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International Baccalaureate · PYP 2

Times Tables 3 and 4

⌚ ~98 min ▢ 10 blocks ✓ 64 exercises ➣ Prerequisites : Times Tables 2, 5 and 10, Odd and Even Numbers
I The 3s Times Table

Each bunch has 3 bananas. How many bananas are there altogether?
Figure

We have 4 groups of 3. We can skip-count by 3s: 3, 6, 9, 12.
Figure
There are $$\begin{aligned}[t]4\times 3 &= 3+3+3+3 && \text{(4 groups of 3)}\\ &= 12\end{aligned}$$ bananas.


Proposition — The 3s Times Table
\(\begin{aligned}\textcolor{colordef}{3}\times \textcolor{colorprop}{0}&=\textcolor{olive}{0}\\\textcolor{colordef}{3}\times \textcolor{colorprop}{1}&=\textcolor{olive}{3}\\\textcolor{colordef}{3}\times \textcolor{colorprop}{2}&=\textcolor{olive}{6 }\\\textcolor{colordef}{3}\times \textcolor{colorprop}{3}&=\textcolor{olive}{9 }\\\textcolor{colordef}{3}\times \textcolor{colorprop}{4}&=\textcolor{olive}{12 }\\\textcolor{colordef}{3}\times \textcolor{colorprop}{5}&=\textcolor{olive}{15 }\\\textcolor{colordef}{3}\times \textcolor{colorprop}{6}&=\textcolor{olive}{18 }\\\textcolor{colordef}{3}\times \textcolor{colorprop}{7}&=\textcolor{olive}{21 }\\\textcolor{colordef}{3}\times \textcolor{colorprop}{8}&=\textcolor{olive}{24 }\\\textcolor{colordef}{3}\times \textcolor{colorprop}{9}&=\textcolor{olive}{27 }\\\textcolor{colordef}{3}\times \textcolor{colorprop}{10}&=\textcolor{olive}{30}\end{aligned}\) \(\quad \quad\) \(\begin{aligned}\textcolor{colordef}{0}\times \textcolor{colorprop}{3}&=\textcolor{olive}{0}\\\textcolor{colordef}{1}\times \textcolor{colorprop}{3}&=\textcolor{olive}{3}\\\textcolor{colordef}{2}\times \textcolor{colorprop}{3}&=\textcolor{olive}{6}\\\textcolor{colordef}{3}\times \textcolor{colorprop}{3}&=\textcolor{olive}{9}\\\textcolor{colordef}{4}\times \textcolor{colorprop}{3}&=\textcolor{olive}{12}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{3}&=\textcolor{olive}{15}\\\textcolor{colordef}{6}\times \textcolor{colorprop}{3}&=\textcolor{olive}{18}\\\textcolor{colordef}{7}\times \textcolor{colorprop}{3}&=\textcolor{olive}{21}\\\textcolor{colordef}{8}\times \textcolor{colorprop}{3}&=\textcolor{olive}{24}\\\textcolor{colordef}{9}\times \textcolor{colorprop}{3}&=\textcolor{olive}{27}\\\textcolor{colordef}{10}\times \textcolor{colorprop}{3}&=\textcolor{olive}{30}\end{aligned}\)
Skills to practice
  • Counting by 3s Using a Number Line
  • Multiplying by 3 Using Cubes
  • Multiplying by 3
II The Double of the Double: the 4s Table
Proposition — Doubles to Know by Heart
Doubling a number means multiplying it by \(2\). Three families to know without counting:
\(2 \times 11 = 22\) \(2 \times 20 = 40\) \(2 \times 100 = 200\)
\(2 \times 12 = 24\) \(2 \times 25 = 50\) \(2 \times 150 = 300\)
\(2 \times 13 = 26\) \(2 \times 30 = 60\) \(2 \times 200 = 400\)
\(2 \times 14 = 28\) \(2 \times 35 = 70\) \(2 \times 250 = 500\)
\(2 \times 15 = 30\) \(2 \times 40 = 80\) \(2 \times 300 = 600\)
\(2 \times 16 = 32\) \(2 \times 45 = 90\) \(2 \times 500 = 1\,000\)
\(2 \times 17 = 34\) \(2 \times 50 = 100\)
\(2 \times 18 = 36\)
\(2 \times 19 = 38\)
To rebuild a forgotten double, split the number: \(35 = 30 + 5\), so \(2 \times 35\) is \(60 + 10 = 70\); and \(150 = 100 + 50\), so \(2 \times 150\) is \(200 + 100 = 300\).
Example
Complete: (a) \(2 \times 14 = \ldots\), (b) \(2 \times \ldots = 70\), (c) \(2 \times 150 = \ldots\), (d) \(1\,000 = 2 \times \ldots\).

(a) \(28\). (b) \(35\). (c) \(300\). (d) \(500\): half of \(1\,000\).

Method — The Double of the Double
Multiplying by \(4\) is doubling, then doubling again.
To find \(4 \times 6\): double \(6\) is \(12\), and double \(12\) is \(24\). So \(4 \times 6 = 24\).
You already know the doubles — so you can build the whole 4s table from the 2s table.
Example
Find \(4 \times 7\) by doubling, then doubling again.

Double \(7\) is \(14\). Double \(14\) is \(28\). $$4 \times 7 = \textbf{28}$$

Skills to practice
  • Doubles to Know by Heart
  • Building the 4s Table by Doubling Twice
  • Finding the Harder 4s Facts
III The 4s Times Table

If each butterfly has 4 wings, how many wings are there in total?
Figure

There are 5 groups of 4. We can skip-count by 4s: 4, 8, 12, 16, 20.
Figure
There are $$\begin{aligned}[t]5\times 4 &= 4+4+4+4+4 && \text{(5 groups of 4)}\\ &= 20\end{aligned}$$ wings.


Proposition — The 4s Times Table
\(\begin{aligned}\textcolor{colordef}{4}\times \textcolor{colorprop}{0}&=\textcolor{olive}{0}\\\textcolor{colordef}{4}\times \textcolor{colorprop}{1}&=\textcolor{olive}{4}\\\textcolor{colordef}{4}\times \textcolor{colorprop}{2}&=\textcolor{olive}{8 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{3}&=\textcolor{olive}{12 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{4}&=\textcolor{olive}{16 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{5}&=\textcolor{olive}{20 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{6}&=\textcolor{olive}{24 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{7}&=\textcolor{olive}{28 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{8}&=\textcolor{olive}{32 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{9}&=\textcolor{olive}{36 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{10}&=\textcolor{olive}{40}\end{aligned}\) \(\quad \quad\) \(\begin{aligned}\textcolor{colordef}{0}\times \textcolor{colorprop}{4}&=\textcolor{olive}{0}\\\textcolor{colordef}{1}\times \textcolor{colorprop}{4}&=\textcolor{olive}{4}\\\textcolor{colordef}{2}\times \textcolor{colorprop}{4}&=\textcolor{olive}{8}\\\textcolor{colordef}{3}\times \textcolor{colorprop}{4}&=\textcolor{olive}{12}\\\textcolor{colordef}{4}\times \textcolor{colorprop}{4}&=\textcolor{olive}{16}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{4}&=\textcolor{olive}{20}\\\textcolor{colordef}{6}\times \textcolor{colorprop}{4}&=\textcolor{olive}{24}\\\textcolor{colordef}{7}\times \textcolor{colorprop}{4}&=\textcolor{olive}{28}\\\textcolor{colordef}{8}\times \textcolor{colorprop}{4}&=\textcolor{olive}{32}\\\textcolor{colordef}{9}\times \textcolor{colorprop}{4}&=\textcolor{olive}{36}\\\textcolor{colordef}{10}\times \textcolor{colorprop}{4}&=\textcolor{olive}{40}\end{aligned}\)
Skills to practice
  • Counting by 4s Using a Number Line
  • Multiplying by 4 Using Cubes
  • Multiplying by 4
IV Going further
Skills to practice
  • Completing Times Tables with Pictures
  • Quiz