linn and Petersen, 1985; Tracy,
1987; Hegarty and Waller, 2005). Moreover, the positive relation
between spatial ability and mathematical word problem-solving
performance is also commonly investigated (Casey et al., 1997,
2001, 2008; Hegart y and Kozhevnikov, 1999). A relation between
constructive play and mathematical word problem-solving per-
formance is, however, not reported yet. A limited amount of
studies have shown a positive relation between constructive play
and more general math skills (Serbin and Connor, 1979; Caruso,
1993; Wolfgang et al., 2001). For example, the studies of Wolf-
gang et al. (2001) and Beentjes (2008) revealed that block play
among preschoolers was a predictor of later school achievement
in mathematics, when controlled for IQ and gender. All these
studies did, however, not have a focus on mathematical word
problem solving in particular. To our knowledge, this is one of
the first studies that investigate the relation between construc-
tive play and mathematical word problem-solving performance
with spatial ability serving as a mediator. According to the sta-
tistical literature, a mediator explains the relation between the
independent and the dependent variable. Rather than hypothesiz-
ing a direct causal relationship between the independent variable
and the dependent variable, a mediational model hypothesizes
that the independent variable causes the mediator variable, which
in turn causes the dependent variable (for more information,
see Shrout and Bolger, 2002; Preacher and Hayes, 2008; Hayes,
2009).
The mediating role of spatial ability in the relation between
constructive play and mathematical word problem-solving perfor-
mance is reflected in the hypothetical (mediation) model reported
in Figure 1.
As studies have demonstrated that there is a difference in
the extent in which boys and girls are engaged in constructive
play a ctivities (see e.g., Serbin and Connor, 1979; Tracy, 1987;
Scholten, 2008), sex is added as a covariate to the mediation
model.
MATERIALS AND METHODS
SAMPLE
This study contained data from 128 Dutch sixth-grade children
(64 boys, M
age
= 11.73 years, SD
age
= 0.43 years and 64 girls,
M
age
= 11.72 years, SD
age
= 0.39 years) from eight elementary
schools in The Netherlands. Parents/caretakers provided written
informed consent based on printed information about the purpose
of the study.
INSTRUMENTS AND MEASUREMENT PROCEDURE
Children’s mathematical word problem-solving performance and
spatial ability were administered by three trained independent
research assistants in a session of approximately 25 min. Con-
structive play was examined with a questionnaire filled out by one
of the parents/caretakers.
FIGURE 1
|
Hypothesized mediation model including the independent
variable (i.e., constructive play, x), mediator (i.e., spatial ability, m),
and dependent variable (i.e., word problem solving performance, y ).
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Mathematical word problem-solving performance
Mathematical word problem-solving performance was examined
with the Mathematical Processing Instrument (MPI), which was
first translated to Dutch. The MPI consisted of 14 mathemat-
ical word problems based on previous studies (Hegarty and
Kozhevnikov, 1999; Van Garderen and Montague, 2003,see
Appendix A). The internal consistency (Cronbach’s α) of this
instrument, measured in American participants, is 0.78 (Hegarty
and Kozhevnikov,1999). The Cronbach’s α of the MPI in this study
was 0.72. The word problems were printed on cards and presented
in four different orders. All problems were read out loud to the
children to control for differences in decoding skill. Furthermore,
children were allowed to solve each word problem within a max-
imum of 3 min and during this time the experimenter did not
speak to the child. To be sure those children had enough time
to solve the mathematical word problems, a pilot study was con-
ducted w ith five sixth-gr ade students. The results of the pilot study
showed that every child was able to solve each of the 14 items of
the MPI within the required 3 min. The number of mathematical
word problems solved correctly was used as the dependent variable
in the analyses.
Constructive play
In order to determine to what extent children show constr u ctive
play behavior, a short questionnaire was forwarded to their par-
ents/caretakers. They were asked to indicate on a 4-point Likert
scale (1 = never, 4 = often) to what extent their child has under-
taken the, for this study, representative constructive play activities
(i.e., playing with Legos, blocks, and jigsaw puzzles). The inter-
nal consistency of this questionnaire was sufficient (Cronbach’s
α = 0.71). A sum score was created by adding the scores on the
three, for this study representative, constructive play activities.
The higher is the sum score, the more the student is involved
in constructive play activities. The sum score was added as the
independent variable in the analyses.
Spatial ability
The picture rotation task (Quaiser-Pohl, 2003) is a standard-
ized task that was used to measure mental rotation. In the
picture rotation task, children were asked to rotate a non-
manipulated picture of an animal at the left of a vertical line.
The three pictures at the right of the vertical line showed the
rotated and/or mirrored image of that same animal. One of
these three pictures was only rotated; two of these pictures
were both rotated and mirrored. Children had to decide which
of the three pictures was only rotated. Children had 1.5 min
to finish this task. The internal consistency of this measure in
the present study was high (Cronbach’s α = 0.93). Figure 2
shows one of the 30 test items of the picture rotation task.
The accuracy on this task was used as the mediator in the
analyses.
DATA ANALYSIS
The mediating effect of constructive play on word problem-solving
performance v ia spatial ability was tested using bootstrap meth-
ods (Shrout and Bolger, 2002; Hayes, 2009). Bootstrap method
has been validated in the literature and is preferred over other
methods in assessing the existence of mediation among variables.
Preference based on the fact that other methods for testing indirect
effects assume a standard normal distribution when calculating
the p-value for the indirect effect, whereas bootstrapping does
not assume normality of the sampling distribution. In addition,
bootstrap method repeatedly samples from the dataset, estimat-
ing the indirect effect with each resampled dataset. This process is
repeated thousands of times, producing bias-corrected accelerated
confidence intervals for the indirect effect (Preacher and Hayes,
2008).
RESULTS
DESCRIPTIVE STATISTICS
Tab l e 1 presents the correlations between, and the means and
standard deviations of, the four measures of this study. The table
shows that the correlations among the constructive play, spatial
ability and word problem-solving performance are moderate to
strong. No significant correlation is found among sex and the
three key measures of this study.
INVESTIGATING THE MEDIATING ROLE OF SPATIAL ABILITY
Mediation was tested by regressing the dependent variable (i.e.,
word problem-solving performance) on spatial ability in the
presence of constructive play and sex. Analyses utilizing the
FIGURE 2
|
The picture rotation task (based on Quaiser-Pohl, 2003).
Table 1
|
Intercorrelations, means, standard deviations, and ranges of the measures of this study.
1234NM SD Range
1. Constructive play – 73 7.22 2.22 9.00
2. Spatial ability 0.25* – 128 13.25 7.45 27.00
3. Word problem-solving performance 0.35** 0.55** – 128 6.68 2.87 14.00
4. Sex −0.16 −0.14 −0.16–128– – –
*p < 0.05, **p < 0.001.
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Table 2
|
Parameter estimates of the model examining the mediation role of spatial ability in the relation between constructive play and word
problem-solving performance.
Model Estimate SE p CI (lower) CI (upper)
Model without mediator
Intercept 4.57 1.11 <0.01 2.36 6.78
CP→WPS (c) 0.38 0.14 <0.01 0.11 0.66
Sex→WPS −1.44 0.60 <0.05 −2.63 −0.24
R
2
(y, x) 0.19 – – – –
Model with mediator
Intercept 2.86 1.04 <.01 0.78 4.94
Model 1: SP as dependent variable
CP→SP (a) 0.75 0.41 <0.05 −0.06 1.56
Sex→SP −3.33 1.79 0.07 −6.90 0.25
Model 2: WPS as dependent variable
SP→WPS (b) 0.16 0.04 <0.001 0.09 0.23
CP→WPS (c’ ) 0.26 0.12 <0.05 0.02 0.51
Sex→WPS −0.89 0.54 0.10 −1.97 0.18
Indirect effects (a x b) 0.12 0.08 <0.05 0.128 0.27
R
2
(m, x) 0.10 – – – –
R
2
(y, m, x) 0.38 – – – –
Regression weights a, b, c, and c’ are illustrated in Figure 3.R
2
(y, x) is the proportion of variance in y explained by x, R
2
(m, x) is the proportion of variance in m
explained by x and m. the 95% CI for a
× b is obtained by the bias-corrected bootstrap wit 50 00 resamples. CP (constructive play) is the independent variable (x),
SP (spatial ability) is the mediator (m), and WPS (word problem-solving performance) is the outcome (y). CI (lower
= lower bound of 95% confidence interval; CI
(upper)
= upper bound.
FIGURE 3
|
Results of the mediation analysis (N = 128). Sex was
included in the equations as a statistical control but is not presented for
reasons of clarity.
bootstrap method (5000 bootstrap samples were used) confirmed
the existence of a mediation effect of constructive play on word
problem-solving performance via spatial ability (see Tab le 2).
However, the results showed that there is a partial, but not com-
plete mediation, because the measured effect between constructive
play and word problem-solving performance is not zero upon fix-
ing the mediator variable (i.e., spatial ability, Preacher and Hayes,
2008). The value of the indirect effect of spatial ability can be
calculated as follows:
B
indirect
= B
(a)
∗
B
(b)
= 0.75 × 0.16 = 0.12, and
B
indirect
/B
total
= 0.12/0.38 = 0.3158.
Thus, spatial ability explained 31.58% of the relation between
constructive play and students’ mathematical word problem-
solving performance. The absence of a zero in the confidence
interval for the indirect pathways indicated that the indirect effect
was significantly different from zero at p < 0.05, two-tailed.
The complete model (including constructive play, spatial abil-
ity, and sex) explained 38.16% of the variance in students word
problem-solving performance (R
2
= 0.38), which is a large effect
(Green and Salkind, 2008; Fairchild et al., 2009).
DISCUSSION
The purpose of the present study was to investigate if spatial ability
acts as a mediator in the relation between constructive play and
mathematical word problem-solving performance in sixth-grade
elementar y school children. To our knowledge, this is one of the
first studies that examined the mediating role of spatial ability
in this particular relation. In previous studies, relations between
constructive play and spatial ability (e.g., Brosnan,1998; Bjorklund
and Douglas-Brown, 2008), and between spatial abilit y and math-
ematical word problem-solving perfor mance (e.g., Hegarty and
Kozhevnikov, 1999; Van Garderen and Montague, 2003; Blatto-
Vallee et al., 2007) are reported. The relation between constructive
play and mathematical word problem-solving performance has,
however, not been established yet.
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The results of this study showed that spatial ability acted as
a partial mediator in the relation between constructive play and
children’s mathematical word problem-solving performance. This
implies that children who were frequently engaged in construc-
tive play in their past have better spatial skills and, as a result,
show a higher performance on mathematical word problems.
The variables in this study (i.e., constructive play, spatial abil-
ity, and sex) explained 38.16% of the variance in performance
on solving mathematical word problems. Furthermore, 31.58%
of the relation between constructive play and mathematical word
problem-solving performance is explained by spatial ability.
Note that the findings of this study support the assessment
of a mediating effect based on current recommendations using
bootstrap approaches (Shrout and Bolger, 2002; Hayes, 2009)
1
.
LIMITATIONS
Three limitations of the study should be mentioned. The first lim-
itation of this study included the fact that only one task was used
in the analyses to measure spatial ability (i.e., mental rotation).
Ideally, method triangulation should be applied. The use of more
tasks allows a more reliable measurement of the construct “spatial
ability” and reduces the chance of possible measurement errors
(Woolderink, 2009). The second limitation pertains to the cor-
relational nature of the data, which made it impossible to draw
conclusions about any causal relationships among constructive
play, spatial ability, and mathematical word problem-solving per-
formance. The results of this study only showed that these variables
were associated with each other. Future experimental studies in
which the variables will be manipulated should make it possi-
ble to draw stronger conclusions concerning causal relationships
between the aspects which are important in mathematical word
problem solving. The last limitation covers the way in which the
constructive play activities of the children were administered. In
the present study, a third party (i.e., the parents), filled out the
questionnaires regarding the extent to which children show con-
structive play behavior. Although parents were able to provide a
reliable image of the constructive play activities in which their chil-
dren are/were involved, in future studies it would be even more
reliable to directly observe these play activities.
IMPLICATIONS AND DIRECTIONS FOR FUTURE RESEARCH
The present study contributed to the increasing amount of scien-
tific literature regarding the processes that are involved in learning
mathematics, particularly mathematical word problem solving.
An interesting focus of future research is to investigate the existence
of individual differences in the specific relations between the three
key variables of this study (i.e., constructive play, spatial abilit y,
and mathematical word problem-solving performance). Although
not supported by the results of the present study, several authors
have demonstrated that boys and girls differ in the extent in which
they engage in constructive play (Serbin and Connor, 1979; Tracy,
1987; Scholten, 2008). That is, boys tend to play more with so-
called masculine or constructive toys, like Legos and blocks, than
1
This assessment of mediation is also support by the statistical approach that Baron
and Kenny (1986) used in their research.
girls (Serbin and Connor, 1979; Tracy, 1987). Because the scien-
tific literature gives no clear indications that sex differences exist in
spatial ability (e.g., McGee, 1979; Voyer et al., 1995), examining the
mediating role of spatial ability for both boys and girls separately
might be an interesting topic for follow-up studies.
The results of this study also have a strong practical relevance.
Parents/caretakers should be aware of the importance of construc-
tive play activities in childhood. According to the findings of this
study, activities like playing with Legos, blocks, and jigsaw puz-
zles, are positively related to students’ spatial skills, which, in turn,
is positively related to their performance on mathematical word
problems. Parents/caretakers should, therefore, create opportuni-
ties to play with constructive toys. Also elementary school teachers
should provide constructive learning material to their children
and stimulate to use it by giving them appropriate instruction.
Finally, this research accentuated the importance of spatial abil-
ity in mathematical word problem-solving performance. In line
with previous research (e.g., Hegarty and Kozhevnikov, 1999; Van
Garderen, 2006), spatial ability was found to play a key role in
solving mathematical word problems, especially in the produc-
tion of visual-schematic representations. The training of spatial
skills and the development of visual-schematic representations
should, therefore, have a prominent role in word problem-solving
instruction of primary school mathematics education.
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Conflict of Interest Statement: The authors declare that the research was conducted
in the absence of any commercial or financial relationships that could be construed
as a potential conflict of interest.
Received: 14 April 2014; accepted: 02 July 2014; published online: 17 July 2014.
Citation: Oostermeijer M, Boonen AJH and Jolles J (2014) The relat ion between
children’s constructive play activities, spatial ability and mathematical word problem-
solving performance: a mediation analysis in sixth-grade students. Front. Psychol.
5:782. doi: 10.3389/fpsyg.2014.00782
This article was submitted to Educat ional Psychology, a section of the journal Frontiers
in Psychology.
Copyright © 2014 Oostermeijer, Boonen and Jolles. This is an open-access article
distributed under the terms of the Creative Commons Attribution License (CC BY).
The use, distribution or reproduction in other forums is permitted, provided the original
author(s) or licensor are credited and that the original publication in this journal is cited,
in accordance with accepted academic practice. No use, distribution or reproduction is
permitted which does not comply with thes e terms.
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Oostermeijer et al. Constructive play and word problem-solving
APPENDIX A
The mathematical word problems on the MPI (Hegarty and
Kozhevnikov, 1999):
1. At each of the two ends of a straight path, a man planted a tree
and then e very 5 m along the path he planted another tree. The
length of the path is 15 m. How many trees were planted?
2. On one side of a scale, there isalkgweightandhalf a brick.
On the other side, there is one full brick. The scale is balanced.
What is the weight of the brick?
3. A balloon first rose 200 m from the ground, then moved 100 m
to the east, then dropped 100 m. It then traveled 50 m to the
east, and finally dropped straight to the ground. How far was
the balloon from its original starting point?
4. In an athletics race, Jim is 4 m ahead of Tom and Peter is 3 m
behind Jim. How far is Peter ahead of Tom?
5. A square (A) has an area of 1 m
2
. Another square (B) has sides
twice as long. What is the area of square B?
6. From a long stick of wood, a man cut 6 short sticks, each 2 feet
long. He then found he had a piece of 1 foot long left over. Find
the length of the original stick.
7. The area of a rectangular field is 60 m
2
. If its length is 10 m,
how far would you have traveled if you walked the whole way
around the field?
8. Jack, Paul, and Brian all have birthdays on 1 January, but Jack is
1 year older than Paul and Jack is 3 years younger than Brian. If
Brian is 10 years old, how old is Paul?
9. The diameter of a tin of peaches is 10 cm. How many tins will
fit in a box 30 cm × 40 cm (one layer only)?
10. Four young trees were set out in a row 10 m apart. A well
was situated beside the last tree. A bucket of water is needed
to water two trees. How far would a g ardener have to walk
altogether if he had to water the four trees using only one
bucket?
11. A hitchhiker set out on a journey of 60 miles. He walked the
first 5 miles and then got a lift from a lorry driver. When the
driver dropped him, he still had half of his journey to travel.
How far had he t raveled in the lorry?
12. How many picture frames 6 cm long and 4 cm wide can be
made from a piece of framing 200 cm long?
13. On one side of a scale, there are three pots of jam and a 100 g
weight. On the other side, there are a 200 g and a 500 g
weight. The scale is balanced. What is the weight of a pot of
jam?
14. A ship was sailing North-West. It made a turn of 90
◦
to the
right. An hour later it made a turn of 45
◦
to the left. In what
direction was it then traveling?
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