Ways of Explaining Math to first Graders

As a high school math teacher who sometimes substitutes in the primary grades, I find teaching math to first graders rewarding but challenging. First graders like to move around, are full of curiosity and have absolutely no math anxiety! 

It makes me sad to see first graders poring over tedious worksheets. Research in how students learn mathematics has proved that young children learn math best by handling concrete objects (manipulatives). Abstract thinking comes much later.

The following are some of the activities I use whenever I teach first grade. 

Activities that teach numeration:

1. As I read a number story (five little monkeys, 10 little dinosaurs or other) a group of children play out the story, one child dropping out of the group every time a character drops out.

2. I hand out cards with digits (0, 1, 2, up to 10) written on them. I show the children pictures with up to 10 similar objects printed on them. The child with the correct number of objects holds up his card.

3. I hand out cards, some with numerals (1, 2, 3, etc.) and others with numbers in words. The children have to find their pairs. 

Activities that teach number sense:

4. I write numbers from 1 to 50 on the board. The children represent these numbers using a variety of tools (connecting cubes, 10 frames, base 10 materials).

5. The children use their representations to do simple additions and subtractions (without regrouping).

6. I show the children a set of objects (five teddy bears, six spoons, etc.). The children make another set with the same number using their manipulatives.They then write the corresponding number in words or digits.

7. The children learn the concepts of more/less/equal by matching objects in sets of various sizes.

8. The children use play money to “buy” objects from a make-believe store.

9. The children join numbered dots to make pictures. This teaches the correct sequence of numbers.

10. I write a number on the board. The children compose and decompose this number in various ways using connecting tubes or other variables.

11. The children skip-count by 2’s, 3’s and 5’s by jumping over floor tiles.

Activities that teach geometry and spatial sense:

1. The children identify shapes (circle, triangle, square) in picture books.

2. The children first make pictures with tangrams. They then identify the shapes they used.

3. I hand out a number of shapes in different sizes and colors. The children have to find and put together identical shapes in groups (triangles together, even though they may be of different sizes and colors).

4. The children make geometric designs with common shapes and describe how they made them.

5. The children identify and describe common three-dimensional shapes: cubes, cones, cylinders. They then find common objects with these shapes. (“My lunchbox is a rectangular prism. The pencil is a cylinder.”)

6. The children construct three-dimensional objects and then describe the shapes they used. (“I made a castle with cubes, cylinders, cones, and a sphere.”)

7. The children try to find an object from its position. (“It is on top of the chair under the book.”)

Activities that teach measurement:

1. The children make a map of the classroom using stickers to represent various objects. (Rectangles for desks, circles for chairs etc.)

2. The children use common objects (pencil, paper clip, etc.) to measure the lengths of the desks, the width of the room, etc.

3. The children make play-dough by measuring salt, flour and water in small containers.

4. The children cover the surface of a book, table, etc., with smaller squares to determine its area.

5. The children mark their birthdays on a calendar.

6. The children read the time on analog and digital clocks. 

Activities that teach patterning and algebra:

1. The children use manipulatives (colored blocks, sticky shapes, buttons, etc.) to create patterns (blue button, red button, green button, blue button, red button, etc.). They then identify the pattern.

2. The children represent a given repeating pattern in a variety of ways. (Clap for blue button, make a ‘meow’ sound for red button, make a ‘bow wow’ sound for green button.)

3. The children identify the rule for a given pattern.

4. The children identify the number of identical objects that must be added or subtracted to establish equality on a play balance.

5. The children identify a number. (Add 2 to me and I become 5.)

Activities that teach Probability and Data Management: 

The children organize objects into categories by attribute. (All the blue objects together. All the cubes together. All the blue cubes together.) The children collect and organize data like the favorite fruit the students like to eat, their favorite cartoon, color, etc. The students then display this data using a variety of recording methods (pictographs, tally marks, etc.). They then answer questions about this data: What is the favorite fruit in the class? (Least liked fruit, etc.)

I encourage the children to use mathematical language (impossible, unlikely, less likely, more likely, certain) to describe the likelihood that everyday events will occur. For example, “It is impossible for me to eat 10 hamburgers in one sitting…It is unlikely that it will snow tomorrow.”

I only hand out worksheets when I am convinced that the children have basically understood the concept.

I admit that sometimes my class is the noisiest in the hall. But who said math was not an exciting subject?

One of the wonderful things about this approach is how the kids explain the concepts to each other and even come up with problems of their own. My best day was when one little girl cried at the end of class. Too tired? Fed up with math? No way. She wanted more math!