Question

understand vocabulary

1. circle the property shown by 4×(6 + 2)=(4×6)+(4×2).

associative commutative distributive

1. circle the property shown by 2×134 = 134×2.

associative commutative distributive

1. circle the property shown by (1×3)×7 = 1×(3×7).

associative commutative distributive

1. draw a line from each vocabulary word to its example.

array
compatible numbers
estimate
numerical expression
partial products
7×19 is about 140.
7×19
estimate 3×48→3×50
15×2 = 10+20
use vocabulary in writing

1. find 4×114. use at least three terms from the word list to describe how to find the product.

word list
array
standard algorithm
associative property of multiplication
commutative property of multiplication
compatible numbers
distributive property
estimate
numerical expression
partial product

Explanation:

Step1: Recall property definitions

The distributive property is $a\times(b + c)=(a\times b)+(a\times c)$. So for $4\times(6 + 2)=(4\times6)+(4\times2)$, it is the distributive property.

Step2: Recall commutative - property definition

The commutative property of multiplication is $a\times b=b\times a$. So for $2\times134 = 134\times2$, it is the commutative property.

Step3: Recall associative - property definition

The associative property of multiplication is $(a\times b)\times c=a\times(b\times c)$. So for $(1\times3)\times7 = 1\times(3\times7)$, it is the associative property.

Step4: Match vocabulary

• An array is a set of objects arranged in rows and columns. The blue - square example can be an array.
• Compatible numbers are numbers that are easy to compute with mentally. For $3\times48\to3\times50$, 48 and 50 are compatible numbers.
• An estimate is an approximate answer. $7\times19$ is about 140 is an estimate.
• A numerical expression is a mathematical phrase involving numbers and operations. $7\times19$ is a numerical expression.
• Partial products are the products you get when you multiply each digit of a multi - digit number by a single - digit number separately. For $15\times2=(10\times2)+(5\times2)=10 + 20$, 10 and 20 are partial products.

Step5: Calculate $4\times114$

We can use the distributive property. $4\times114=4\times(100 + 10+4)=(4\times100)+(4\times10)+(4\times4)=400+40 + 16=456$. We used the terms 'distributive property', 'numerical expression' and 'partial products'. The numerical expression is $4\times114$. We applied the distributive property to get partial products $4\times100 = 400$, $4\times10=40$ and $4\times4 = 16$.

Answer:

1. Distributive
2. Commutative
3. Associative
4. array - blue - square example; compatible numbers - $3\times48\to3\times50$; estimate - $7\times19$ is about 140; numerical expression - $7\times19$; partial products - $15\times2=10 + 20$
5. $4\times114 = 456$. Using the distributive property on the numerical expression $4\times114=4\times(100 + 10+4)$ to get partial products $4\times100 = 400$, $4\times10 = 40$ and $4\times4=16$.