Mathematics: Class 2 — Chapter 3: Fun with Numbers

The Ginladi is a powerful tool for understanding base-10 and place value through counting beads grouped in patterns.

• Counting Beads: Students count beads to identify specific numbers on blank cards.
• Placing Number Cards: Placing specific numbers such as $38$, $44$, $58$, $65$, and $98$ at their correct positions on the bead string.

Using a number strip from $49$ to $100$ to solve positional problems based on forward and backward movements:

• Forward Steps: Moving from a starting number to a target number (e.g., a butterfly or honey bee moving forward to reach flowers).
• Multi-step Jumps: Combining forward and backward jumps. For example:
  • A squirrel starting at a position, jumping $2$ steps backward, $5$ steps forward, and $3$ steps backward.
  • A frog jumping $2$ steps forward, $7$ steps backward, and $3$ steps backward.

A cooperative game where one child thinks of a number and others guess it by asking Yes/No questions. Examples of questions include:

• Is it more than $50$?
• Are the two digits of the number the same?
• Is it less than $20$?
• Does it have $0$ as a digit?

Identifying and marking positions on a continuous number line bounded by $20$ and $80$:

• Determining the exact numbers where different colored ants (Black, Red, Brown) are sitting.
• Plotting specific numbers like $65$ and $79$ on the number line.

Completing sequences by identifying the constant interval (common difference) between consecutive numbers:

• Pattern A: $1, 4, 7, 10, 13, 16, 19$ (Skip counting by $+3$)
• Pattern B: $40, 45, 50, 55, 60, 65, 70, 75$ (Skip counting by $+5$)
• Pattern C: $50, 60, 70, 80, 90$ (Skip counting by $+10$)

Using a $1$ to $100$ grid to perform skip counting and find common multiples:

• Twos and Fives: Identifying numbers common to skip counting in $2$s and $5$s (e.g., $10, 20, 30, \dots$).
• Twos, Threes, and Fives: Finding numbers common to all three sequences (e.g., $30, 60, 90$).
• Fives and Sevens: Finding numbers common to skip counting in $5$s and $7$s (e.g., $35, 70$).

Practicing subtraction and reverse sequences:

• Basic Backward Counting: $10, 9, 8, 7, 6, 5, 4, 3, 2, 1$
• Pattern A: $40, 37, 34, 31, 28, 25, 22, 19$ (Skip counting by $-3$)
• Pattern B: $70, 65, 60, 55, 50, 45, 40$ (Skip counting by $-5$)
• Pattern C: $100, 90, 80, 70, 60$ (Skip counting by $-10$)
• Pattern D: $100, 80, 60, 40, 20$ (Skip counting by $-20$)

Observing diagonal sequences on the number chart, such as the green-shaded diagonal starting from $1$:

$$1, 12, 23, 34, 45, 56, 67, 78, 89, 100$$

Each step along this diagonal increases the value by exactly $11$.

A cross-shaped spatial tool placed over any number $x$ on a $100$-chart to reveal neighboring values:

• Top: $x - 10$ ($10$ less)
• Bottom: $x + 10$ ($10$ more)
• Left: $x - 1$ ($1$ less)
• Right: $x + 1$ ($1$ more)

For example, if the center is $28$:

• Top is $18$, Bottom is $38$, Left is $27$, Right is $29$.

• Triangular Pattern: Blocks growing as $1, 3, 6, 10, \dots$ (adding $+2$, $+3$, $+4$, etc.)
• Square Pattern: Blocks growing as $1, 4, 9, 16, \dots$ (perfect squares: $1^2, 2^2, 3^2, 4^2, \dots$)
• Linear Step Pattern: Blocks growing as $5, 8, 11, 14, \dots$ (adding $+3$ at each step)