Can't scale parent object separately from its children sprites

I have a bunch of square tile sprites which are going to be put together as children of an empty transform Board. Once they are there, Board is to be re-scaled to fit the screen. For some reason, though, when I re-scale Board, each individual sprite is also re-scaled by the exact amount that counteracts Board's resizing, such that in total the re-scaling is none.

The following script is a component of Board:

 using UnityEngine;
 using System.Collections;
 
 public class boardResizer : MonoBehaviour
 {
     public GameObject sampleSprite;
     private SpriteRenderer sr;
     private int rows;
     private int columns;
 
     void Start ()
     {
         sr = sampleSprite.GetComponent<SpriteRenderer>();
 
         float worldScreenHeight = Camera.main.orthographicSize * 2;
         float worldScreenWidth = worldScreenHeight / Screen.height * Screen.width;
 
         rows = PlayerPrefs.GetInt("Rows", 10);
         columns = PlayerPrefs.GetInt("Columns", 10);
 
         if(rows >= columns)
         {
             transform.localScale = new Vector3(
                 worldScreenHeight / (sr.sprite.bounds.size.y * rows),
                 worldScreenHeight / (sr.sprite.bounds.size.y * rows), 1);
         }
         else
         {
             transform.localScale = new Vector3(
                 worldScreenWidth / (sr.sprite.bounds.size.x * columns),
                 worldScreenWidth / (sr.sprite.bounds.size.x * columns), 1);
         }
     }
 }

Does anybody know the culprit? I already checked to make sure that nothing else was re-scaling; when I commented out this code, both the board and the sprites remained at their original scale (1,1,1).