Complete parts (a) and (b) below.
(a) Make a suitable drawing of units and strips to illustrate the product .
(b) Make a suitable sketch of place-value cards to illustrate the product .
(a) Select the correct answer below and fill in the answer boxes to complete your choice.
(i) Click the icon to view exchange b. Exchange the units for strips and units.
(1) Click the icon to view exchange a. Exchange the units for strips and units.
(b) Select the correct answer below and fill in the answer boxes to complete your choice.
(i) Click the icon to view exchange a. Exchange ones for tens and there will be ones left over.
(1) Click the icon to view exchange b. Exchange ones for tens and there will be ones left over.

Ask by Moran Grant. in the United States

Mar 31,2025

Question

Complete parts (a) and (b) below.
(a) Make a suitable drawing of units and strips to illustrate the product .
(b) Make a suitable sketch of place-value cards to illustrate the product .
(a) Select the correct answer below and fill in the answer boxes to complete your choice.
(i) Click the icon to view exchange b. Exchange the units for strips and units.
(1) Click the icon to view exchange a. Exchange the units for strips and units.
(b) Select the correct answer below and fill in the answer boxes to complete your choice.
(i) Click the icon to view exchange a. Exchange ones for tens and there will be ones left over.
(1) Click the icon to view exchange b. Exchange ones for tens and there will be ones left over.

Ask by Moran Grant. in the United States

Mar 31,2025

UpStudy AI · Accepted Answer

$$
\textbf{Drawing with Units and Strips (a)}
$$

First, think of the number $$13$$ as made up of a \textbf{strip} of 10 units plus 3 extra units. In a units‐and‐strips model a strip represents 10 units. So, the number $$13$$ is pictured as

• 1 strip (=10 units)  
• 3 individual units

Since the product is $$3\cdot 13$$, you have three copies of the number 13. In your drawing you could show three groups, each consisting of:

• $$\underline{1}$$ strip (that is, a bar of 10 units)  
• $$\underline{3}$$ single units

When you count everything you get:
$$
3\text{ strips} \quad \text{and} \quad 3\times 3=9\text{ units,}
$$
which together represent the number 39.

Now complete the exchange boxes as follows for part (a):

• Option (i), using exchange b (from units into strips):  
  “Exchange the units for $$\boxed{10}$$ units to form $$\boxed{1}$$ strip and $$\boxed{3}$$ units remain.”

• Option (1), using exchange a (again, exchanging 10 units into 1 strip):  
  “Exchange the units for $$\boxed{10}$$ units to form $$\boxed{1}$$ strip and $$\boxed{3}$$ units remain.”

$$
\textbf{Place-Value Cards (b)}
$$

With place-value cards the number $$13$$ is represented by a \textbf{tens card} and an \textbf{ones card}. For $$13$$ you have:

• 1 card in the tens place (value 10)  
• 1 card in the ones place (value 3)

When you multiply by 3, you get cards corresponding to:
$$
3\cdot 13 = 3\text{ tens} \quad \text{and} \quad 3\cdot 3=9\text{ ones,}
$$
which is the number 39.

Now, when we “exchange” ones into tens we use the rule: 10 ones can be exchanged for 1 ten. Starting with 39 ones (if you imagine working only with ones) you exchange groups of 10 ones.

Thus complete the exchange boxes as follows for part (b):

• Option (i), using exchange a:  
  “Exchange $$\boxed{10}$$ ones for $$\boxed{1}$$ ten and there will be $$\boxed{9}$$ ones left over.”

• Option (1), using exchange b:  
  “Exchange $$\boxed{10}$$ ones for $$\boxed{1}$$ ten and there will be $$\boxed{9}$$ ones left over.”

These exchanges show the regrouping process that underlies the equalities
$$
13=10+3\quad\text{and}\quad 39=30+9.
$$

This completes the step‑by‑step explanation of the product $$3\cdot 13 =39$$ using both units + strips drawings and place‑value cards.
To illustrate $$3 \times 13 = 39$$: **a) Units and Strips:** - Draw 3 groups. - Each group has 1 strip (10 units) and 3 individual units. - Total: 3 strips (30 units) and 9 units. - So, $$3 \times 13 = 39$$. **b) Place-Value Cards:** - Use 3 tens cards and 9 ones cards. - This represents 30 (from tens) and 9 (from ones). - So, $$3 \times 13 = 39$$. **Exchange Boxes:** - **a)** - Option (i): Exchange 10 units for 1 strip, leaving 3 units. - Option (1): Exchange 10 units for 1 strip, leaving 3 units. - **b)** - Option (i): Exchange 10 ones for 1 ten, leaving 9 ones. - Option (1): Exchange 10 ones for 1 ten, leaving 9 ones.

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