Here are the solutions to the activities and homework. Activity 1: Copy and Complete the number sentence. a) The rule is to add 4 to the previous number. $$5, 9, 13, 17, 21, 25, \boxed{29}, \boxed{33}$$ b) The rule is to add 4 to the previous number. $$3, 7, 11, 15, 19, 23, 27, 31, \boxed{35}, \boxed{39}$$ c) The rule is to square the term number ($1^2, 2^2, 3^2, \dots$). $$1, 4, 9, 16, 25, \boxed{36}, \boxed{49}, \boxed{64}$$ d) The rule is to multiply the previous number by 2. $$2, 4, 8, 16, 32, 64, 128, 256, \boxed{512}, \boxed{1024}$$ Activity 2: Copy and complete. Write down the rule. a) The numbers are $3^2, 4^2, 5^2, \dots$. The differences between consecutive terms are increasing odd numbers ($16-9=7$, $25-16=9$). $$9, 16, 25, \boxed{36}, 49, \boxed{64}$$ Rule: Add consecutive odd numbers starting from 7 (or square the term number starting from 3) b) The rule is to add 2 to the previous number. $$21, 23, 25, 27, 29, 31, 33$$ Rule: +2 c) The rule is to subtract 2 from the previous number. $$12, 10, 8, 6, 4, 2$$ Rule: -2 Homework Complete the table by applying the rule to the starting number to find the next 4 numbers. | Starting number | Rule | Next 4 number | | :-------------- | :--- | :------------ | | 7 | +8 | 15, 23, 31, 39 | | 11 | +9 | $\boxed{20, 29, 38, 47}$ | | 12 | +15 | $\boxed{27, 42, 57, 72}$ | | 15 | -2 | $\boxed{13, 11, 9, 7}$ | | 25 | -5 | $\boxed{20, 15, 10, 5}$ | What's next? Send 'em! 📸