← Atlas of Difficulties
S-32
The child can't find the odd one out or group objects together
Type: practognostic
What the research says
Forming the quantitative concept of number and of arithmetic operations is inseparably linked to the ability to classify. Classification is based on grouping elements according to their features.
Lalaeva R.I. Dyscalculia in Children, p. 137 (2005)
The mental operation of comparison is part of many kinds of thinking. To master counting forwards and backwards, a child needs to compare the preceding and the following number.
Lalaeva R.I. Dyscalculia in Children, p. 144 (2005)
Forming the operation of classification is tied to the concept of a set: a common feature is identified, and on that basis objects are combined into a group. The process of classification is linked to developing the ability to analyze and synthesize.
Baryaeva L.B., Kondratyeva S.Yu. Dyscalculia in Children, p. 32 (2013)
Exercises at home — free
Odd one out (objects)
Builds: Classifying by one feature — shape, color, size, function
You need: 4–5 objects or picture cards
- Place 4 objects in front of the child: for example, 3 round ones and 1 square one.
- Ask: “Three of them go together. Which one is the odd one out?”
- After the answer: “Why is it the odd one out? What feature do the others share?”
- Important: the child should name the feature, not just point.
- Harder: one object can be the odd one out by two different features — discuss both.
Lalaeva R.I. Dyscalculia in Children, 2005, pp. 137–138
Sort the geometric shapes
Builds: Classifying by several features
You need: a set of geometric shapes of different colors, shapes and sizes
- Give 12 shapes: circles/squares/triangles, big/small, red/blue.
- First task: “Sort them by shape” — three groups.
- Mix them up. “Now by size.”
- Mix them up. “Now by color.”
- Conclusion: “The same shapes can be grouped in different ways — what matters is choosing the feature.”
Lalaeva R.I. Dyscalculia in Children, 2005, p. 141
Find the difference between two objects
Builds: The operation of comparison — the basis for understanding “more/less”
You need: two similar objects or pictures
- Show two similar objects: a big cup and a small cup, or a circle and an oval.
- Ask: “How are they alike? How are they different?”
- The child names what they have in common first, then the differences.
- Harder: two picture scenes — find 5 differences.
- Link to math: “We compare numbers the same way: what's the same, what's different (7 is 2 more than 5).”
Lalaeva R.I. Dyscalculia in Children, 2005, pp. 144–145
Find the artist's mistake
Builds: Visual analysis, critical thinking
You need: a picture with a deliberate mistake, a pencil
- Draw a scene with a mistake: a glove with 6 fingers, a tree with square leaves.
- Ask: “The artist drew something wrong. Find the mistake.”
- The child explains: “There should be 5 fingers, but here there are 6.”
- Harder: several mistakes in one picture.
- Link to math: “We check a calculation the same way — we look for where the mistake is.”
Lalaeva R.I. Dyscalculia in Children, 2005, pp. 148–149
Dienes logic blocks — sort by a rule
Builds: Classifying by one and by two features
You need: Dienes logic blocks or cards with shapes of different colors and sizes, two hoops or sheets of paper
- Put all the blocks in a pile. The rule: “All the red ones go here, the rest go there.”
- Check: “Did all the red ones get in? Are there any among them that don't belong?”
- Harder, with two hoops: “Big ones on the left, round ones on the right.” What do you do with the big round ones?
- Next step: the child makes up a rule, and the adult guesses it.
- Classification is the basis of how the brain organizes numbers into place values and types of operations.
Baryaeva L.B., Kondratyeva S.Yu. Dyscalculia in Children, 2013, p. 48
Shop — sort and count
Builds: Classification in an everyday context
You need: toy food or picture cards, 3 baskets or plates
- Lay out the “goods” all mixed up. The task: sort them into categories — fruit, vegetables, dishes.
- Afterwards: “How many fruits? How many vegetables? Which are there more of? By how many?”
- Variation: “3 apples and 2 pears were delivered. How many fruits are there in total?”
- Harder: “Take 2 from each basket. How many did you take in total?”
- A pretend-play game is a natural setting where classification helps solve problems.
Baryaeva L.B., Kondratyeva S.Yu. Dyscalculia in Children, 2013, p. 49
Sorting shapes three ways
Builds: Classifying by color, shape and size in turn
You need: 12–16 cut-out shapes: circles and triangles, red/blue/green, big and small
- Spread all the shapes out in random order.
- Round one: “Sort them by color.” The child sorts and names the groups.
- Round two: mix them up, “By shape.”
- Round three: mix them up, “By size.”
- After each round: “Tell me what you did.”
- Harder: “Is there another way?” — let the child suggest a feature of their own.
Baryaeva L.B., Kondratyeva S.Yu. Dyscalculia in Children, 2013, pp. 81–82
Find the word that doesn't belong — classifying concepts
Builds: Grouping math terms by category
You need: word cards: circle, rectangle, square, triangle, one, four, zero, round, big, triangular
- Read: “Circle, rectangle, square, triangle, one.” Which one doesn't belong?
- Discuss: “one” is a number, the rest are shapes.
- Second set: “Rectangle, square, one, four, circle, triangle, zero.” Split them into groups.
- Third: “Round, square, big, triangular.” Which one doesn't belong?
- Discuss: “big” is size, the rest are shape.
- Harder: the child makes up a word puzzle of their own.
Baryaeva L.B., Kondratyeva S.Yu. Dyscalculia in Children, 2013, p. 73
Worksheets — print and practice
Odd one out — classifying geometric shapes
↓ Download printable PDF (in Russian)Without help
- Doesn't see what numbers in the number sequence have in common — treats numbers as separate labels
- Difficulty with the multiplication table — doesn't notice its group structure
- Mistakes when comparing numbers and choosing the operation in a word problem