Grade 1 Mental Math A – Pre-Operational Number Strategies – Part 1

A – Pre-operation Number Strategies There are 3 pre-operational number strategies in Part 1 –Set Recognition –Part-Part-Whole –Ten Frame Visualization

Set Recognition Strategy (Introduction) In grade 1, students should be able to recognize common configurations of sets of numbers, such as the dots on a standard die and dominoes. Most students should be able to instantly recognize up to sets of 6, and through experience they can extend this to sets of 10. Set recognition should be reinforced through flash math activities where students are presented with a number configuration for a few seconds, and are asked to identify the number after it is hidden. Sets of number configurations on overhead transparencies, on cards, and on paper plates would be good sources of materials for these reinforcements. Through playing dominoes and games with standard dice, students would have naturally developed set recognition.

Set Recognition Examples (Introduction) For this paper plate displayed for about 2 seconds and then hidden, think: This looks like the 5 on a die. For this display shown for 2 seconds on an overhead, think: I see 4 dots.

Set Recognition Reinforcement (Day 1)

Set Recognition Reinforcement (Day 1 cont.) How many triangles did you see?

Set Recognition Reinforcement (Day 1 cont.)

What number did you see?

Set Recognition Reinforcement (Day 1 cont.)

How many squares did you see?

End of Lesson

Set Recognition Reinforcement (Day 2)

Set Recognition Reinforcement (Day 2 cont.) What number did you see?

Set Recognition Reinforcement (Day 2 cont.)

How many squares did you see?

Set Recognition Reinforcement (Day 2 cont.)

What number did you see?

Set Recognition Reinforcement (Day 2 cont.)

How many triangles did you see?

Set Recognition Reinforcement (Day 2 cont.)

What number did you see?

End of Lesson

Set Recognition Reinforcement (Day 3)

Set Recognition Reinforcement (Day 3 cont.) How many circles did you see?

Set Recognition Reinforcement (Day 3 cont.)

What number did you see?

Set Recognition Reinforcement (Day 3 cont.)

How many squares did you see?

Set Recognition Reinforcement (Day 3 cont.)

How many dots did you see?

Set Recognition Reinforcement (Day 3 cont.)

What number did you see?

End of Lesson

Set Recognition Reinforcement (Day 4)

Set Recognition Reinforcement (Day 4 cont.) What number did you see?

Set Recognition Reinforcement (Day 4 cont.)

What number did you see?

Set Recognition Reinforcement (Day 4 cont.)

How many dots did you see?

Set Recognition Reinforcement (Day 4 cont.)

How many triangles did you see?

Set Recognition Reinforcement (Day 4 cont.)

What number did you see?

End of Lesson

Set Recognition Reinforcement (Day 5)

Set Recognition Reinforcement (Day 5 cont.) What number did you see?

Set Recognition Reinforcement (Day 5 cont.)

What number did you see?

Set Recognition Reinforcement (Day 5 cont.)

What number did you see?

Set Recognition Reinforcement (Day 5 cont.)

What number did you see?

Set Recognition Reinforcement (Day 5 cont.)

What number did you see?

End of Lesson

Set Recognition Reinforcement (Day 6)

Set Recognition Reinforcement (Day 6 cont.) How many dots did you see?

Set Recognition Reinforcement (Day 6 cont.)

What number did you see?

Set Recognition Reinforcement (Day 6 cont.)

How many dots did you see?

Set Recognition Reinforcement (Day 6 cont.)

How many dots did you see?

Set Recognition Reinforcement (Day 6 cont.)

What number did you see?

End of Lesson

Set Recognition Reinforcement (Day 7)

Set Recognition Reinforcement (Day 7 cont.) How many dots did you see?

Set Recognition Reinforcement (Day 7 cont.)

How many dots did you see?

Set Recognition Reinforcement (Day 7 cont.)

What number did you see?

Set Recognition Reinforcement (Day 7 cont.)

What number did you see?

Set Recognition Reinforcement (Day 7 cont.)

What number did you see?

End of Lesson

Set Recognition Reinforcement (Day 8)

Set Recognition Reinforcement (Day 8 cont.) How many squares did you see?

Set Recognition Reinforcement (Day 8 cont.)

How many dots did you see?

Set Recognition Reinforcement (Day 8 cont.)

How many triangles did you see?

Set Recognition Reinforcement (Day 8 cont.)

How many dots did you see?

Set Recognition Reinforcement (Day 8 cont.)

How many circles did you see?

End of Lesson

Set Recognition Reinforcement (Day 9)

Set Recognition Reinforcement (Day 9 cont. ) What number did you see?

Set Recognition Reinforcement (Day 9 cont. )

What number did you see?

Set Recognition Reinforcement (Day 9 cont. )

What number did you see?

Set Recognition Reinforcement (Day 9 cont. )

What number did you see?

Set Recognition Reinforcement (Day 9 cont. )

What number did you see?

End of Lesson

Set Recognition Assessment (Day 10)

Set Recognition Assessment (Day 10 cont.) Record the number you saw.

Set Recognition Assessment (Day 10 cont.)

Record the number you saw.

Set Recognition Assessment (Day 10 cont.)

Record the number you saw.

Set Recognition Assessment (Day 10 cont.)

Record the number you saw.

Set Recognition Assessment (Day 10 cont.)

Record the number you saw.

End of Lesson

Part-Part-Whole Strategy (Introduction) Set recognition can easily be extended to the recognition of two parts in a whole by presenting for a few seconds number configurations made up of two colours or two shapes, or number configurations in two parts. Ask students to identify the number and the two parts.

Part-Part-Whole Example (Introduction) For this paper plate shown for about 3 seconds, think: I see 5. I see 4 squares and 1 circle. For this display shown for 3 seconds on an overhead, think: I see 6 dots inside and 1 dot outside, so there are 7 dots.

Part-Part-Whole Reinforcement (Day 1)

Part-Part-Whole Reinforcement (Day 1 cont.) How many dots did you see? How many were inside the box? How many were outside the box?

Part-Part-Whole Reinforcement (Day 1 cont.)

How many circles did you see? How many were white? How many were grey?

Part-Part-Whole Reinforcement (Day 1 cont.)

What number of shapes did you see? How many were circles? How many were triangles?

End of Lesson

Part-Part-Whole Reinforcement (Day 2)

Part-Part-Whole Reinforcement (Day 2 cont. ) What number of shapes did you see? How many were triangles? How many were circles?

Part-Part-Whole Reinforcement (Day 2 cont. )

How many dots did you see? How many were inside the circle? How many were outside the circle?

Part-Part-Whole Reinforcement (Day 2 cont. )

How many triangles did you see? How many are blue? How many are grey?

Part-Part-Whole Reinforcement (Day 2 cont. )

How many shapes did you see? How many were circles? How many were squares?

Part-Part-Whole Reinforcement (Day 2 cont. )

How many squares did you see? How many were grey? How many were white?

End of Lesson

Part-Part-Whole Reinforcement (Day 3)

Part-Part-Whole Reinforcement (Day 3 cont.) How many dots did you see? How many were inside the rounded rectangle? How many were outside the rounded rectangle?

Part-Part-Whole Reinforcement (Day 3 cont.)

How many shapes did you see? How many were white? How many were grey?

Part-Part-Whole Reinforcement (Day 3 cont.)

What number did you see? How many circles did you see? How many squares did you see?

Part-Part-Whole Reinforcement (Day 3 cont.)

How many triangles did you see? How many were inside? How many were outside?

Part-Part-Whole Reinforcement (Day 3 cont.)

How many shapes did you see? How many were circles? How many were squares?

End of Lesson

Part-Part-Whole Reinforcement (Day 4)

Part-Part-Whole Reinforcement (Day 4 cont.) What number did you see? How many were inside the box? How many were outside?

Part-Part-Whole Reinforcement (Day 4 cont.)

How many shapes did you see? How many were triangles? How many were circles?

Part-Part-Whole Reinforcement (Day 4 cont.)

How many squares did you see? How many were grey? How many were white?

Part-Part-Whole Reinforcement (Day 4 cont.)

What number of shapes did you see? How many were inside the box? How many were outside?

Part-Part-Whole Reinforcement (Day 4 cont.)

How many circles did you see? How many were inside the box? How many were outside?

End of Lesson

Part-Part-Whole Reinforcement (Day 5)

Part-Part-Whole Reinforcement (Day 5 cont.) How many shapes did you see? How many were inside the circle? How many were outside the circle?

Part-Part-Whole Reinforcement (Day 5 cont.)

How many squares did you see? How many were green? How many were white?

Part-Part-Whole Reinforcement (Day 5 cont.)

How many dots did you see? How many were inside the circle? How many were outside?

Part-Part-Whole Reinforcement (Day 5 cont.)

How many triangles did you see? How many were grey? How many were white?

Part-Part-Whole Reinforcement (Day 5 cont.)

How many squares did you see? How many were inside? How many were outside?

End of Lesson

Part-Part-Whole Reinforcement (Day 6)

Part-Part-Whole Reinforcement (Day 6 cont.) What number do you see? How many triangles? How many circles?

Part-Part-Whole Reinforcement (Day 6 cont.)

How many dots did you see? How many were grey? How many were white?

Part-Part-Whole Reinforcement (Day 6 cont.)

How many shapes did you see? How many were inside? How many were outside?

Part-Part-Whole Reinforcement (Day 6 cont.)

What number do you see? How many triangles? How many squares?

Part-Part-Whole Reinforcement (Day 6 cont.)

How many squares did you see? How many white? How many grey?

End of Lesson

Part-Part-Whole Reinforcement (Day 7)

Part-Part-Whole Reinforcement (Day 7 cont.) How many circles did you see? How many were inside the box? How many were outside?

Part-Part-Whole Reinforcement (Day 7 cont.)

What number did you see? How many squares did you see? How many triangles did you see?

Part-Part-Whole Reinforcement (Day 7 cont.)

How many shapes did you see? How many were red? How many were white?

Part-Part-Whole Reinforcement (Day 7 cont.)

How many squares did you see? How many were inside the box? How many were outside the box?

Part-Part-Whole Reinforcement (Day 7 cont.)

What number did you see? How many were squares? How many were circles?

End of Lesson

Part-Part-Whole Reinforcement (Day 8)

Part-Part-Whole Reinforcement (Day 8 cont.) How many shapes did you see? How many were red? How many were blue?

Part-Part-Whole Reinforcement (Day 8 cont.)

How many dots did you see? How many were inside the circle? How many were outside?

Part-Part-Whole Reinforcement (Day 8 cont.)

What number did you see? How many dots did you see? How many squares did you see?

Part-Part-Whole Reinforcement (Day 8 cont.)

How many triangles did you see? How many were grey? How many were white?

Part-Part-Whole Reinforcement (Day 8 cont.)

How many squares did you see? How many were inside? How many were outside?

End of Lesson

Part-Part-Whole Reinforcement (Day 9)

Part-Part-Whole Reinforcement (Day 9 cont.) What number did you see? How many squares did you see? How many triangles did you see?

Part-Part-Whole Reinforcement (Day 9 cont.)

How many dots did you see? How many were blue? How many were white?

Part-Part-Whole Reinforcement (Day 9 cont.)

How many shapes did you see? How many were triangles? How many were squares?

Part-Part-Whole Reinforcement (Day 9 cont.)

What number did you see? How many triangles were inside? How many were outside?

Part-Part-Whole Reinforcement (Day 9 cont.)

How many dots did you see? How many were white? How many were grey?

End of Lesson

Part-Part-Whole Assessment (Day 10)

Part-Part-Whole Assessment (Day 10 cont.) Record the number you see. Record the number of each shape.

Part-Part-Whole Assessment (Day 10 cont.)

Record the number you see. Record the number of each shape.

Part-Part-Whole Assessment (Day 10 cont.)

Record the number you see. Record the number of each shape.

Part-Part-Whole Assessment (Day 10 cont.)

Record the number you see. Record the number of each shape.

Part-Part-Whole Assessment (Day 10 cont.)

Record the number you see. Record the number of each shape.

End of Lesson

Ten Frame Visualization Strategy (Introduction) Students’ work with ten frames should eventually lead to a mental math stage where students can visualize the standard ten-frame representations for numbers and answer questions from their visual memories.

Ten Frame Visualization Example (Introduction) While this ten frame is displayed for a few seconds, think: I see 8 dots: 5 in the full top row and 3 in the bottom row. There are 2 empty cells to make 10.

Ten Frame Visualization Reinforcement (Day 1)

Ten Frame Visualization Reinforcement (Day 1 cont.) How many dots were in the Ten Frame? If you added 2 dots how many would you have?

Ten Frame Visualization Reinforcement (Day 1 cont.)

How many dots were in the Ten Frame? If you removed 1 dot how many would you have?

Ten Frame Visualization Reinforcement (Day 1 cont.)

How many dots were in the Ten Frame? If you added 3 dots how many would you have?

End of Lesson

Ten Frame Visualization Reinforcement (Day 2)

Ten Frame Visualization Reinforcement (Day 2 cont. ) How many dots were in the Ten Frame? If you added 2 dots how many would you have? How many dots would you need to add to get 5?

Ten Frame Visualization Reinforcement (Day 2 cont. )

How many dots were in the Ten Frame? If you removed 2 dots how many would you have? If you removed 3 dots how many would you have?

Ten Frame Visualization Reinforcement (Day 2 cont. )

How many dots were in the Ten Frame? If you added 1 dot how many would you have? If you removed 3 dots how many would you have?

Ten Frame Visualization Reinforcement (Day 2 cont. )

How many dots were in the Ten Frame? If you added 2 dots how many would you have? If you removed 1 dot how many would you have?

Ten Frame Visualization Reinforcement (Day 2 cont. )

How many dots were in the Ten Frame? If you added 2 dots how many would you have? If you added 3 dots how many would you have?

End of Lesson

Ten Frame Visualization Reinforcement (Day 3)

Ten Frame Visualization Reinforcement (Day 3 cont. ) How many dots were in the Ten Frame? If you added 2 dots how many would you have? If you removed 1 dot how many would you have?

Ten Frame Visualization Reinforcement (Day 3 cont. )

How many dots were in the Ten Frame? If you added 3 dots how many would you have? If you added 1 dot how many would you have?

Ten Frame Visualization Reinforcement (Day 3 cont. )

How many dots were in the Ten Frame? If you added 2 dots how many would you have? How many dots would you need to add to get 9?

Ten Frame Visualization Reinforcement (Day 3 cont. )

How many dots were in the Ten Frame? If you added 2 dots how many would you have? If you added 3 dots how may would you have?

Ten Frame Visualization Reinforcement (Day 3 cont. )

How many dots were in the Ten Frame? If you added 2 dots how many would you have? If you removed 3 dots how many would you have?

End of Lesson

Ten Frame Visualization Reinforcement (Day 4)

Ten Frame Visualization Reinforcement (Day 4 cont. ) How many dots were in the Ten Frame? If you added 4 dots how many would you have? If you added 6 dots how may would you have?

Ten Frame Visualization Reinforcement (Day 4 cont. )

How many dots were in the Ten Frame? If you removed 2 dots how many would you have? If you removed 3 dots how many would you have?

Ten Frame Visualization Reinforcement (Day 4 cont. )

How many dots were in the Ten Frame? If you added 2 dots how many would you have? If you added 4 dots how many would you have?

Ten Frame Visualization Reinforcement (Day 4 cont. )

How many dots were in the Ten Frame? If you added 1 dot how many would you have? If you added 3 how many would be in the second row?

Ten Frame Visualization Reinforcement (Day 4 cont. )

How many dots were in the Ten Frame? If you added 2 dots how many would you have? How many dots would you need to add to fill both rows?

End of Lesson

Ten Frame Visualization Reinforcement (Day 5)

Ten Frame Visualization Reinforcement (Day 5 cont. ) How many dots were in the Ten Frame? If you removed 2 dots how many would you have in the second row? If you removed 3 how many would you have?

Ten Frame Visualization Reinforcement (Day 5 cont. )

How many dots were in the Ten Frame? If you added 2 dots how many would you have in the second row? If you removed 1 how many would you have in the second row?

Ten Frame Visualization Reinforcement (Day 5 cont. )

How many dots were in the Ten Frame? If you added 2 dots how many would you have? If you removed 4 dots how many would you have?

Ten Frame Visualization Reinforcement (Day 5 cont. )

How many dots were in the Ten Frame? If you added 3 dots how many would you have in the second row? If you removed 2 dots how many would you have in the first row?

Ten Frame Visualization Reinforcement (Day 5 cont. )

How many dots were in the Ten Frame? If you removed 2 dots how many would you have? If you removed 2 dots how many would you have in the second row?

End of Lesson

Ten Frame Visualization Reinforcement (Day 6)

Ten Frame Visualization Reinforcement (Day 6 cont. ) How many dots were in the Ten Frame? If you added 2 dots how many would you have in the second row? If you added 3 dots how many would you have?

Ten Frame Visualization Reinforcement (Day 6 cont. )

How many dots were in the Ten Frame? If you removed 2 dots how many would you have? If you added 1 dot how many would you have in the second row?

Ten Frame Visualization Reinforcement (Day 6 cont. )

How many dots were in the Ten Frame? If you added 2 dots how many would you have? How many dots do you need to add to fill both rows?

Ten Frame Visualization Reinforcement (Day 6 cont. )

How many dots were in the Ten Frame? If you added 2 dot how many would you have? If you removed 3 dots how many would you have in the first row?

Ten Frame Visualization Reinforcement (Day 6 cont. )

How many dots were in the Ten Frame? If you removed 2 dots how many would you have? If you removed 2 dots how many would you have in the second row?

End of Lesson

Ten Frame Visualization Reinforcement (Day 7) Visualize 3 in a Ten Frame

Ten Frame Visualization Reinforcement (Day 7 cont. ) How many dots do you need to add to fill the first row?

Ten Frame Visualization Reinforcement (Day 7 cont. ) Visualize 2 in a Ten Frame

Ten Frame Visualization Reinforcement (Day 7 cont. ) If you added 2 dots how many would you have?

Ten Frame Visualization Reinforcement (Day 7 cont. ) Visualize 5 in a Ten Frame

Ten Frame Visualization Reinforcement (Day 7 cont. ) If you removed 2 dots how many would you have? If you removed 1 dot how many would you have?

Ten Frame Visualization Reinforcement (Day 7 cont. ) Visualize 4 in a Ten Frame

Ten Frame Visualization Reinforcement (Day 7 cont. ) If you removed 1 dot how many would you have? If you added 1 dot how many would you have?

Ten Frame Visualization Reinforcement (Day 7 cont. ) Visualize 1 in a Ten Frame

Ten Frame Visualization Reinforcement (Day 7 cont. ) How many dots would you have if you added 2 dots? How many dots must be added to fill the first row?

End of Lesson

Ten Frame Visualization Reinforcement (Day 8) Visualize 6 in a Ten Frame

Ten Frame Visualization Reinforcement (Day 8 cont. ) If you added 2 dots how many would you have? If you added 3 dots how many would you have?

Ten Frame Visualization Reinforcement (Day 8 cont. ) Visualize 7 in a Ten Frame

Ten Frame Visualization Reinforcement (Day 8 cont. ) If you removed 2 dots how many would you have? If you removed 1 dot how many would you have?

Ten Frame Visualization Reinforcement (Day 8 cont. ) Visualize 4 in a Ten Frame

Ten Frame Visualization Reinforcement (Day 8 cont. ) If you added 2 dots how many would you have in the first row? If you added 3 dots how many would you have in the first row?

Ten Frame Visualization Reinforcement (Day 8 cont. ) Visualize 5 in a Ten Frame

Ten Frame Visualization Reinforcement (Day 8 cont. ) If you added 5 dots how many would you have? If you added 3 dots how many would you have?

Ten Frame Visualization Reinforcement (Day 8 cont. ) Visualize 8 in a Ten Frame

Ten Frame Visualization Reinforcement (Day 8 cont. ) If you added 2 dots how many would you have in the second row? If you removed 1 dot how many would you have in the second row?

End of Lesson

Ten Frame Visualization Reinforcement (Day 9) Visualize 10 in a Ten Frame

Ten Frame Visualization Reinforcement (Day 9 cont. ) If you removed 1 dot how many would you have? If you removed 3 dots how many would you have?

Ten Frame Visualization Reinforcement (Day 9 cont. ) Visualize 7 in a Ten Frame

Ten Frame Visualization Reinforcement (Day 9 cont. ) If you removed 1 dot how many would you have in the first row? If you removed 1 dot how many would you have in the second row?

Ten Frame Visualization Reinforcement (Day 9 cont. ) Visualize 8 in a Ten Frame

Ten Frame Visualization Reinforcement (Day 9 cont. ) How many dots do you need to add to fill the second row? How many dots do you need to remove to empty the second row?

Ten Frame Visualization Reinforcement (Day 9 cont. ) Visualize 6 in a Ten Frame

Ten Frame Visualization Reinforcement (Day 9 cont. ) If you removed 2 dots how many would you have? If you removed 2 dots how many would you have in the first row?

Ten Frame Visualization Reinforcement (Day 9 cont. ) Visualize 9 in a Ten Frame

Ten Frame Visualization Reinforcement (Day 9 cont. ) How many dots do you need to remove to empty the second row? If you removed 3 dots how many would you have in the second row?

End of Lesson

Ten Frame Visualization Assessment (Day 10)

Ten Frame Visualization Assessment (Day 10 cont.) How many dots were in the Ten Frame? If you added 2 dots how many would you have? If you added 4 dots how many would you have?

Ten Frame Visualization Assessment (Day 10 cont.)

How many dots were in the Ten Frame? If you added 2 dots how many would you have? If you removed 4 dots how many would you have?

Ten Frame Visualization Assessment (Day 10 cont.)

How many dots were in the Ten Frame? If you removed 2 dots how many would you have? If you removed 2 dots how many would you have in the second row?

Ten Frame Visualization Assessment (Day 10 cont.) Visualize 7 in a Ten Frame

Ten Frame Visualization Assessment (Day 10 cont.) If you removed 2 dots how many would you have? If you removed 1 dot how many would you have?

Ten Frame Visualization Assessment (Day 10 cont.) Visualize 9 in a Ten Frame

Ten Frame Visualization Assessment (Day 10 cont.) How many dots do you need to remove to empty the second row? If you removed 3 dots how many would you have in the second row?

End of Lesson